Abstract:
A method, a process and an audio system for embedding bit stream in a voice signal is disclosed. A voice/data interference signal is composed and supplied to the mixer of the voice signal and the data signal such that the resulting mixed signal effectively cancels the interference and allows the interference-free signal being transmitted to the audio signal receiver/decoder. The decoder may decode the data without interference errors. A method using profile shaping to mask the noise due to modulated carrier signal is also disclosed.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to a patent application titled “System and method for communicating data during an audio conference,” by Jeffrey Rodman and David Drell, assigned to the same assignee, Ser. No. 10/378,709, filed on May 3, 2003, which was a Continuation-in-Part of an application Ser. No. 10/335,108 filed on Dec. 31, 2002, which claimed priority of a provisional patent application, Ser. No. 60/360,984, filed on May 1, 2002. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to embedding digital data in an audio signal, especially related to methods and apparatuses to reduce error rates in the digital data recovery and to reduce the perception of noise in the audio signal. 
     2. Description of the Related Art 
     Using audible sound to transmit information is as old as human speech. When one speaks, the speaker is conveying information to his human listener. Using audible sound to transmit digitized information came somewhat later but it can be traced back at least to the days when people communicated using Morse code through telegraphy. In the recent years of the computer age, audio signals are also used for communicating digitized data through computer network. For example, Plain Old Telephone Service, or POTS has been used to transmit digital information using modulators and demodulators (modems). Most of the time, though, an audio channel is either used to communicate human speech, i.e. analog speech signals which are comprehensible to humans, or to communicate digitized information which is comprehensible to computers, but not both at the same time. 
     DSL (Digital Subscriber&#39;s Line) technology may look like an exception. Using DSL technology, a single traditional copper telephone line may transmit both digital data and voice signals at the same time. But the digital data and the voice signals are transmitted at quite different frequency bands carried by the same telephone line. The digital information is carried by high frequency signals and the analog voice signals are carried by low frequency electric waves with frequencies typically lower than about 4000 Hz. The DSL technology has a big limitation in terms of distance. A subscriber of the DSL service has to be within a short distance, e.g. three miles, from the service provider&#39;s server. 
     More recently, using various techniques, analog audio speech and digital data are transmitted simultaneously and commingled together, as illustrated in  FIG. 1  and as described in more detail in a related patent application Ser. No. 10/378,709, filed on May 3, 2003. For simplicity, only the signal path from left to right is discussed here. The signal path from right to left is the same. A generic system  100  shown in  FIG. 1  includes an ordinary audio conference system having units  102 ,  143  and  142  connected through a usual Plan Old Telephone System (POTS) network  122 . In addition to the regular voice conference, this system  100  can also transmit digital data. Data source  104  (typically a computer) at the near end site can transmit data  106 , which are mixed with audio signal  136  by a data and voice mixer  112  to create a data signal embedded in the voice signal. The combined audio signal  154  is transmitted through the POTS network  122  to a far end site. At a far end site, the mixed audio signal  156  can be separated by data and voice separator  132  into digital data  108  and voice signal  138 . Digital data  108  goes into a data sink  144 . Voice signal  138  goes to a voice sink  142 , which is typically a speakerphone that can reproduce the sound of voice signal  138 . In a far end that does not have a capable separator, mixed audio signal  156  can still be branched into a signal  139  and be reproduced by a voice sink  143 , e.g. a speakerphone. To voice sink  143 , mixed audio signal  139  is treated as if it is voice signal  136  and the data signal  106  is ignored. For conference participants using voice sink  143 , the embedded data does not exist because the sound due to the embedded data is substantially imperceptible. 
       FIG. 1  shows the functional block diagram of audio system  100 . For clarity, the data source (sink) and voice source (sink) are shown as separate entities and only one for each is shown. In actual implementation, more than one of each, data source, data sink, voice source or voice sink, may be present in a system. In many actual implementations, these different items may be the same physical entity that has multiple functionalities. In other implementations, the different functions, or their combinations, may be performed by different physical entities with the necessary interfaces connecting them. 
     There are many ways to combine the digital data and voice signals together. For example, several methods are disclosed in a patent application entitled “System and method for communicating data during an audio conference,” by Jeffrey Rodman and David Drell, filed on Mar. 3, 2003, Ser. No. 10/378,709, assigned to the same assignee as the current application, which is incorporated by reference herein. In that patent application, digital data is received from a data source. The digital data is then modulated onto an audio carrier signal which is an analog audio signal. That audio carrier signal is mixed with a regular speech signal to form an audio signal for transmission, recording or other further processing. The audio carrier signal can be a notched narrow-band audio tone or a spread spectrum audio carrier signal, which is a signal covering a wide audio spectrum. In some other cases, the carrier signal can be a narrow-band spectrum, but the frequency is hopping throughout a wide audio spectrum (signal hopping). In such a system, data and speech are transmitted simultaneously, in the same medium and same frequency spectrum range. For a human listener, only the speech portion of the signal is generally perceptible. The data portion is unknown to the listener. The data portion is imperceptible and masked by the speech portion or perceived as background noise when the audio channel is noisy. The data can be obtained only if there is a decoder at the receiver. 
       FIG. 2  illustrates another way of encoding/modulating digital data into audio signal, which is called Phase Shifting Keying (PSK). An audio tone  226 , shown as a sine wave, is used to encode the digital data in a bit stream  222 . Bit stream  222  is fed into a modulator/encoder  224  to be combined with audio carrier signal  226 . The output from the modulator/encoder is an audio signal u(t)  228 . What modulator  224  does is to change the phase of sine wave  226  according to bit signal  222 : when the bit is a 1 then the phase is 0, or when the bit is 0 then the phase is 180°. The phase of the encoded sine wave indicates the digital data as 1 or 0. In the time domain, the corresponding bit stream is represented by a step curve  212  and the encoded carrier wave is shown as wave  214 . The same modulation is also shown in the frequency domain, where the initial bit stream is shown as a curve  202 , which is centered at the zero frequency or DC, while the encoded carrier signal is shown as a curve  204 , which is centered at the audio carrier frequency Fc. On the receiver side, transmit signal u(t)  228  becomes a received signal x(t)  238 . It is demodulated at demodulator  234  with audio carrier signal  226 , which is same as the one used in modulator  224 . Passing demodulated signal  236  through a Low Pass Filter  244 , a bit stream  242  can be retrieved, which is the same as the original bit stream B(n)  222 . 
     An audio system which can transmit additional data has many different uses. As in the cited patent application, such additional data are related to the ongoing audio conference or video conference calls. The data can be used by the conference equipment to automate many routine tasks, such as exchange parties&#39; phone numbers, names etc; or remotely control related equipment, for example, adding a video portion of the conference call to make it a video conference call or transmitting a web address of an interested website. 
     The data embedded in the audio stream may also be used as a means for intellectual property right management, such as digital watermarks. It may also be used to as a watermark aircraft identification tag within voice communication between pilot and control tower, which can reduce errors in the communication between them. 
     In the most applications where digital data is embedded in audible signals, the digital data must have small amplitudes in order to avoid interference with the primary audible signals. Most of the time, the audio carrier signals with digital data are heard by people as “noises.” The noise level has to be as low as possible. But with low audio carrier signal amplitude, the carrier signal is more susceptible to real noise. It may not have enough signal to noise ratio (SNR) to be decoded properly at the receiver. It is found that a typical system using the data-in-speech method, the data error rate is as high as 10% of the data transmitted. The data processing system has to use other methods to correct the transmission or decoding errors. For example, one may increase the redundancy of the data encoding, transmitting/encoding the same data over and over to ensure the correct reception and decoding. 
     It is desirable to reduce the error rate without adversely affecting the primary audible signal. It is desirable to increase the carrier signal amplitude without raising the perceived noise level in the primary speech or music signal. 
     BRIEF SUMMARY OF THE INVENTION 
     The current invention discloses methods and devices to avoid data errors due to the interference between the voice signals and data signals. A voice/data interference signal is composed and supplied to the mixer of the voice signal and the data signal such that the composed interference signal effectively cancels the actual interference and allows the interference-free signal to be transmitted to the audio signal receiver. The output of the decoder may be the original data without the interference error. After using the embodiments of the current invention, the data error rate can be reduced from about 10% of the data transmitted in a typical prior art system to virtually zero. 
     The current invention may also change the spread spectrum frequency profile, such that the data encoding carrier signal profile mimics the real time speech spectrum profile. In that way, the data encoding audio carrier signal can have much higher total energy but still with less perceived noise. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       A better understanding of the invention can be had when the following detailed description of the preferred embodiments is considered in conjunction with the following drawings, in which: 
         FIG. 1  shows a typical prior art system which can transmit speech signal and data signal at the same time. 
         FIG. 2  shows a basic phase shifting keying (PSK) encoding scheme. 
         FIG. 3  shows a diagram for direct sequence spread spectrum. 
         FIG. 4  shows the effect of spreading in frequency domain for the system as shown in  FIG. 3 . 
         FIG. 5  shows a system with direct sequence spread spectrum encoder and decoder according to the present invention, assuming there is no distortion and noise in the communication channel. 
         FIG. 6  illustrates the voice interference between the speech signal and the data signal according to the present invention, assuming there is no distortion and noise in the communication channel. 
         FIG. 7  shows a system with the voice interference remover according to the present invention. 
         FIG. 8  shows the interference estimator of the system as illustrated in  FIG. 7 . 
         FIG. 9  shows a diagram for shaping signal for masking according to the present invention. 
         FIGS. 10   a ,  10   b  and  10   c  show some application systems implementing the current invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     For most systems using audio signals to carry digital data, the following are some desirable properties and capabilities: 1) to share data across an audio channel, such as a POTS network, radio broadcast or music CD, 2) to make the noise associated with the additional data be below a perceptible level; 3) to make the system multi-user capable; and 4) to share the data reliably with low or no errors due to transmission or encoding/decoding. 
     It is found that one way to lower perceptibility of the noise associated with the additional data in the audio signal is to use spread spectrum. The spread spectrum method has been used in many other applications. It is generally regarded as robust against jamming and interference. It can be hidden and masked due to the low amplitude at any given frequency, and it is robust such that even if many channels are impaired, the overall signal can still go through. The spread spectrum can naturally support multi-user implementation, for example, it is used in the CDMA cellular telephone system. 
       FIG. 3  illustrates the direct sequence spread spectrum method. On the transmitter/encoder side, instead of using bit stream  302  to directly modulate carrier audio signal  312 , the bit stream is XOR&#39;ed by a chip sequence  314  at combiner  322 . Chip sequence  314  is generated by chip sequence generator  308 . It is a pseudo random bit stream at much higher frequency. In other words, the period T c  of chip sequence  314  is much shorter than the period T b  of bit stream  302 , as illustrated in  FIG. 3 . The resulting sequence  316  from combiner  322  is then used as if it is the digital data to be encoded or modulated onto audio carrier signal  312 . Modulator  324  is similar to modulator  224  as shown in  FIG. 2 . Modulated signal u(t)  318  can be transmitted for further processing. Any modulation methods, such as those discussed earlier in the prior art section can be employed to modulate digital data on an audio carrier signal. One method used in implementing the current invention is the Phase Shift Keying method. 
     On the receiver/decoder side, the process is similar to the transmitter/encoder side in a reversed order. A received signal x(t)  338 , which is the same as transmitted signal u(t)  318 , is demodulated with audio carrier signal  332  at demodulator  354 . Demodulated signal  336  is then multiplied by chip sequence signal  334 , which is the same as chip sequence  314 , at a combiner  352 . A retrieved bit stream  362  from combiner  352  should be essentially the same as the original bit stream  302 . 
       FIG. 4  illustrates the effect of using the spread spectrum, namely spreading the original narrow spectrum to a wider spectrum. The original bit stream has a long period T b    412 . The chip sequence has a much shorter period T c    414 . It is well known that the bandwidth is proportional to the inverse of the period. When looking at the frequency domain, bandwidth  402  of the original bit stream is much narrower than chip sequence bandwidth  404 . It has been confirmed in experiments that at the same bit stream error rates, the encoded signal using chip sequencing can have an amplitude that is as much as 17 dB less than the encoded signal when the chip sequence period T c  is about 1/50 (i.e. −17 dB) of the original bit period T b . Therefore, using chip sequencing and spread spectrum can greatly reduce the digital data noise, or greatly improve the digital data transmission accuracy at the similar noise level, or both. 
     The amount of data that can be transmitted through an audio channel depends on the bandwidth of the channel and the quality of the channel, in terms of SNR. A rule of thumb is that:
 
Bit rate=Ideal Bandwidth*log 2 ( SNR+ 1).
 
     For example, if the ideal bandwidth is 4000 Hz, and the SNR=−13 dB, then the capacity of the channel, i.e. the bit rate is 282 bps. 
     In a typical practical system, the bit rate may be lower. Assuming useable bandwidth to be 2000 Hz, and SNR=−13 dB, with 6 dB allowance, then the bit rate is 36 bps, i.e. the audio channel may transmit 36 bits of information per second while it is also transmitting a normal audible signal. 
       FIG. 5  illustrates the direct spread spectrum encoding and decoding process according to a model used in the current invention, assuming there is no distortion and no noise in the communication channel. Bit stream B(n)  502  is XOR&#39;ed at a combiner  520  with chip sequence C(k)  514  to become S(k)  516 . Chip sequence C(k)  514  is generated by a chip sequence generator  508  as usual. Modulating signal S(k)  516  modulates the carrier signal F c    512  to form a signal  517  u(t). Then signal  517  u(t) is transmitted through a channel  522 , for example a POTS line, to become a signal  537  x(t) to a receiver where signal  537  x(t) is demodulated by an identical carrier signal F c    531 . The demodulated signal passes a low pass filter  533  and becomes a receiver signal R(k)  518 . Receiver signal R(k)  518  is combined with chip sequence C(k)  546  at chip sequence decoder  532  to generate decoded signal  524 . Chip sequence C(k)  546  and its generator  558  are identical to chip sequence C(k)  516  and its generator  508 . Decoded signal  524  is further summed together to form signal  542 , which removes the effect of the chip sequence C(k). As shown in equation  546 , the contribution from the chip sequence, when they are added together, becomes a constant. By removing or normalizing that constant, signal  542  becomes signal  544 , which is same as the original bit stream  502 . More details are shown in a mathematic model discussed below. 
     But this is not what actually happens in a real system, where digital data is transmitted together with an audio signal.  FIG. 6  illustrates a more realistic system according to a model of the current invention, still assuming there is no distortion and noise in the communication channel. Most parts of the system shown in  FIG. 6  are the same as in  FIG. 5 , for example, bit stream B(n)  602 , chip sequence signals  614  and  646 , chip sequence generators  608  and  658 , combiner  620 , channel  622 , low pass filter  633 , decoder  632  and combiner  642 . The audio carrier signals F c    612  and F c    631  are modulated and demodulated after and before the combiner  620  and decoder  632  respectively. The additions in  FIG. 6  include voice signal v(t)  605  and combiner  621  after the modulating the carrier signal F c    612  and before transmission through the channel  622 . The new sender signal  606  is now a combination of signal S(k)  616  (which is similar to S(k)  516  in  FIG. 5 ), the audio carrier signal  612  and voice signal  605 . On the receiver side, signal x(t)  637  is demodulated by the audio carrier signal  631 , similar to the process in  FIG. 5 . The receiver signal R(k)  618 , which comes out of LPF  633 , goes through the same decoding process, but the resulting signal  652  is not exactly the same as the original bit stream  602 . Comparing to the result in  FIG. 5 , there is an additional term in decoded bit stream signal  652 , which is a function of the voice signal v(t) and other signals. Depending on the size of this additional term, bit stream B(n), which is supposed to be −1 or +1, may be different. It is determined that this additional term, which is the result of the interference between voice signal  605  and modulated carrier signal u(t)  617 , is responsible for most of the errors in the real system. The modulated carrier signal u(t)  617  is the combination of the bit stream  602 , the chip sequence signal  614 , and the carrier signal  612 . With this source of the errors identified, the current invention includes methods and devices to eliminate such errors. 
     The audio carrier signal  617  is a combination of the bit stream  602 , the chip sequence  614  and the audio carrier signal  612 , all of which are known. Since the interference is only between modulated audio carrier signal  617  and audio signal  605 , and both of which are known at the encoder within the transmitter, the amount of interference can be calculated and analyzed at the transmitter. When such interference is known at the transmitter, it is possible to remove such interference from the signal at the transmitter before the signal is transmitted to the receiver. Therefore when the receiver demodulates the signal, there is no interference contribution. After the receiver goes through the normal decoding process, the original bit stream can come out. This way, there will be no error theoretically due to the voice/data interference. 
       FIGS. 7 and 8  illustrate such a system that removes the data/voice interference.  FIG. 7  shows a system where the voice interference is removed on the transmitter side. Voice signal  705  is analyzed and normalized. It is then combined with the chip sequence  714  and the audio carrier signal  712  to emulate the interference between the voice and the data signal at interference estimator  723 . The resulting interference  713 , which is between the voice and the digital stream, is subtracted from bit stream  702  at subtractor  725 . The resulting signal, which is the bit stream minus the interference, is multiplied by chip sequence  714 , to become signal S(k)  716 , modulated by audio carrier signal  712  to become signal u(t)  717 , and combined with voice signal  705  at combiner  721  in the same way as shown before in  FIG. 6 . Signal  706  is now interference-free. Such interference-free signal  706  can be transmitted through a channel  722  to a receiver. At the receiver, the interference-free signal  718  is demodulated, filtered (at LPF  733 ) and decoded as usual. The digital data  752  is interference-free and is the same as the original bit stream  702 . 
       FIG. 8  illustrates more detail of interference estimator  723 . The time-domain voice signal v(t)  705  is combined at modulator  820  with audio carrier signal  712  and chip sequence  714 . The resulting signal  813  is summed by summer  821  to become signal  815 . Signal  815  can then be normalized by normalizer  822  as signal  713 , which is the estimated interference between voice signal  705 , audio carrier signal  712  and chip sequence signal  714 . The input signals are all known, i.e. voice signal  705 , audio carrier signal  712  and pseudo random chip sequence  714 . A mathematical model discussed below describes more precisely the process to derive the output signal W(n)  713 . 
       FIG. 9  shows another way to further reduce the perceived noise due to the digital data. It is well known that if the noise signal is underneath a main voice signal, i.e. the noise profile is the same as the speech profile, then even if the absolute energy of the noise is quite large, human ears may not perceive such a noise because of a masking effect of the larger energy of the voice signal. Such a masking effect can be used advantageously for digital data encoding. In the method shown in  FIG. 9 , bit stream  912  is encoded using one or more of the methods described above, including spread spectrum and interference removing etc. Encoded signal  914  has a normal distribution profile. But unlike the direct spread spectrum encoder as discussed in  FIGS. 4 and 5 , the signal is not used for transmission or combining with a speech voice yet. Speech signal  916  is sampled and analyzed by a psychoacoustic analyzer  944 . The psychoacoustic analyzer extracts the voice signal profile and sends that profile  934  to a masking shaper  924 . Knowing the real time voice signal profile that will be combined with the data bit stream modulated signal, masking shape  924  changes the profile of the audio carrier stream, such that the modulated carrier signal has the same profile as the voice signal as shown in  916 . After the modulated audio carrier signal  917  and voice signal  918  are combined by an accumulator  926 , the resulting signal becomes signal  936 . As illustrated by profile  936 , modulated audio carrier  956  is under real voice signal  952 . This way, even if the carrier signal energy is quite large, the human ears cannot distinguish it from the speech signal, i.e. there is no noise. 
     On the receiver side, the process is the same process as on the transmitter/encoder side, except in a reversed order. Another psychoacoustic analyzer  994  is used to extract voice signal profile  984  from received signal  985 . With this voice signal profile  984 , a masking un-shaper  974 , which is the reverse of masking shaper  924 , can un-shape modulated audio carrier signal  985  back to the normal profile. Unmasked modulated audio carrier signal  964  may then go through the same process as shown in  FIG. 7  to extract the bit stream. Eventually, bit stream  962 , which should be the same as original bit stream  912  can be recovered. 
       FIGS. 10   a ,  10   b  and  10   c  show some application systems using the current invention.  FIG. 10   a  is the encoding part that implements the current invention.  FIG. 10   b  is one decoding implementation that does not know or use the current invention.  FIG. 10   c  is one decoding implementation that does make use of the current invention. 
     The encoding part as shown in  FIG. 10   a  is similar to the transmission side of the system shown in  FIG. 1 . Data source  1004  sends data  1006  and voice source  1002  send its voice signal  1036  to a signal processor  1012 . Signal processor  1012  combines the two signals and forms a signal audio signal  1016 . In making audio signal  1016 , processor  1012  employs the spread spectrum method and the voice-data interference remover discussed above. Mixed audio signal  1016  is stored in some medium  1020 . Medium  1020  may also have some further processing before it transfers audio signal  1016 . Medium  1020  can be any medium that can carry the audio signal, permanently or temporarily. For example, medium  1020  can be an analog audio tape which records audio signal  1016  with a magnetic tape. Medium  1020  can be analog audio broadcast that transmits audio signal  1016  using radio waves. The radio wave is a transient or temporary carrier, but it can be easily converted into permanent medium by radio receivers. Medium  1020  can also be an audio CD or a hard-drive. 
     Medium  1020  can be reproduced by different devices or methods.  FIG. 10   b  shows a regular audio system, or a voice sink  1030  that reproduces audio signal  1022 . Even though the audio signal has data  1006  embedded in it, as far as voice sink  1030  is concerned, data  1006  does not exist, or is just background noise. Voice sink  1030  reproduces mixed audio signal  1022  together with data  1006 . To a human listener who hears the mixed audio with data, the data is unperceivable. So only audio signal is perceived. Since data  1006  is embedded in the audio signal, it is not affected by any audio signal processing. As long as audio signal  1022  is intact, data  1006  is intact. 
     If an audio receiver has a proper separator, as shown in  FIG. 10   c , then embedded data  1006  can be retrieved from mixed audio signal  1022 . As shown in  FIG. 10   c , the mixed audio signal is received by separator  1040 , which has a matching processor that can separate the mixed audio signal and data signal. 
     Pure audio signal  1042  is sent to a voice sink  1050  and data  1044  is sent to a data sink  1060 . Audio signal  1042  is data free. Data signal  1044  can be recovered and be used as intended. 
     The audio signal with embedded data has many different applications. One application could be intellectual property management. Since the digital data are embedded as an audio signal within the regular analog audio (e.g. music), they are unperceived by human listeners. The mixed audio signals are not affected by the usual digital or analog processing of the music in a codec and other processors, as long as the regular audio stream can be reproduced. So if a copyrighted song is embedded with copyright information, authorized seller&#39;s information (and even buyer&#39;s information), then such information is with the song even if it is copied without authorization many times. If a copy of such song is played, a receiver with an appropriate separator may listen to the song and retrieves the embedded data, if any. If there are embedded data in the song, then one can know who the author, or original seller (or buyer) is. If the person possesses the song is not the original buyer, then he may have received the song without authorization. 
     Mathematical Models 
     The embodiments of the current invention may also be described by the following mathematical models with more accuracy. 
     Modulation and Demodulation 
     Referring to  FIG. 2 , let S(k) be the bit stream signal to be modulated and sent. In our case, S(k) is a sequence of 1 and −1 indexed by k. That is: S(kε{−1, 1} for all kε           .           is the set of all integers, including positive integers, zero and negative integers.
     Continuous time is represented by t. That is: tε           .           is the set of all real numbers.
     The index k is sampled in time running at a period of T c . Here T c  is bounded to satisfy the Nyquist criteria. For a given index k, we can compute t as follows:
 
t=kT c  for all kε           

     The inverse is computed as: k=└t/T c ┘ for all tε           , Where └·┘ is the floor operator, which returns the largest integer that is less than the operand. In a practical system, S(k) will only be defined over a finite set of consecutive indices and therefore t will only span a finite time, but one can safely generalize to all time without affecting the results.
     Let us modulate by multiplying S(k) by a carrier tone: u(t)=2S(└t/T c ┘)cos(2 πf c t), where f c  is a real positive carrier frequency. u(t) is the modulated audio carrier signal that is transmitted. The received signal is x(t). 
     For a noise free situation: assuming that we get x(t) in the receiver with no noise, as shown in  FIG. 5 . On the receiver side we will demodulate x(t) to compute R(k). Assuming that LPF[ ] is a Low Pass Filter operator, we get: 
     
       
         
           
             
               
                 
                   
                     R 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     LPF 
                     ⁡ 
                     
                       [ 
                       
                         
                           x 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 f 
                                 c 
                               
                               ⁢ 
                               t 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   
                     = 
                     
                       LPF 
                       ⁡ 
                       
                         [ 
                         
                           2 
                           ⁢ 
                           
                             S 
                             ⁡ 
                             
                               ( 
                               
                                 ⌊ 
                                 
                                   t 
                                   / 
                                   
                                     T 
                                     c 
                                   
                                 
                                 ⌋ 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               cos 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   f 
                                   c 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           = 
                           
                             LPF 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   S 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       ⌊ 
                                       
                                         t 
                                         / 
                                         
                                           T 
                                           c 
                                         
                                       
                                       ⌋ 
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       cos 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           4 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             πf 
                                             c 
                                           
                                           ⁢ 
                                           t 
                                         
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             S 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     Note that R(k)=S(k). So we can recover what we had encoded, i.e. the modulation and demodulation works. As shown in  FIG. 5 , signal R(k)  518  and signal S(k)  516  are the same. In a noise free condition, the modulation/demodulation introduces no theoretical error. 
     Shaping Signal for Masking 
     Now we define a pair of filters. The Masking Shaping Filter is designed to shape the spectrum of u(t) to give an acoustically less perceptible sound to x(t).
 
 x ( t )= MSF[u ( t )]
 
     Here MSF is the Masking Shaping Filter operator. We define the inverse filter called Masking Unshaping Filter. It has an operator of USF[•]. The inverse property ideally guarantees.
 
 u ( t )= USF[MSF[u ( t )]]
 
Chip Sequence
 
     Let us define a chip sequence p(k) as follows:
 
p(k)ε{−1, 1} only defined for indices kε{1, 2, 3, . . . L}.
 
     Now we define a periodic chip pattern C(k)
 
 C ( k )= p (( k− 1)mod  L )+1) for all kε           
 
That is
 
 C ( k+nL )= p ( k ) for all nε          and kε{1, 2, 3, . . . L}.

     The chip sequence pattern is designed with two criteria
 
Σ k=1,2, . . . L C(k)C(k)=L,  (chip sequence condition 1)
 
and we minimize the offset correlation (ideally, it is zero)
 
Σ k=1,2, . . . L C(k)C(k+m) for m≠0 and m&lt;k  (chip sequence condition 2)
 
     The length of the chip sequence is a design choice, which is typically between 10 to about 50. A longer chip sequence is preferred, which can provide more benefits of spectrum spreading. But more spreading requires more bandwidth in the audio stream, which is typically limited by the audio stream. 
     Modulation/Demodulation with Chip Sequence 
     When we have a bit sequence we wish to transmit, we map the bit sequence to a pattern of +1 or −1, instead of +1 and 0, i.e. replace the 0 with −1. This becomes B(n). B(n)ε{−1, 1} for all nε           .
     The index n is bit time running at a period of T b . We set the period such that T b =L T c . 
     We may compute the synchronous chip time k from the bit time n with the relationship k=nL. The inverse is computed as: n=└k/L ┘. 
     We can now define how we generate S(k) from the bit sequence:
 
 S ( k )= C ( k ) B (└ k/L ┘).
 
     On the receiver side after demodulation we find, R(k)=S(k)=C(k)B(└k/L┘) 
     We now multiply by the chip sequence pattern one more time.
 
 C ( k ) R ( k )= C   2 ( k ) B (└ k/L ┘)
 
     Note that since C(k)ε{−1, 1} then C 2 (k)=1 such that C(k)R(k)=B(└k/L┘). The original bit stream is recovered. Again, with chip sequencing, the modulation/demodulation still works fine. So signal B(n)  544  is the same as signal B(n)  502  as shown in  FIG. 5 . 
     Modulation/Demodulation with Noise 
     In a more realistic system, there are random noises. But on average, random noises tend to average out. We do this with a summation. 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           k 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                             
                         
                         ⁢ 
                         
                           … 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           L 
                         
                       
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         R 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       ∑ 
                       
                         
                           k 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                             
                         
                         ⁢ 
                         
                           … 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           L 
                         
                       
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       B 
                       ⁡ 
                       
                         ( 
                         
                           ⌊ 
                           
                             
                               ( 
                               
                                 k 
                                 + 
                                 nL 
                               
                               ) 
                             
                             / 
                             L 
                           
                           ⌋ 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         LB 
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                             
                         
                         ⁢ 
                         
                             
                         
                       
                       ⁢ 
                       for 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       all 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       n 
                     
                     ∈ 
                     
                       Z 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       k 
                     
                     ∈ 
                     
                       
                         { 
                         
                           1 
                           , 
                           2 
                           , 
                           3 
                           , 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         } 
                       
                       . 
                     
                   
                 
               
             
           
         
       
     
     The gain factor L is just a scaling factor. We can recover B(n) by looking at the sign of G(n)B′(n)=sign(G(n))=sign(LB(n)) 
     In the absence of noise, B′(n)=B(n) always. So adding random noises in the model, the modulation/demodulation still works as desired. 
     With Voice/Data Interference 
     When considering the interaction between the voice signal and the data signal, the situation is different. When we add voice to the channel, we transmit a modified x(t) given by: 
     x(t)=MSF[u(t)]+v(t), Where v(t) is the voice signal that is being mixed with the data. 
     Spread Spectrum Decoding with Voice 
     When we transmit the data with voice signal, the demodulator on the receiver side will have a second term which is a function of voice. 
     
       
         
           
             
               
                 
                   
                     R 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     LPF 
                     ⁡ 
                     
                       [ 
                       
                         
                           USF 
                           ⁡ 
                           
                             [ 
                             
                               
                                 x 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               + 
                               
                                 v 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 f 
                                 c 
                               
                               ⁢ 
                               t 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     LPF 
                     ⁡ 
                     
                       [ 
                       
                         
                           2 
                           ⁢ 
                           
                             S 
                             ⁡ 
                             
                               ( 
                               
                                 ⌊ 
                                 
                                   t 
                                   / 
                                   
                                     T 
                                     c 
                                   
                                 
                                 ⌋ 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               cos 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   f 
                                   c 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           
                             USF 
                             ⁡ 
                             
                               [ 
                               
                                 v 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ] 
                             
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   f 
                                   c 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     LPF 
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             S 
                             ⁡ 
                             
                               ( 
                               
                                 ⌊ 
                                 
                                   t 
                                   / 
                                   
                                     T 
                                     c 
                                   
                                 
                                 ⌋ 
                               
                               ) 
                             
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 cos 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     4 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       f 
                                       c 
                                     
                                     ⁢ 
                                     t 
                                   
                                   ) 
                                 
                               
                             
                             ) 
                           
                         
                         + 
                         
                           
                             USF 
                             ⁡ 
                             
                               [ 
                               
                                 v 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ] 
                             
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   f 
                                   c 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       S 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       LPF 
                       ⁡ 
                       
                         [ 
                         
                           
                             USF 
                             ⁡ 
                             
                               [ 
                               
                                 v 
                                 ⁡ 
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                               ] 
                             
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 2 
                                 ⁢ 
                                 π 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   f 
                                   c 
                                 
                                 ⁢ 
                                 t 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       S 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       V 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
               
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               V 
               ⁡ 
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               
                 LPF 
                 ⁡ 
                 
                   [ 
                   
                     
                       USF 
                       ⁡ 
                       
                         [ 
                         
                           v 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ] 
                       
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             f 
                             c 
                           
                           ⁢ 
                           t 
                         
                         ) 
                       
                     
                   
                   ] 
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 ( 
                 
                   discrete 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   voice 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     equation 
                     . 
                   
                 
                 ) 
               
             
           
         
       
     
     This confirms the discussion in reference to  FIG. 6 . Signal R(k)  618  is now a function of the voice signal v(t)  605  also. The voice signal v(t) may be expressed in discrete domain signal V(k), as shown above. The voice signal v(t) (or V(k)) creates an interference in the receiver. In the receiver we multiply by the chip sequence pattern. 
     
       
         
           
             
               
                 
                   
                     
                       C 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ⁢ 
                     
                       R 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         S 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         V 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           C 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         B 
                         ⁡ 
                         
                           ( 
                           
                             ⌊ 
                             
                               k 
                               / 
                               L 
                             
                             ⌋ 
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         V 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       B 
                       ⁡ 
                       
                         ( 
                         
                           ⌊ 
                           
                             k 
                             / 
                             L 
                           
                           ⌋ 
                         
                         ) 
                       
                     
                     + 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         V 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     We do the summation. 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           k 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                             
                         
                         ⁢ 
                         
                           … 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           L 
                         
                       
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         R 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         ∑ 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           2 
                           , 
                           
                               
                           
                           ⁢ 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         
                             
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         B 
                         ⁡ 
                         
                           ( 
                           
                             ⌊ 
                             
                               
                                 ( 
                                 
                                   k 
                                   + 
                                   nL 
                                 
                                 ) 
                               
                               / 
                               L 
                             
                             ⌋ 
                           
                           ) 
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           2 
                           , 
                           
                               
                           
                           ⁢ 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         
                             
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           C 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               nL 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           V 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               nL 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       LB 
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           2 
                           , 
                           
                               
                           
                           ⁢ 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         
                             
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           C 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               nL 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           V 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               nL 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         LB 
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       + 
                       
                         
                           W 
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         for 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         all 
                         ⁢ 
                         
                           
                               
                           
                           ⁢ 
                           
                               
                           
                         
                         ⁢ 
                         n 
                       
                     
                     ∈ 
                     
                       Z 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       and 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       k 
                     
                     ∈ 
                     
                       
                         { 
                         
                           1 
                           , 
                           2 
                           , 
                           3 
                           , 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         } 
                       
                       . 
                     
                   
                 
               
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               
                 W 
                 ⁡ 
                 
                   ( 
                   n 
                   ) 
                 
               
               = 
               
                 
                   ∑ 
                   
                     
                       k 
                       = 
                       1 
                     
                     , 
                     2 
                     , 
                     
                       … 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       L 
                     
                   
                   
                       
                   
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   
                     C 
                     ⁡ 
                     
                       ( 
                       
                         k 
                         + 
                         nL 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     V 
                     ⁡ 
                     
                       ( 
                       
                         k 
                         + 
                         nL 
                       
                       ) 
                     
                   
                 
               
             
             ⁢ 
             
                 
             
           
         
       
       
         
           
             ( 
             
               &#39;&#39; 
               ⁢ 
               voice 
               ⁢ 
               
                 
                     
                 
                 ⁢ 
                 
                     
                 
               
               ⁢ 
               
                 i 
                 ⁢ 
                 nterference 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 equation 
                 ⁢ 
                 &#39;&#39; 
               
             
             ) 
           
         
       
     
     We try to recover B(n) by looking at the sign of G(n),
 
 B ′( n )=sign( G ( n ))=sign( LB ( n )+ W ( n ))
 
     Signal G(n)  652  is a resulting signal after all the signal processing as shown in  FIG. 6 . W(n) is a voice interference in the recovered bit stream. We will have an error if W(n) is large enough to change the sign of sign(L B(n)). 
     This is the problem of the voice interference discovered by the current invention. When the interference term is sizeable relative to the modulated digital signal, the digital signal may be corrupted and unrecoverable by the decoder, i.e. Prob(Bit Error)≧Prob(W(n)&gt;sign(L B(n))). Since this interference depends on the profile and amplitude of the voice signal, in certain situations, the interference is small and the bit error rate is small. Only when the correlation between the voice signal and the chip sequence is large, the interference is large and causing more errors. Due to the randomness of the chip sequence, the voice signal and their correlation, the error rate in the transmitted data is inconsistent and erratic. Due to the inconsistent error rates, it is very hard to overcome the error problem before the current invention. As discussed above, the errors are not due to the random noise in the audio channel, so making audio channel clearer, i.e. with less noise, does not help with the digital data transmission. To increase the energy of the audio carrier signal (the B(n) term) relative the regular voice signal does improved digital data transmission, but that can make the perceived noise in the regular voice noticeable and defeat the original purpose, i.e. transmitting digital data without disturbing the regular voice signal. Before the current invention, it was generally accepted that there will be transmission errors in a system which transmits digital data within an audio channel. The accepted error rate may be as high as 10% of all digital data transmitted. Other methods are employed to eventually correct the errors, for example using repeat data transmission when error occurs, or using error correcting coding etc. 
     Once the nature and source of the errors occurred in a digital data transmission in an audio stream are identified by the current invention, a method or a device to correct them can be designed. By reducing or eliminating this interference, the bit errors are substantially reduced or eliminated. 
     With Interference Remover 
     Since the interference is between the voice signal and the modulated carrier signal, both of which are known, the interference W(n) can be calculated according to the voice interference equation, which in turn uses the discrete voice equation. This is done in an interference estimator  723  as shown in  FIGS. 7 and 8 . As discussed in the modulation/demodulation section, the modulation/demodulation does not change signal properties. For mathematical simplicity, the following derivation is shown in discrete domain. In the transmitter, let us compute W(n) as defined in the voice interference equation and let us replace B(n) with B(n)−W(n)/L. Then we have:
 
 S ( k )= C ( k )( B (└ k/L ┘)− W (└ k/L ┘)/ L )
 
and at the receiver side, R(k)=S(k)+V(k), where (V(k) is the voice signal as defined above.
 
     Now in the receiver we multiply by the chip sequence pattern: 
     
       
         
           
             
               
                 
                   
                     
                       C 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     ⁢ 
                     
                       R 
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         S 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         V 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         
                           C 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             B 
                             ⁡ 
                             
                               ( 
                               
                                 ⌊ 
                                 
                                   k 
                                   / 
                                   L 
                                 
                                 ⌋ 
                               
                               ) 
                             
                           
                           - 
                           
                             
                               W 
                               ⁡ 
                               
                                 ( 
                                 
                                   ⌊ 
                                   
                                     k 
                                     / 
                                     L 
                                   
                                   ⌋ 
                                 
                                 ) 
                               
                             
                             / 
                             L 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         V 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       ( 
                       
                         
                           B 
                           ⁡ 
                           
                             ( 
                             
                               ⌊ 
                               
                                 k 
                                 / 
                                 L 
                               
                               ⌋ 
                             
                             ) 
                           
                         
                         - 
                         
                           
                             W 
                             ⁡ 
                             
                               ( 
                               
                                 ⌊ 
                                 
                                   k 
                                   / 
                                   L 
                                 
                                 ⌋ 
                               
                               ) 
                             
                           
                           / 
                           L 
                         
                       
                       ) 
                     
                     + 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         V 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     We next do the summation. 
     
       
         
           
             
               
                 
                   
                     G 
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                     
                   ⁢ 
                   
                     
                       ∑ 
                       
                         
                           k 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                             
                         
                         ⁢ 
                         
                           … 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           L 
                         
                       
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         R 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         ∑ 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           2 
                           , 
                           
                               
                           
                           ⁢ 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         
                             
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         B 
                         ⁡ 
                         
                           ( 
                           
                             ⌊ 
                             
                               
                                 ( 
                                 
                                   k 
                                   + 
                                   nL 
                                 
                                 ) 
                               
                               / 
                               L 
                             
                             ⌋ 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           2 
                           , 
                           
                               
                           
                           ⁢ 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         
                             
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           W 
                           ⁡ 
                           
                             ( 
                             
                               ⌊ 
                               
                                 
                                   ( 
                                   
                                     k 
                                     + 
                                     nL 
                                   
                                   ) 
                                 
                                 / 
                                 L 
                               
                               ⌋ 
                             
                             ) 
                           
                         
                         / 
                         L 
                       
                     
                     + 
                   
                 
               
             
             
               
                 
                     
                   ⁢ 
                   
                     
                       ∑ 
                       
                         
                           k 
                           = 
                           1 
                         
                         , 
                         2 
                         , 
                         
                             
                         
                         ⁢ 
                         
                           … 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           L 
                         
                       
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         V 
                         ⁡ 
                         
                           ( 
                           
                             k 
                             + 
                             nL 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       LB 
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     - 
                     
                       W 
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           2 
                           , 
                           
                               
                           
                           ⁢ 
                           
                             … 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             L 
                           
                         
                         
                             
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           C 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               nL 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           V 
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               nL 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       LB 
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     - 
                     
                       W 
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     + 
                     
                       W 
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     LB 
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                 
               
             
           
         
       
     
     Note that the output is not a function of the voice signal anymore. If there is noise, then we can try to recover B(n) by looking at the sign of G(n)
 
 B ′( n )=sign( G ( n ))=sign( LB ( n ))
 
     So we can get the original bit stream B(n) back. 
     The current invention identifies the nature and source of the errors in a digital data transmission system where the data is transmitted within an audio channel. The current invention determines that the main source of errors is the interference of the modulated carrier audio signal and the regular audio signal within the audio channel. By calculating and subtracting the interference from the modulated carrier audio signal, the resulting signal can be interference free. When the receiver demodulates the combined modulated audio carrier signal and the audio signal, the original digital data can be obtained without interference, or error free. To further improve the perceived audio quality of the regular audio stream, other methods, such as spread spectrum coding, profile masking may also be used. 
     In the current application, speech signal or voice signal refers to the audio signal in an audio system, which is the designed to process such audio signal. The speech signal or voice signal is not necessarily human speech. It can also be any audio signal or sound. The bit stream or digital data refers to any digital data embedded in or added to the audio signal. 
     While illustrative embodiments of the invention have been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention.