DIGITAL RADIO FREQUENCY RECEIVER

Abstract: The digital receiver (100) contemplates a digital radio receiver which operates on a received analog signal which has been converted to a digital form after preselection at the output of the antenna. The digital receiver (100) of the present invention comprises a preselector (106), a high-speed analog-to-digital (A/D) converter (108), a digitally implemented itermediate-frequency (IF) selectively section (110) having an output signal at substantially baseband frequencies, and digital signalprocessor (DSP) circuit (120) performing demodulation and audio filtering. The radio architecture of the present invention is programmably adaptable to virtually every known modulation scheme and is particularly suitable for implementation on integrated circuits.

Description: Digital Radio Frequency Receiver FIELD OF THE INVENTION This invention relates to the field of radio communications and specifically to a radio frequency receiver which is substantially implemented with digital circuitry. BACKGROUND OF THE INVENTION Conventional radio communications equipment is implemented primarily with analog circuitry. The inherent characteristics of analog components limit the amount of signal processing possible. For example, the noise and gain characteristics of analog amplifiers limit the dynamic range of the processed analog signal. In addition, analog information can not be readily stored in a manner which allows sophisticated signal processing. The use of digital signal processing to replace operations previously performed using analog processing eliminates undesirable variations in those operations which may have resulted from external effects such as temperature, humidity, and aging on analog components. In addition, digital signal processing techniques offer flexibility in terms of programmable operating characteristics and features. For example, a digital intermediate frequency (IF) integrated circuit would be programmable in terms of its channel frequency, its sampling rate, and, to some extent, its filter response. A digital signal processor (DSP), executing alternate stored programs, can perform different filtering and demodulation to implement completely different types of radios. Also, the DSP may be used to introduce advanced processing techniques such as adaptive equalization. An additional advantage of a digital receiver structure is that the DSP and IF circuitry can be designed so that it can be "reversed" to perform the corresponding operations for a digitally implemented transmitter. For half-duplex operation, the circuitry might be switched so that it simply reverses "direction," while for full-duplex operation two IF filters would be needed. The primary technology contribution leading to the feasibility of a substantially digital receiver is a high-speed (20-100 MHz), high-resolution (10-12 bits) A D converter. A secondary factor leading to the technical feasibility of a digital receiver structure is the high level of integration and high speeds attainable in VLSI IC implementations, ultimately permitting, for example, a 4-pole/4-zero double-precision digital filter with a 40-kHz sampling rate to be implemented in apresent-day digital signal processor. The present invention combines these new technologies with improved techniques for front-end analog processing and digital IF filtering to achieve a feasible design for a substantially digital receiver. The receiver structure of the present invention permits a revolutionary change in the manufacturing technology and operating characteristics of mobile radios. Furthermore, this approach permits a radio to be built with a minimal number of parts, which at once reduces parts and manufacturing costs, while also improving radio reliability and serviceabilty. SUMMARY AND OBJECTS OF THE INVENΗON In summary, the present invention contemplates an all digital radio receiver which operates on a received R.F signal which is converted to a digital form after preselection at the output of an antenna. The receiver of the present invention comprises a preselector, a high-speed analog-to-digital (A/D) converter, a digitally implemented intermediate-frequency (IF) selectivity section having an output signal at substantially baseband frequencies, and general-purpose digital signal processor (DSP) integrated circuits performing final selectivity or equalization, demodulation, and post-demodulation processing. Accordingly it is an object of the present invention to provide a digitally implemented radio receiver. It is another object of the present invention to provide a radio receiver structure which is readily adapted to receive a plurality of transmission schemes. It is yet another object of the present invention to provide a radio receiver structure which may be substantially implemented using integrated circuit techniques. It is still another object of the present invention to provide a digital receiver IF filter design which operates at a relatively fast rate so as to reduce the resolution and step size demands on the A/D converter. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a block diagram showing the functions of the digital receiver of the present invention. Figure 2 is a schematic diagram of the front-end circuitry of the digital receiver of the present invention. Figure 3 is a block diagram of the digital zero I.F. selectivity section of the present invention. Figure 4a is a schematic and block diagram of the digital oscillator referenced in Figure 1. Figure 4b is a schematic diagram of a pseudorandom dither generator compatible with the digital zero I.F. selectivity section of Figure 3. Figure 5a is a block diagram of a desired "fast", narrowband lowpass filter. Figure 5b is a block diagram of a decomposed approximation to the fast lowpass filter of Figure 5 a. Figures 6a through 6d are frequency diagrams detailing the characteristics of the fast lowpass filters of Figure 5. Figure 7 is a schematic diagram of the second-order narrowband lowpass infinite-impulse-response (IIR) filter used in the decomposed"fast" lowpass filters of Figure 5b. Figure 8 is a schematic diagram of the second-order finite-impulse-response (FIR) filter with a notch at half the sampling rate used in the decomposed fast lowpass filters of Figure 5b. Figures 9a through 9c are schematic diagrams of the time-division-multiplexed second-order lowpass IIR filter used in the time-division-multiplexed "slow" lowpass filters described in conjunction with Figure 3. Figure 10 is a block diagram of the fifth-order lowpass FER filter used to further reduce the sampling rate from 80 to 40 kHz. Figure 11 is a block diagram of the fourth-order lowpass IIR filter used for final selectivity and passband equalization, prior to demodulation. Figure 12 is a block diagram of an FM demodulator implemented with a general purpose DSP. Figures 13a through 13c are diagrams-detailing the principles of phasors in the context of the present invention. Figures 14a and 14b are flow diagrams detailing the operation of the background routine of the FM demodulator of the present invention. Figures 15a through 15b are flow diagrams of the operation of the scale routine described in conjunction with Figure 15a. Figures 16a through 16c are flow diagrams detailing the operation of the remaining portions of the digital demodulator of the present invention. DETAILED DESCRIPTION OF THE DRAWINGS Figure 1 illustrates the functions of a digital receiver, comprising three major operations. While the diagram shows no example of receiver diversity, it will be obvious to one skilled in the art that various diversity approaches could be applied for use in a receiver of the present invention. In particular, the "front-end" section 104, which is further detailed in Figure 2, interfaces an antenna 102, receiving an analog radio-frequency (RF) signal, to the digitally implemented EF selectivity section 110. The preselector 106 provides wideband filtering of the incoming signal, to prevent aliasing in the subsequent A/D conversion process. The A/D block 108 includes the gain and sample-and-hold operations necessary for the digital processing of the present receiver structure. The next major section, EF selectivity section 110, further detailed below in conjunction with Figure 3, provides a quadrature local oscillator (LO) 116 which generates a complex exponential signal (quadrature signals sine and cosine). The frequency of this signal is selected by the system channel frequency input "A". The quadrature mixers 112 use digital multipliers to frequency-shift the desired narrowband channel down to the EF frequency of approximatly zero Hz. The high-speed selectivity section 114 includes several cascaded narrowband lowpass filter sections, which remove undesired signals at higher frequencies from the desired signal which is centered near zero frequency. This lowpass filtering permits gradual sampling rate reduction from the high rates at the output of the A/D convener 108 to rates comparable to the channel bandwidth at the input to the "back-end" section 120. The "back-end" section 120 is used to "specialize" the general-purpose radio " structure into one specifically tailored to a particular radio application, designated by a system radio-type input "B". Its best implementation may comprise a general-purpose digital signal processor (DSP). The final selectivity section 124 provides any additional filtering needed prior to demodulation of the radio signal in accordance with the type of modulation and channel characteristics. For example, it may provide adaptive channel equalization for a digital data communications system. This filter section 124 also provides adjacent channel attenuation , and passband equalization to compensate for imperfections in the characteristics of the high-speed selectivity filters 114, resulting from the coarse coefficient quantization needed to implement multiplierless (lowpass) filters. The demodulation section 126 may be software-programmed to implement many types of demodulation, including FM demodulation for voice and frequency-shift-keyed (FSK) data. The demodulated voice signal may be converted back to analog form, then amplified and played through a loudspeaker, as suggested by icons 121 and 122. Alternatively, a digital voice message may be stored in digital a digital memory 123 for later playback. In a data communications system (not shown), the demodulated data symbols may be routed to a computer for further processing or to a computer terminal for immediate display. In addition, control information to implement automatic frequency tracking 128 may be generated in the "back-end" section 120. Finally, a clock-generation section 118 is required to control the input sampling rate of the A/D conversion as necessary for accurate down conversion, to operate the 5 digital circuitry in a regular fashion, and to control the output sampling rate, perhaps for synchronizing with subsequent systems. In the exemplary embodiment to be described here, the sampling rate f s is taken to be 20 MHz, and the band of frequencies to be received is centered at approximately 875 MHz. Figure 2 is a schematic diagram of the front end circuitry of the digital o receiver of the present invention. This circuitry functions to digitize a selected band of radio frequency signals. T e present invention provides that sampling is done directly at R.F. frequencies. However, wideband pre-selection is provided by R.F. analog filters prior to sampling. The function of the R.F. filters 202 and 206 is to provide selectivity to spurious responses. These spurious responses included the 5 image, half I.F. spurs, Able-Baker spurs, etc. as found in a conventional receiver front-end. In addition to these spurs, selectivity must be provided to frequencies which can be aliased by the sampling process. Maximum allowable bandwidth is limited to the Nyquist bandwidth (f s /2, where f s is the sampling rate), although practical filters will significantly reduce this. 0 Use of a 2-ρole and 5-poIe filter as shown in Figure 2, each with bandwidths of approximately 4 MHz, will provide greater than 90 dB rejection to aliased frequencies when sampled at a 20 MHz rate. In addition to providing selectivity to signals entering antenna 224, filter 206 bandlimits wideband noise entering the first sample and hold 208 generated by R.F. preamplifier 204. This is s necessary to prevent aliasing of noise, thus effectively increasing the noise figure of the front-end 200. R.F. preamplifier 204 is used to amplify the R.F. signal to a sufficient level to provide the necessary signal-to-noise ratio needed for system sensitivity. Since different filters are needed for different bands, it is practical to include the R.F. amplifier 204 as part of the filter structure (202 and 206). The receiver of the present invention provides an R.F. amplifier 204 having a gain of approximately 28 dB and a noise figure of approximately 5 dB. Clock 212 and sampling pulse generator 210 provide clock signals and sampling pulses to the first sample and hold 208, second sample and hold 220, the ■ analog to digital converter 222, and the digital zero-EF selectivity section (not shown). Clock generation may be accomplished by a 20 MHz crystal oscillator, which is widely available. A 40 MHz signal for use by the digital signal processor (not shown) is derived by doubling the 20 MHz signal by an analog doubling circuit The pulse generator 210 is used to shape the 20 MHz clock signal (an approximate sinusoid) into very narrow pulses. The width of the sampling pulse depends on the highest frequency band desired to be received. A pulse width of approximately 300 psec. will generate a "comb" of harmonics with approximately uniform amplitude to approximately 1 GHz. This is necessary for operation at the operating frequency of approximately 875 MHz of the receiver of the present invention. Pulse generation may be accomplished using a conventional step recovery diode and ringing circuit A circuit of this type is described in a publication entitled Harmonic Generation Using Step Recovery Diodes and SRD modules, Hewlett Packard Application note #920, available from Hewlett Packard Microwave Semiconductor Division, 350 Trimble Rd., San Jose, Ca., 95131. The band of signals amplified and selected by blocks 202, 204, and 206 is sampled by the first sample and hold 208. This is analogous to down-converting in a conventional R.F. receiver. Although a flash analog-to-digital convener effectively samples the signal, practical conveners have bandlimited inputs, thus requiring sampling prior to conversion. Also, to date, all known high resolution (> 10 bits), high speed converters utilize a two-step conversion process. This type of converter necessitates the use of a second sample and hold circuit 220. Double sampling is necessary to overcome the practical limitations of acquisition time, accuracy, and droop. The first sample and hold must acquire extremely fast in the range of 300 psec in the receiver of the present invention. This requires the use of a small hold capacitor in order to charge the capacitor from sample to sample to approximately the voltage of the input signal. The inability to completely charge in the sampling interval to the value of the input signal results in a mild filtering processing which can be considered negligible for narrowband signals typically used for land mobile communications. The use of a small hold capacitor in the first sample and hold results in a droop rate unacceptable for use by a two-step analog to digital converter. Also, settling time of a relatively simple hold circuit as can be used by the first sample and hold may be inadequate for a two-step converter. For these reasons, a high accuracy second sample and hold 220 is used. Since the signal has been effectively down converted, it is changing at a much slower rate. This allows the use of a larger acquisition time and larger hold capacitor. Known two-step converters require the sample and hold to droop less than 1/2 the step size in significantly less than the sampling period (typically less than 1/2 the sampling period). The first sample and hold (208) may be implemented according to conventional techniques using a Schottky diode bridge and a dual gate MOS FET as the buffer amplifier. The second sample and hold may be realized using a Schottky diode bridge, with additional back biasing to limit droop in the hold mode. A high speed amplifier consisting of J-FETS in differential configuration as inputs and high dynamic range bipolar followers serves as a buffer amplifier. Wideband amplifier 209 is necessary to further amplify the signal in order to overcome the quantization noise of the analog to digital converter. The amplifier 209 is used to amplify a sampled signal; hence it must be wideband. High dynamic range is also necessary to prevent amplifier nonlinearities from distorting the signal. The amplier 209 noise figure is dependent on the amount of "takeover" gain provided by R.F. amplifier 204 and overall noise requirements for sensitivity. A Motorola MHW591 CATV wideband amplifier is suitable for use as the wideband amplifier with the 800 MHz receiver of the present invention. An A/D converter structure similar to the type described herein is shown in an article by Muto, Peetz, and Rehner entitled Designing a 10-bit, 20 Ms-Per-Second Analog-to -Digital Converter System, HEWLETT PACKARD JOURNAL, Vol 33, #11, pp. 9-29, Nov 1982. According to the teachings of the present invention, a dither signal 218 is added to the sampled signal at combiner/isolator 214. The combiner/isolator helps prevent nonlinearities present in the wideband amplifier and dither source from translating the low passed noise to other frequencies. The purpose of the dither 218 is to uniformly spread quantization noise of the analog-to- digital converter. The uniform spreading of the noise floor over the Nyquist bandwidth prevents intermodulation distortion caused by quantizing from being an inherent problem, and also allows signal recovery below the least significant bit level, thus reducing gain requirements before the A/D converter and easing the problems caused by non-linearities in the stages preceding the converter. The dither signal 218 must be 8 added before the second sample and hold 220 if a two-step converter is used since the signal must be held constant during the conversion period. The dither source 218 can be realized by using an analog noise source such as a noise diode. The general characteristics and advantages of dither signals are described in a paper by Schuchman, L., Dither Signals and Their Effect on Quantizaύon Noise, IEEE TRANSACTIONS ON COMMUNICATIONS TECHNOLOGY, pp. 162-165 , Dec. 1964. Noise added to the signal should be spectrally isolated from the information. The sampling performed in the 800 MHz receiver of the present invention places the information approximately between 3 and 7 MHz. Low pass filter 216 prevents noise from being added to the information signal. The receiver of the present invention is provided with a 5-pole elliptic filter with a 1.5 MHz cutoff frequency for low-pass filter 216. The average voltage level of the dither signal over the noise equivalent bandwidth of the low pass filter 216 should be greater than approximately 5 step sizes of the analog to digital converter. Care must be exercised to prevent the dither signal from causing clipping at the A/D converter 222. The analog-to-digital converter 222 converts the analog signal to a digital signal. The converter must be capable of accepting signals over the dynamic environment of the intended receiver application. For the land mobile communications application, a minimum of 10 A/D bits is necessary, and theoretical studies indicate the dynamic range provided by a 12-bit converter should be comparable with all existing conventional land-mobile receivers. The two factors of prime importance of the analog to digital converter 222 are sampling speed and step size. The step size determines the amount of gain necessary prior to the converter in order to take over the quantization noise floor. The larger the step size, the larger the gain requirement. Large amounts of gain result in nonlinear effects prior to the converter. Conversion speed is also very important since this determines the allowable bandwidth of the front-end filters, and also reduces the gain requirement by spreading the quantization noise over a larger bandwidth. An analog to digital converter 222 satisfactory for use with the 800 MHz digital receiver of the present invention is a two-step 10-bit converter with a step size of approximately 3 mV, which is capable of converting at rates greater than 50 MHz. According to the principles of the present invention, a front end gain of approximately 54 dB is necessary to realize a post detection signal to noise ratio of approximately 10 dB in a receiver having a 30 kHz bandwidth when receiving a 0.3 μv signal sampled at a 20 MHz rate. The large amount of gain necessary prior to converter 222 limits the nonlinear performance of the system. Intermodulation ratio (IMR) is limited to approximately 65 dB which is somewhat less than that achievable by conventional receivers. It will be obvious to one of ordinary skill in the art that a reduction of the step size to approximately 200 μV will allow an EMR > 80 dB to be achieved. This value is comparable with most existing conventional 800 MHz receivers. Referring now to Figure 3, a digital zero-EF selectivity section (DZISS) compatible with the practice of the present invention is depicted in block diagram form. The digital zero-IF selectivity section is disposed between the ront-end circuitry 200 of Figure 2 and the backend DSP 120 of Figure 1, and it operates to convert the modulated digital RF signal output by front end 200 to the baseband signal processed by the backend DSP 120. The DZISS 300 is comprised of an in-phase mixer 304, a quadrature-phase mixer 306, a digital quadrature local oscillator (L0) 302 (providing an in-phase L0 signal 309 and a quadrature phase L0 signal 311), two "fast" digital lowpass filters 308 and 310, two "slow" digital lowpass filters 312 and 313, and a clock source (not shown). In the practice of the present invention identical digital information is applied to both the in-phase mixer 304 and the quadrature-phase mixer 306 at input ports 303 and 307 respectively. Generally, ports 303 and 307 are not single lines, but are in fact multiple lines representing a multi-bit (e.g., 10 or 12 bits) digital word. The actual length of the digital word used in any given application is dependent upon many factors, including: the resolution required, the dynamic range required and the frequency of sampling the received RF signal. For example, a word length of 12 bits is considered to have an acceptable performance in receiving a typical radio signal sampled at 20MHz. Mixers 304 and 306 have as a second input quadrature L0 lines 309 and 311, respectively. As with the A/D output signal discussed above, the L0 signals are not single connections, but are multi-bit discrete time representations of signals that are 90 degrees apart in phase (i.e., sine and cosine waveforms). Mixers 304 and 306 perform arithmetic multiplications of the A/D input word and the L0 word, rounding the result to form an output word that is applied from the output ports of mixers 304 and 306 to the input ports of digital lowpass filters 308 and 310, respectively. The digital word lengths of the LO and mixer output signals may be selected to yield acceptable noise performance. As the digital word is lengthened, more quantization levels are available to represent the signals. The smaller quantization increments lead to improved noise performance, as is well understood in the art This quadrature mixing process described above is analogous to that performed in an analog "zero-Dr", or direct conversion receiver. However, the use of truly linear digital multipliers precludes second order mixing of undesired signals to D.C, and other undesirable effects, as occurs with analog direct conversion. The quadrature mixing performed by multipliers 304 and 306 acts to frequency-translate the desired signal to a center frequency of approximately zero Hz, where the amount of frequency translation maybe determined by channel frequency control 305. The resultant quadrature signal may then be lowpass filtered to remove out-of-band noise and undesired signals. In the preferred practice of the present invention, this selectivity is provided in two stages. The first stage is formed by fast recursive digital filter sections 308 and 310. Digital filters 308 and 310 are identical in structure and may be formed from a recursive filter topology which will be described below in greater detail. The remaining selectivity is provided by "slower" recursive filters 312, and 313, respectively. This choice of architecture will be discussed in more detail below. Following the filtering process, the digital signals are output to a backend DSP 120 for further processing. Figure 4a is a schematic and block diagram of the digital oscillator described in conjunction with Figure 3. Recall that the function of the quadrature oscillator is to provide digitized, sampled versions of the cosine and sine waveforms utilized in the quadrature mixing process. Implementation of the digital zero-EF selectivity section depends on the ability to generate accurate, stable digital representations of these waveforms. A class of digital oscillator realizations paπicularly suited to the requirements of the present invention is based on the concept of ROM (read only memory) lookup. Consider the generation of a digital signal comprising samples of the complex sinusoid: w(t) = ei 27 ^ where f c is the desired oscillator frequency. According to conventional communications theory, cos2πf c t + jsin2πf c t, Thus the desired cosine and sine waveforms may be regarded as the real and imaginary parts, respectively, of the complex sinusiod waveform. The sampled version of ei 27rf c u is obtained by replacing the continuous time variable t by the discrete time variable nT, where n is a counting integer (1,2,3, ...) and T is the sampling period, which equals 1/f- = 1/sampling rate. This discrete time signal is then equivalent to: w(n) = eJ 2πf c( nT ) ROM lookup methods of generating this signal follow from making the frequency variable f c , as well as the time variable, discrete. If we let f c = kf s /2 N (where k and N are integers), then: w(n) = e J kf s (n/f s )/ 2 N = e j2πnk/ 2 N It can be seen that cosine and sine values for only 2^ different phases need be generated. One method of generating these values, called direct ROM lookup, basically involves the use of ROM table containing the 2^ pairs of values (cosine and sine), which is addressed by a register containing the integer nk (proportion to phase.) The phase register is incremented by the incremented by the value k (corresponding to the desired frequency f c ) at each sample time (corresponding to π). The frequency resolution obtained is Δf = f s /2 , wherein 2' distinct frequencies can be generated. Depending on the application, the direct ROM look-up technique may involve large amounts of ROM. The ROM size may be reduced somewhat by taking advantage of the symmetric properties of cosine and sine waveforms. Such properties allow the number of table entries to be reduced from 2 ; \ to 2 <'8, pairs of numbers. Even with this reduction the ROM size may still be excessive. In such cases, a technique called Factored ROM lookup may be employed to further reduce ROM size. The digital local oscillator 400 of the present invention uses the factored ROM look-up technique utilizing the fact that the unit magnitude phasor can be broken into a complex product of "coarse" and "fine" phasors. Thus, the unit magnitude phasor ei 0 can be represented dividing the signal into eJ 0 c • eJ 0 f. Therefore, the unit magnitude phasor can be realized by having separate 12 coarse value phasors and fine-value phasors stored in ROM which are multiplied together to get thediscrete time sine and cosine values required for the quadrature mixers. The advantage of this factorization is that the amount of ROM necessary to store the coarse-value and fine value phasors is greatly reduced from that required for the direct ROM look-up approach. The expense paid for this ROM size reduction is the introduction of circuitry to perform the complex multiplication of coarse and fine phasors. Generally, a complex multiplication can be implemented with four multipliers and two adders. By proper selection of the fine- value phasor, and recalling that the cosine of a small angle can be approximated by one, the ROM for the cosine fine-value phasor can be eliminated. Further, by approximating the small angle cosine values as one, two multipliers can be eliminated from the multiplication structure required to generate a complex product. This results in both a cost and size savings in the factored ROM implementation. Referring still to Figure 4a, the digital quadrature local oscillator 400, as implemented using a factored-ROM approach, is depicted in block diagram form. Frequency information, in the form of an N bit binary number proportional to the desired frequency, within the band sampled by the A/D converter, is loaded into the channel frequency latch 402. Channel frequency latch 402 may be realized in many different forms. For example, assuming that N=20, five cascaded 74LS175's (Quad D flip-flops), manufactured by Motorola, Inc., and others, provide an acceptable implementation. Those skilled in the art will appreciate that channel frequency latch 402 may be loaded by various means. For example, in a single frequency radio the channel frequency latch could be permanently loaded with a single binary number. For multiple frequency radios, channel frequency latch 402 could be loaded from an EPROM or ROM look-up table or else calculated by and latched from a microprocessor. The output of channel frequency latch 402 is coupled to a binary summer 404. It will be understood by those skilled in the art that in the following discussion of digital quadrature local oscillator 400 all coupling lines in between the functional Q blocks are in fact multi-bit binary words and not single connections. The output of adder 404 is coupled to phase accumulator 406. Phase accumulator 406 can be implemented as an N-bit binary latch which is used to hold the address of the next location of ROM to be addressed. Thus, the output of phase accumulator 406 may be directly coupled to cosine coarse-value ROM 418, sine coarse-value ROM 416, 5 and sine fine-value ROM 414 (recall that fine-value cosine ROM is not required, as it is being approximated by one). Further, the output of phase accumulator 406 is fed back into summer 404 to be added (modulo 2 N ) to the binary number representing the channel frequency information located in the channel frequency latch 402. The output of phase accumulator 406 is updated once every clock pulse, which is generally the sampling frequency. The result of this binary addition is that phase accumulator 406 is holding the binary sum (proportional to phase) of the last address plus a binary vector contained in the channel frequency latch. This number indicates the next address to be required to create the quadrature local oscillator signals cos 2πf c nT and sin 2πf c nT. In the preferred embodiment, the ROM size may be reduced, or equivalently, the frequency resolution may be improved without increasing the ROM size, by adding a digital dither signal to the output of phase accumulator 406 and truncating the result prior to addressing the ROM tables. The frequency resolution of the local oscillator is defined by the data path width (N) of the phase accumulator and the sampling rate f s required. The most straight-forward method of increasing frequency resolution is to add more bits to the phase accumulator and increase the size of the ROM tables. However this can be an expensive solution since the ROM must double in size for each bit added to the phase accumulator. Another option would be to add bits to the phase accumulator but truncate the additional bits before performing the ROM look-up. This introduces severe phase rounding and causes spurs in the local oscillator output. In order to avoid these spurs a low level dither signal is added to the accumulator output before truncation. According to the principles of the present invention, the frequency resolution of the digital oscillator may be enhanced, without increasing ROM size and without introducing spurs in the output, by adding a binary dither signal to the output of phase accumulator 406 before truncating. To accomplish this, digital oscillator 400 is provided with an L-bit dither source 408, which generates an L-bit wide, uniform probability density, pseudorandom "white noise" signal. Dither source 408 is clocked at the sampling frequency f s , so as to provide a new L-bit dither word for every phase word output from phase accumulator 406. An N-bit dither word is formed by appending M = N - L leading zeroes to the L-bit dither word output from dither source 408. This composite N-bit dither signal is added to the N-bit output of phase accumulator 406 by N-bit binary adder 410, in Modulo 2 N fashion. The sum output of adder 410 is then truncated to M bits (truncation not shown). In practice this truncation process is achieved by simply ignoring the least significant bits produced at the output of digital adder 410. The truncation operation itself allows for reduced ROM size. Quantization or truncation of the binary phase word produces distortion or noise in the generated sine and cosine waveforms. Since the phase is a periodic function (sawtooth), the noise produced by quantization would also be periodic unless it is randomized somehow. Periodic noise would result in discrete "spurs" in the oscillator output spectrum which are undesirable in most applications if their level exceeds some threshold. Addition of the dither signal prior to phase quantization randomizes the phase noise, resulting in a more desirable white noise spectrum at the output The binary phase word is represented by a binary word of N bits. The dither signal comprises a pseudo-random binary word of L bits which is summed with the N bit phase word. The process results in a binary word N = L + M bits. This binary word is then truncated to a binary phase word of M bits which is relatively free of the spurious signals described above. The effect of phase quantization on oscillator output noise can be shown by the following analysis. The desired oscillator output is described by the following equation: w(n) = eJ 2πf c nT = eJ 0 ( n ) If the phase angle is quantized with error 3(n), the actual output is described as follows: w(n) = ei£ 0 ( n ) +a ( n) ] The error introduced is: E(n) = w(n) - w(n) = e t 0 n ) -*-3(n ] _ ^øfn ) ^ eJøO teβW- i] For the case of interest where θ(n) is very small (<< 1), eJ°( n ^ can be approximated by l-rj3(n), thus yielding: E(n) = eJ 0 ( n ) ' j-(n) The spectrum of E(n) can be seen as simply a frequency translation (and unimportant scaling by j) of the spectrum of the phase quantization noise d(n). Thus if 9(n) is random or "white", so is E(n). Furthermore, the power of E(n) equals the power of 3(n), allowing the output noise level created by the phase noise to be easily estimated. Choosing the power level of the dither signal involves a tradeoff between noise whitening effect and output noise power level. As the dither power is increased (by increasing the number of bits, L, in the dither signal), the noise becomes more whitened, but the total phase noise power increases as well. It can be shown that if the dither signal exhibits a uniform probability density, . the choice of L = N-M results in the preferred level of dither power since it represents the smallest dither signal necessary to completely whiten the phase quantization noise. Thus, in the preferred implementation, the number of dither bits L equals the number of bits discarded in the truncation process. It may be noted that dither signals exhibiting other than uniform probability density may be utilized. However, a uniform density is preferred as it is the most easily generated. With L = N-M, the variance (power) of the phase noise is equal to 2 times the equivalent phase variance of the dither signal. Given a desired frequency resolution, determined by N and f s , then L and M, and hence the required ROM size, are determined by the allowable level of white noise at the oscillator output. As an example, with f s = 20 MHz, and N = 20 bits, the frequency resolution is 19.07 Hz. Truncating to M=17 bits (to reduce ROM size by a factor of 8) without dither creates spurs in the oscillator output, which for one particular frequency are 98 dB below the level of the desired signal. Addition of a 3-bit dither signal prior to truncation whitens the error signal, eliminating the spurs. According to the principles of the present invention, the frequency resolution of the digital oscillator, for a given level of output noise, can be increased indefinitely by simply adding more bits to the frequency and phase latches, and to the dither signal. The ROM size, determined by M, remains constant The M-bit binary word retained after truncation is coupled to the ROM address latch 412, whose output is coupled to ROM's 418, 416, and 414. Upon receiving an address, ROM's 418, 416, and 414 output the digital binary word located at the received address on their respective output ports. The digital quadrature signals are then arithmetically generated from the three binary numbers. As stated previously, the output signals of ROM 416, and 418 are binary numbers proportional to the cosine and sine of the coarse phase. The output signal of ROM 414 is a binary number proportional to the sine of the fine phase. In order to minimize the error in the fine cosine approximation, the fine phase values used are the values centered around the positive axis. The output of ROM address latch 412 16 is an M bit number that is divided into a M c bit coarse address and an M bit fine address where M = M- + Mf. The coarse phase is 2π(Pc + 1/2) /2 M c, where P is the integer corresponding to the M c bit coarse address. The fine phase is 2π(p f - 2 M f-l)/2 M , where P is the integer corresponding to the Mf bit fine address. For example, if M c = 10 and Mf = 7, the ROM table entries may be configured as shown below in Tables 1 and 2. TABLE 1 TABLE 2 To generate the cosine waveform (i.e., the real component of the complex waveform), the outputs of sine coarse-value ROM 418 and sine fine-value ROM 414 are first multiplied in multiplier 426. The output of multiplier 426 is fed to summing circuit 440 where it is subtracted (2's complement form) from the output of cosine coarse-value ROM 416. This arithmetic process yields the cosine-value which is output on port 441 and coupled to quadrature mixer 304 of Figure 3. To generate the sine values of the digital quadrature L0 the outputs of the cosine coarse-value ROM 416 and sine fine value ROM 414 are multiplied in multiplier 428. The output of multiplier 428 is fed to a summing circuit 442 where it is summed with the output of sine coarse-value ROM 418. Summing circuit 442 outputs via connection 443 the discrete time sine value digital word which is coupled to quadrature mixer 306 of Figure 3. Therefore, since the discrete time values of the sine and cosine signals are calculated mathematically, perfect 90° phase control is achieved using minimal ROM space. Latches 420, 422, 424, 434 and 438 provide pipelining which facilitates high operating speed of the digital oscillator. Delays 430 and 436 are provided to equalize the delays of the various signal paths. The factored ROM LO reduces the ROM area while maintaining acceptable frequency resolution. For example, to implement a digital quadrature LO that operates at 20 MHz, the coarse-value ROM's 416, 418 could each be implemented in a 1024 x 16 ROM and the fine-value sine ROM 414 could be implemented in a 128 X 8 ROM. This would result in frequency resolution of approximately 20 Hz using approximately 34,000 bits of ROM. The factored-ROM configuration is preferred for operation at high sampling rates, since, except for the phase accumulator, there is no circuitry connected in a feedback manner. This allows the rest of the LO circuitry (especially multipliers 426 and 428, which represent the main speed bottleneck) to be pipelined to achieve a very high operating rate. Pipelining would consist of introducing latches at certain critical points, such as within the multipliers themselves, as is well understood in the art. Thus, a factored-ROM LO is described which outputs discrete time digital quadrature signals which exhibit a selected frequency. A digital adder suitable for use with the apparatus of the present invention may be of a type constructed with several 74LS181 4-bit arithmetic logic unit devices, connected in parallel. These devices are shown and described in a data manual entitled "Motorola Schottky TTL Data Book", available from Motorola, Inc., Box 2092 Phoenix, Arizona, 85036. ROMs 418, 416 and 414 may be formed by a variety of well known ROM devices such as a 82LS181 available from Signetics Corporation, 811 E. Argues Avenue, P.O. Box 3409, Sunnyvale, Calif. 94088, and < 18 described in the "Signetics Bipolar Memory Data Manual", 1984. Both multiplier 426 and 428 may be realized as, for example, an MPY016K manufactured by TRW Inc., TRW Electronic Components Group, P.O. Box 2472, LaJolla, Ca. 92038. The amount of coarse- value ROM required can be further reduced by taking advantage of symmetries in the cosine and sine wave forms, and thereby storing only the values of the unit magnitude phasor residing in the first octant (i.e., the first 45°) of the phasor unit circle. Those skilled in the art will appreciate that the unit magnitude phasor represents sine or cosine values rotating through 360°. Due to the symmetrical nature of sinusoidal waveforms, the values of the cosine and sine waveforms over the first octant of the unit circle are identical to the values of these waveforms over any other octant except for possible sign changes and reversal of roles (i.e., sine becomes cosine and vice versa). Therefore, the only coarse-value phasors that are required are those in the first octant provided there is an indicator of which octant the phasor is currently residing, and there is circuitry present to negate (i.e., change sign) and/or exchange the outputs of coarse-cosine ROM 416 and coarse-sine ROM 418 according to the current octant. An octant indicator is readily implemented using three binary bits of the ROM address. For example, the three most-significant-bits (MSB's) could be used to indicate the octant, and the remaining bits used to address the ROM for the coarse-valued phasor. Figure 4b is a schematic diagram of an example of a type of digital dither generator compatible with the digital oscillator of the present invention. A digital dither signal can be generated by any of several well-known pseudorandom sequence generation techniques. One type of dither, or random number generator is shown and described in a paper by G. I. Donov, A High-Speed Random-Number Generator , RADIO ELECTRONICS AND COMMUNICATION SYSTEMS, Vol. 25, No.4, pp. 88-90, 1982. Referring now to Figure 4b, a feedback shift register pseudorandom sequence generator which may be advantageously employed in the practice of the present invention is shown in schematic form. The sequence generator of Figure 4b is used to provide an L-bit digital dither signal to the binary adder 410 of Figure 4a. The dither generator 408 includes an R-bit shift register 460 which may be formed of a plurality of flip-flops 464 through 499 which are connected in a cascade fashion. In the preferred practice of the present invention, a parallel 3-bit dither signal is tapped from the shift register at the outputs of flip-flops 478, 491 and 499 respectively. The inputs to an Exclusive-Or gate 462 are coupled to the outputs of flip-flops 464; 493, 498 and 499. The output of Exclusive-Or gate 462 is coupled to the input of flip-flop 464. The shift register produces a 3-bit pseudo-random dither signal which is added to the output of the phase accumulator 406 of Figure 4a. The flip-flops 464-499 and the Exclusive-Or gate 462 as well as the other devices used in the practice of the present invention may be any of several well known logic devices; however, high speed TTL devices are particularly well adapted for the practice of the present invention. Implementations employing other logic families will also be obvious to one of ordinary skill in the art. The dither generator of Figure 4b is set forth as an example of one type of digital dither generator which performs satisfactorily with the digital oscillator of the present invention. It would be obvious to one skilled in the art that many other digital dither generators could also be advantageously employed, provided the digital dither generator provides a pseudorandom sequence of L-bit numbers whose period is at least as long as 2^ samples, and whose probability density is uniform, in order for the phase noise produced by truncation to be "whitened". As shown in Figure 3, the intermediate-frequency (EF) filter section accepts data from the A/D converter at the rate of 20M samples/sec, mixes the received signal to dc (the zero EF frequency), lowpass filters the received signal to extract the desired signal, and sends the signal to the backend 120 of Figure 1 at a (drastically) reduced sampling rate. In the preferred implementation, the lowpass filtering and sample-rate reduction are not separate operations; instead, the sampling rate is gradually reduced between filter sections, as undesired signals (which could cause aliasing if not removed) are filtered out The only filtering section which operates at the input sampling rate (f s =20 MHz in the exemplary embodiment described here) is the first section. The only other circuitry which operates at that rate are the quadrature local oscillator (LO) and mixers. Thus it is this high-speed circuitry which sets an upper limit on the overall operational speed of the digital zero-EF selectivity section. High-speed operation is very important to the digital receiver of the present invention, to minimize intermodulation problems occurring with the front-end sample-and-hold and A D converter and to allow a sufficiently wideband signal to be accepted. Figure 5a is a block diagram of the "fast", narrowband lowpass filters 308 and 310 of Figure 3. The quadrature local oscillator 302 and mixers 304 and 306 are non-feedback circuits (primarily ROMs and multipliers) which are amenable to pipelining or other forms of parallelism to increase their speed. However, because the lowpass filter sections 308, 310 are implemented as recursive (infinite impulse response) filters, they cannot be pipelined to increase their speed. Their speed is determined by the maximum delay around a closed (feedback) path. For the lowpass filter implementation of the present invention, this path includes two digital 20 adders and one latch. It is this path which limits the A/D sampling rate and, therefore, potentially limits the overall performance of a digital receiver. Because of problems in attaining this very high speed die filter was designed by interleaving two 10-MHz TTL filters. The aliasing problems that would ordinarily be associated with using a lower sampling rate are alleviated by adding zeroes near the unwanted filter poles. The "Fast" lowpass section 546 of Figure 5a is decomposed into two half-speed sections plus a combining filter, as is shown in Figure 5b. This modification permits the digital EF section to operate at twice the speed that would otherwise be possible, and potentially allows improved performance of die digital receiver of the present invention. The "decomposed" filter of the present invention is shown in conjunction witi Figures 3 and 5. Other filter decomposition techniques have been discussed, for example, in a paper, M. Bellanger, G. Bonnerott and M. Coudreuse, Digital Filtering by Polyphase Network: Application to Sample-Rate Altera ή on and Filter Banks. IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, Vol. ASSP-24, No. 2, April 1976. The combining filter 554 is a nonrecursive filter. The combining filter, which is shown in greater detail in Figure 8, uses two zeros at f s /2 (z = -1) to cancel the poles introduced by the decomposition. Such a filter can be implemented with only adders and latches (i.e., without multipliers), and so adds minimal hardware. Note that although decomposition requires additional-hardware, it nominally increases power consumption (with a CMOS implementation), since two half-speed circuits require approximately the same power as a single full-speed circuit, (ignoring the additional power of the combining filter. Figure 6 illustrates the decomposition process in detail with several magnitude plots. In particular, Figure 6a shows the response of the original version of the first two-pole section, for an input sampling rate f s of 20 MHz. Figure 6b shows the "decomposed" characteristic which results from two 10-MHz sections, while Figure 6c shows the response of the subsequent "combining" filter. Finally, Figure 6d shows the composite (i.e., cascade) of Figure 6b and Figure 6c, which is virtually indistinguishable from Figure 6a, except for the "notch" at 10 MHz (which results from the two zeros at f s 12, which cancel the two nearby poles). The decomposed filter can be represented as follows: 2N D y (n) = ∑ y (n -i ) h d (i ) + x (n ) i =l where x and y are complex filter inputs and outputs, respectively (i.e., they have both a real part and an imaginary part). Also, h d are the decomposed filter polynomial coefficients, and NQ = 2 is the order of the original full-speed filter. Since the decomposed 20-MHz filter is expressed in terms of z" 2 (as will be shown in the next section), it can be implemented in terms of a 10-MHz circuit wherein: h d (i ) = h h (i II), i even 0, i odd where htø are the original high speed coefficients. Then the decimating filter can be reexpressed as: 2N D y (π ) = Σ y (n -i ) h h (i /2) + x (n ) i =2 step 2 The change of variables i fi 2j simplifies this summation to: N D y (n ) = ∑ y (n -2j ) h h (j ) + x (n) j -l From this formulation, decimating-filter inputs x and outputs y can be decomposed into two streams, as shown in Figure 5a: x M(m ) = 2_ (2m + y ) where: y = mod(n, 2) o {0,l } Substituting n fi 2m + 1 in the above decimating-filter summation yields: N D y (n ) = Σ y (2m -2j +1) h h 0 ' ) + * (2m + y) j-l 22 Finally, the two decomposed decimating filters ( y = 0,1) may be represented as: y (y)(m ) = Σ y M(m -j ) h h (j) + M(m ) j =l Assume that the desired filter has a pole z = z_. Then the corresponding filter characteristic may be represented as: If this pole is "repeated" 180° away, the following characteristic is obtained: . - 1 Since the resulting characteristic is in terms of z " , it can be decomposed (as was shown in the previous section) into two half-speed filters, each with pole z - = z_-. The lowpass filter sections in the digital zero-EF selectivity implementation of the present invention is realized using the following form, which is written in terms of coefficients a and b, where b = ca . For a pole-pair z-, z ", where: z p = (l-d )e i c l (d, q « l) the coefficients are: a @ 2d and b = d 2 + q 2 For the half-speed filters, the pole-pairs are 7. 7- and (z_ 7- *. Since z p 2 = [(l-d ) e iψ @ (l-2d ) ei 2c ' Then the coefficients for the half-speed filter may be obtained in terms of those for the full-speed case by analogy to the full-speed case: a ' = 2(2d ) = 2a and b ' = (2d ) 2 + (2q) 2 = 4(d 2 + q 2 ) = 4b This design is illustrated in Figure 5b. A second-order HR filter is described in a paper, Agarwal, A.C., Burrus C.S., New Recursive Digital Filter Structures Having Very Low Sensitivity and Roundoff Noise, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, Vol. CAS-27, No. 12, Dec. 1975. The filter structure II proposed by Agarwal and Burrus has been modified for minimum delay around all feedback loops for the purposes of the present invention. The filter structure of the present invention is illustrated in Figure 7. All digital filter structures are made up of basically the same three components: adders, multipliers, and delay circuits (generally latches or RAM). The factors affecting the performance of a digital filter all have to do with the fact that the various parameters of the filters are quantized, that is, they have finite precision rather than the infinite precision available in analog -filters. The finite precision of a digital filter basically gives rise to three major performance effects that must be controlled in any implementation of a digital filter. Coefficient roundoff is one of these effects. The constant valued coefficients found in a digital filter determine its frequency response. The result of rounding these coefficients so that they may be represented digitally in a finite number of bits causes a permanent, predictable change in the filter response. This is analogous to changing the RLC values in an analog filter, however, digital filters do not suffer the detriment of temperature variations as in analog filters. Generally, the higher Q of the filter (i.e. narrow bandwidth compared to the sampling rate) the more the frequency response is distorted by coefficient rounding, unless special structures are employed. Judicious selection of the filter structure is of key importance in light of the fact that EF filters are generally extremely narrow band, or high-Q filters. Round-off noise is another of the performance characteristics that must be controlled in a digital filter. Data entering a digital filter has been rounded to a finite number of bits, and it is almost always necessary to perform additional roundings at certain points within the filter. Such rounding operations create an error or noise signal in the digital filter. For example, if the digital word length used in a filter is 16 bits and the coefficients are represented in 10 bits each multiplication operation would create a 25 bit product, which must be rounded to 16 bits before the result may be put back into memory. The last major effect that is controlled in a digital filter is the overflow level. The fact that data samples are represented in a finite number of bits means that there is a maximum allowable absolute value associated with every node in the filter which, if exceeded, results in an overflow phenomenon (generally wrap-around if 2's complement binary arithmetic is used). This largest allowed data value, coupled with the level of roundoff noise described previously, determines the dynamic range of the filter. Several conventional structures are available to implement digital filters. A straight forward design approach is to cascade sections of first and second order direct- form filters until the desired filter order is achieved. The advantages of this method are its simplicity, regularity, and the ease of actual filter design. However, the conventional approach also suffers from many detriments mostly stemming from the fact that high precision (for example 16 bit) filter coefficient representation is required to implement a narrowband filter. This necessitates highly complex multiplications (for example 16 • 20 bits) be performed in the feedback paths of the filter sections. The multiplications place severe speed and time limitations on the operation of the filters. Further, pipelining, a common technique used to speed logic circuits, cannot be employed in feedback loops. Lastly, high precision, high speed multipliers consume tremendous amounts of power. Referring now to Figure 7, a digital lowpass filter section 700 is depicted in block diagram form. The filter employed in the DZISS is a recursive filter (i.e., the output signal is fed back, scaled, and summed at strategic points in the filter structure) having a narrow bandwidth and optimized for high-speed and low-sensitivity to the previously described detrimental effects of parameter quantization on digital filters. The second-order narrowband lowpass infinite-impulse response (IER) filter of Figure 7 is used in the decomposed "fast" lowpass filter of Figure 5b, which operates at the speed of die A/D convener. Decomposition is useful in attaining this high operational speed, but requires additional hardware: two second-order IIR sections instead of one, and a second-order FIR section which would not otherwise be needed. The digital low pass filter 700 provides the function depicted by the function blocks 550 and 552 of Figure 5b. The digital lowpass filter 700 consists of four digital adders (2's complement) 704, 708, 712, and 716, two digital delays or latches 710 and 718, and two binary shifters 706 and 714. As mentioned previously in the discussion of the digital quadrature local oscillator 400, the individual connections of lowpass filters 308, 310, and 312, and 313, as described in Figure 3, are multi-bit digital words and not single electrical lines. The input signal to the digital filter 700 is applied to a non-inverting input 702 of the digital adder 704. A second inverting input to the digital adder 704 is taken from digital delay 718 which is fed back from the output 720 of the filter circuit. The difference (2's complement) result of digital adder 704 is next applied to the input of gain element 706 which presents the shifted first sum signal as one input of digital adder 708. Bit shifter 706 shifts all bits of the data word outputted from digital adder 704 to the right (i.e., toward the least significant bit) by N c bits, effecting multiplication by a coefficient c equal to 2 "Nc . This bit shift may be implemented by an appropriate routing of the data lines from digital ladder 704 to adder 708. Thus, high operating speed of digital filter section 700 is facilitated, since there is no time delay associated with bit shifter 706, as there would be in a coefficient multiplication implemented by a conventional multiplier circuit Digital adder 708 adds to the shifted first sum signal the last output of digital adder 708 as held in delay 710. Further, the last or previous output of digital adder 708 is applied to digital adder 712. A second inverted input to digital adder 712 is taken from digital delay 718 which, as previously mentioned, is taken from the output 720 of the digital filter. The result of digital adder 712 is applied to bit shifter 714 which is coupled to digital adder 716. Bit shifter 714 shifts all bits of the data word outputted from digital adder 712 to the right by N a bits, effecting multiplication by a coefficient a equal to 2"^a. Bit shifter 714 also facilitates high operating speed since no time delay is incurred. The parameters N c and N a associated with bit shifters 706 and 714 respectively, control the frequency response of digital filter section 700, and may be chosen to yield the response appropriate to the intended application, as shown by the previous analysis. Digital adder 716 adds the second shifted sum signal to the previous output of 716 as held in delay 718. The output of delay 718 is also the output of the digital lowpass filter section 700 and represents a band-limited representation of the input signal 702 that was previously applied to the input of summing circuit 704. Figure 8 is a block diagram of the second-order combining finite-impulse*response (FIR) filter with a notch at half the sampling rate used in the decomposed fast lowpass filters of Figure 5b. The input 802 to filter 800 is 26 coupled to the output 720 of filter 700, as pictured in Figure 5b. According to Figure 8, the digital filter 800 comprises digital shifters 804, 806, and 808 coupled to digital delays 810 and 814 and digital summers 812 and 816, respectively. The digital shifters 804, 806, and 808 use gains of 1/4, 1/2, and 1/4, respectively, to implement a filter with two zeros on the unit circle, at half the sampling frequency. These digital shifters perform right shifting of the input 802 by 2, 1, and 2 bits, respectively. Since such "bit shifting" may be implemented by routing the wiring connections in the appropriate manner, these gain operations consume no actual time and require no actual hardware. A first partial sum is formed in adder 812 using the scaled output of gain element 806 as the first input and the previous, or last, scaled output of gain element 804 as the second input obtained from delay element 810. Similarly, the output 818 is obtained as the second partial sum formed in adder 816 using the scaled output of gain element 808 as the first input and the previous, or last, first partial sum of adder 812 as the second input, obtained from delay element 814. The transfer function of this filter may be written: H(z) = Y(z) / X(z) = (1/4)[1 + z Λ (2 + z '1 )] To compute an output, this FIR filter needs only to perform one addition and one latch operation, compared witii two additions and one latch operation in the IER sections, so that the F R combining filter easily operates at the full input sampling rate (20-MHz). An alternative design would allow the adder to run at a lower sampling rate by the use of additional control circuitry. This would permit the FIR filter to operate more slowly by incorporating decimation into the filter operation, i.e., computing only the outputs needed by subsequent filter sections operating at a reduced sampling rate. In a CMOS implementation, power consumption is typically reduced when operational speed is reduced. Therefore, the power consumption of the FER combining filter could be reduced at the expense of some control circuitry. Between the "fast" filters 308 and 310 and "slow" lowpass filters 312 and 313 of Figure 3, it is desirable to perform sampling rate reduction, or decimation. As is well known in the art the degree of sampling rate reduction possible depends on the amount of attenuation provided by the "fast" lowpass filters. For example, if a 20 MHz input sampling rate is used, and the "fast" filters are implemented as decomposed filters with coefficients as listed below in table 3, then an output 27 sampling rate of 2 MHz can be used with over 100 Db of aliasing protection provided by die "fast" filters. TABLE 3 The "slow" lowpass filters 312 and 313 can be implemented by several stages of two pole filter sections. For example, if three stages, each having the structure of 5 Figure 9a, 9b, and 9c and the coefficients listed in Table 3 are used, wherein slow 1 slow 2 and slow 3 correspond to Figures Figure 9a, 9b, and 9c, respectively, then the sampling rate can be reduced from 2 MHz to 80 KHz. An alternative hardware-saving design involves interleaving the in-phase and quadrature sample sample streams and using three stages of time-division- o multiplexed filtering. This requires that the filters run at twice the rate they would operate with a non-multiplexed design but since the sampling rate is reduced by a factor of 10 from the fast filter, this multiplexed filter still can operate at one-fifth the rate of the first filtering stage. Figure 9a is a block diagram of the first time-division-multiplexed 5 second-order lowpass EER filtering stage used in the time-division-multiplexed implementation of the "slow" lowpass filters. Figure 9a through 9c represent a time-division multiplexed version of a filter structure similar to that depicted in Figure 7. The main difference between the structure in Figure 7 and the multiplexed version in Figure 9 is that the delay elements have been doubled in length. Thus o instead of using z" 1 elements, implemented in hardware as single latches, z " elements are used which are implemented as two latches configured in series. The effect of this structure is that the filter alternates each sample between processing in-phase and quadrature samples. In the following discussion, the operation of Figure 9 is discussed in detail. After processing by digital filter 900a, the signal is 5 coupled to the second filtering stage 900b and subsequently to the third filtering stage, depicted by Figure 900c. The overall filter structure of digital filters 900a, 900b, and 900c is identical, so only digital filter 900a is discussed in detail. 28 However, the data paths and filter responses of digital filters 900a, 900b and 900c vary slightly between the various stages, as shown by Figures 9a, 9b and 9c, respectively, as well as Table 3. The digital lowpass filter 900a consists of four digital adders (2's complemen t ) 904a, 908a, 912a, and 916a, four digital latches two each in 910a, and 918a, and two binary shifters 906a and 914a. The input signal to the digital filter 900a is applied to a non-inverting input 902a of the digital adder 904a. A second inverting input to the digital adder 904a is taken from digital latch pair 918a which is fed.back from the output 920a of the filter circuit. The difference (2's complement) result of digital adder 904a is next applied to the input of bit shifter 906a which presents the shifted first sum signal as one input of digital adder 908a. Bit shifter 906a shifts all bits of the data word outputted from digital adder 904a to die right (i.e., toward the least significant bit) by N c bits, effecting multiplication by a coefficient equal to 2 ' ^c. This bit shift may be implemented by an appropriate 5 routing of the data lines from digital adder 904a to adder 908a. Thus, high operating speed of digital filter section 900a is facilitated, since there is no time delay associated with bit shifter 906a, as there would be in a coefficient multiplication implemented by a conventional multiplier circuit. Digital adder 908a adds to the shifted first sum signal the output of digital adder o 908a from two sample times past as held in latch pair 910a. Further, the output of digital adder 908a as held in latch 910a is applied to digital adder 912a. A second inverting input to digital adder 912a is taken from latch pair 918a which, as previously mentioned, is taken from the output 920a of the digital filter. The result of digital adder 912a is applied to bit shifter 914a which is coupled to digital adder 5 912a. Bit shifter 914a shifts all bits of the data word outputted from digital adder 912a to the right by N a bits, effecting multiplication by a coefficient equal to 2 " N l Ta. Bit shifter 914a also facilitates high operating speed since no time delay is incurred. The parameters N c and N a associated with bit shifters 906a and 914a respectively, control the frequency response of digital filter section 900a, and may be chosen to Q yield the response appropriate to the intended application. Digital adder 916a adds the second shifted sum signal to the previous output of 916a as held in delay 918a. The output of delay 918a is also the output of the digital lowpass filter section 900a and represents a band-limited representation of the input signal 902a that was previously applied to the input of summing circuit 904a. 5 It will be obvious to one skilled in the art that more gradual sample-rate reduction could be employed, say, between each of the four (total) lowpass filter sections. Gradual sample-rate reduction offers a significant advantage in that it gives 29 much flexibility in establishing the overall ratio of the input to the output sampling rates. This permits the A/D sampling rate to be established almost arbitrarily to match a desired preselector passband, subject to a constraint on the output sampling rate. At the output of the third (and last) "slow" lowpass filter section, sufficient attenuation has been applied to channels at higher frequencies, so that the aliasing caused by decimation from 2 MHz to 80 kHz does not interfere with the desired band, centered at approximately zero frequency. After filter processing and decimation by the high speed selectivity sections 114 of Figure 1, the recovered digital signal comprises a received digital signal having quadrature components. The quadrature characteristics of the received digital signal insures that phase information present in the original RF signal is preserved through the processing chain. The received quadrature digital signals are coupled to the digital receiver backend 120 of Figure 1, which is advantageously implemented by a programmable, general purpose digital signal processing I.C., as mentioned above. The radio backend 120 performs the additional processing required to generate the digital baseband signal used to provide a recovered data or audio signal. In addition, the radio backend 120 can provide final predemodulation filtering and post-demodulation processing of the recovered signal. Figures 10 and 11 detail digital filter structures suitable for performing final predemodualtion selectivity in o the context of a digital signal processing I.C. Figure 12 below details one technique which is suitable for demodulating an FM signal in accordance witii the teachings of the present invention. Figure 10 shows a fifth-order nonrecursive filter 1000 which provides additional attenuation so that the sampling rate may be further reduced from 80 to 40 5 kHz while causing negligible aliasing distortion of the desired band. Because this filter is operating at the relatively low output sampling rate of 40 kHz (complex samples), it is possible to implement it in a general-purpose digital signal processor. Such processors are typically well suited to pipelined multiply operations 1 04, 1010, 1016, 1026, 1030, 1036, and accumulate operations 1006, 1012, 1020, o 1024, and 1032, so that the "direct-form" filter structure was chosen. Figure 11 shows a direct-form filter structure 1100 with four poles and four zeros, which is employed to smooth out the passband response of the composite receiver filter, it may be implemented with a series of multiply operations 1104, 1112, 1118, 1120, 1126, 1132, 1140, 1146, and 1150, an-accumulate operations 5 1106, 1114, 1116, 1122, 1108, 1130, 1136, and 1144 in a general-purpose digital signal processor. Because single-precision (typically 16-bit wordlength) operations do not afford sufficient dynamic range for mobile-radio applications, it is necessary to use double-precision calculations in the DSP implementation. It will be apparant to one skilled in die art that different bandwidths for the final selectivity section could be programmably obtained by choosing different filter coefficients in the back-end DSP. Also, different selectivity bandwidths may be obtained through use of different downsampling rates, or through different wired-gain elements (via two-to-one selectors, for example) in the multiplierless lowpass filter sections. Figure 12 is a diagram of a digital FM demodulator compatible with the digital radio architecture of the present invention. In reality, digital demodualtion is one task, among others, performed by a digital signal processor I. C. According to Figure 12, limiter section 1202 comprises the scaling stage 1204 together with the in-phase channel inverse calculation generator 1210 and the product multiplier 1212 where the reciprocal of the scaled and rotated in-phase (I) component is multiplied with the scaled and rotated out-of-phase (Q') component producing a term equal to the value of the tangent of the phase angle of the scaled and rotated signal vector sample. The action of digital multiplier 1212 performs an ideal limiting of any amplitude variations of the input signal vector that may be present The term passed from the digital multiplier 1212 represents die tangent of the rotated and scaled signal vector sample. This term is processed by the arctangent generator stage 1214 whose output equals the phase angle of the rotated and scaled signal vector. This quantity when added by digital summer 1214 to the coarse phase value output from the coarse phase accumulator 1206 represents the total phase angle of the input signal vector sample. The difference signal generated at the output of digital summer 1218 between the phase angle of the current signal vector sample and the negative of the delayed output generated by digital delay 1220 represents 1 sample of the output demodulated message. Figures 13a through 13c are diagrams detailing the principles of phasors in the context of the present invention. Referring now to Figure 13a, the sealer's 1204 function is to scale the amplitude of the input signal vector of varying magnitude to the shaded region shown. The coarse phase accumulator 1206 determines the coarse phase angle of the signal vector, 0 C , and the output of the arctangent generator stage 1212 equals the fine phase of the signal vector, 0f, as depicted in fig. 13b. The signal vector 0f is constrained by the vector rotation to lie in the range of -π/4 < 0 f < +π 4 (shaded region of Figure 13b.) The sum of these 2 quantities generated at the output of digital summer 1214 represents the total phase angle of the input signal vector sample, 0(n). The difference value Δ(0(n)) generated by digital summer 1218 between the current phase sample, 0(n), and the phase sample, 0(n-l) generated by digital delay 1220, as shown in Figure 13c, represents one sample of the demodulated output message. The stream of samples representing the demodulated output message may be low passed filtered to remove noise outside the message bandwidth, as is typically performed " subsequent to FM detection. It would be obvious to one of ordinary skill in the art that the digital demodulator described in the figures above could be implemented with discrete hardware digital multipliers, adders, registers, etc. The digital demodulator of the present invention is particularly suitable for implementation with a class of devices known as digital signal processors. The present invention would perform satisfactorily with a variety of well known digital signal processors such a NEC D7720, available from NEC Electronics U.S.A. Inc., One Natick Executive Park, Natick, Mass. 01760, or a TMS 32010 available from Texas Instruments Inc, P.O. Box 225012, Dallas, Texas 752265. Digital signal processors generally include hardware high speed digital multipliers as well as the ability to process a digital data stream in accordance with a predetermined algorithm. Figures 14a and 14b are flow diagrams detailing the background processing of the present invention as implemented with a digital signal processor. In all descriptions of the present invention, the in-phase and out-of-phase signal vector components will hereinafter be referred to as the components I and Q respectively. The algorithm of the present invention begins at 1402, which causes the digital signal processor to execute decision 1404 to determine the sign of the I component. Based on the outcome of decision 1404, the sign of the Q component is determined by decisions 1406 and 1448. Next, the difference of the I and Q components is determined by items 1410, 1408, 1472, and 1450 which generate values comprising the values of Q -I, I -Q, Q - 1, and Q + I, respectively. The sign of the respective results is determined by decisions 1430, 1412, 1474, and 1452, respectively. Based on the results of tiiese decisions, the component (I or Q) which has the greater absolute value is known, and the octant (i.e. multiple of π/4) in which the signal vector lies is also known. This value, if less than zero, is complemented by items 1420, 1486, 1476, and 1462, respectively. The value that represents the greatest absolute value of either the I or Q channel is pushed onto a program stack by items 1442, 1432, 1422, 1414, 1488, 1478, 1466, or 1454, respectively, and is hereafter referred to as the quantity SMAX. The quantity SMAX is used by the call to the scale subroutine by items 1444, 1434, 1424, 1416, 1490, 1480, 1466, or 1456, respectively, to determine me correct amount of scaling to be applied to the input signal vector sample. The scale subroutine returns correcdy scaled signal vector components I and Q. Next a coarse phase value, based on the octant location of the signal vector is stored to a temporary storage location by items 1446, 1436, 1426, 1418, 1492, 1482, 1468, or 1460, respectively. This value will always be a multiple of π 2 radians over d e range of -π ≤ 0(c) ≤ κ. The signal vector is tiien geometrically rotated by the negative of the coarse phase value that was saved by items 1440, 1428, 1492, 1484, 1470, or 1460, respectively. The scaled and rotated signal components that result are hereafter referred to as the I' and Q' signal vector components. The effect of this vector rotation is to rotate the signal vector such that the rotated signal vector components I * and Q' yield a composite vector with a phase angle in the range of -π 4 < 0 < π/4. Figures 15a and 15b are flow diagrams of me operation of the scale subroutine described in conjunction with Figure 14a above. The scaling subroutine 1500 examines the value of SMAX to determine the correct amountofscaling to.be applied to the signal vector components I and Q. The operation of this subroutine is dependent on the resolution or number of bits used to represent the signal vector components. The operation of the scale subroutine will be explained in the context of using 32 bit long words to represent the signal vector components. Upon entry to the scale subroutine at 1502, the most significant word (MSW) of the quantity SMAX is compared to zero by decision 1504. If the MSW of SMAX is greater than zero, the least significant word (LSW) of SMAX will be discarded, and the MSW will be compared to a scaling threshold value by item 1506. If the MSW of SMAX is found to equal zero, then the MSW will be discarded, and the LSW will be compared to a scaling threshold value by item 1528. The results of the comparisions generated by items 1506, and 1528, respectively, are tested against zero by decisions 1508, and 1530, respectively, and if the result is found to be greater than zero, no scaling of the signal vector components is necessary, and the subroutine exits through item 1550 to d e point where the routine activated subroutine 1500. If the retained word (i.e. MSW or LSW) of SMAX is less than the threshold value, die retained word is tested to see if it absolute magnitude is greater than 255 by decisions 1510, and 1532, respectively. This is equivalent to determining if die upper 8 bits of the retained word of SMAX are greater than or equal to zero. If the result of this test is true (i.e. the MSW or the LSW of SMAX is greater than 255), die retained word is divided by 256 by items 1514 or 1536. respectively. This has the effect of shifting the upper 8 bits of the retained word of SMAX into the lower 8 bits of this word. If the result of decision 1510, or 1532 indicates that die retained word is less than 255, then no division is performed. This quantity is now used as an address offset by items 1516, 1512, 1538, or 1534 to select values stored in ROM data table, and a scaling factor is retrieved from a ROM by items 1520, 1540. This factor is adjusted to the correct value necessary to scale this signal vector components, depending on previous decisions 1510 or 1532. Finally the signal vector components are scaled to the correct region for use by the approximations applied within the demodulator by items 1522 and 1524 or 1542 and 1546 and the routine exists back to the calling procedure tiirough items 1526 or 1548. Referring now to Figure 16a, the inverse or reciprocal of the I' vector component is now determined. This processing is accomplished by implementing a 6dι order Chebyshev polynomial approximation to the function f(x) = l/x. The polynomial which approximates this function is: f(x) = (l/x) ~ {[[[[[ C7(x-1HC6 .( -U-T-C5 ](x-l)+C4 ](x-l)+C3 ](x-l)-C2 ](x-l)÷Cl } where, x = I' and, Cl = - ^ 1.00000, C2 = -1.0027, C3 = -1.00278, C4 = -0.91392, C5 = +0.91392, C6 = -1.62475, C7 = - 1.62475. According to the principles of the present invention, the Q ' component is pushed On a program stack storage area by item 1604 and the quantity d ' - l ) is calculated by item 1606, hereinafter referred to as the quantity ARG. Coefficient C7 is fetched from data ROM by item 1608 and is multiplied with ARG by item 1610 forming a quantity TMP. Coefficient C6 is fetched from as data ROM by item 1612 and added to TMP by item 1614 yielding the new value for TMP. This pattern is successively repeated by items 1616 through 1644 until the Q' component is then fetched from the program stack storage by item 1648 and multiplied with TMP by item 1650 yielding an approximation to the quantity tan øf = QVT. The arctangent of die quantity obtained by item 1650 is now determined. This processing is performed by implementing a 5th order Chebyshev polynomial approximation to me function: 0f = arctan(x) The polynomial mat approximates this function is: arctan(x) - x {[.[_ C6(y) + C5 ] y + C4 ] y + C3 ] y + C2 ] y + Cl } where, x = QVΓ and, C6 = -0.01343, C5 = -0.05737, C4 = -0.12109, C3 = +0.19556, C2 = -0.33301, Cl = -0.99997. The quantity x = (Q7_ ) is push onto program stack storage by item 1652, . and the value of me squared quantity y = x 2 , hereinafter referred to as ARG is calculated by item 1654. In a chain like manner, similar to the calculation of the inverse value described previously, the value of the arctangent of the quantity (Q' T) is computed by items 1656 through 1692. The result of this process is a signed value representing the phase angle of the rotated signal vector, or the fine phase angle of the input signal vector sample. The value of the coarse phase of the input signal vector sample is retrieved from a temporary storage location by item 1694 and is summed with the result of the arctangent calculation by item 1696. This result represents the phase angle of the input signal vector sampie. The phase angle of the previous input signal vector sample. On- 1, is fetched from a program stack by item 1700. The current phase sample is pushed onto a program stack by item 1702. Finally, the difference of the previous phase sample and the current phase sample is calculated by item 1704 thus yielding an output sample of the demodulated message m(n) The message sample m(n) comprises the demodulated voice signal in a sampled . form. The demodulated voice signal may be converted back to analog form, then amplified and played through a loudspeaker^as mentioned above. Alternatively, a digital voice message may be stored in digital a digital memory 123 for later use In a data communications system (not shown), demodulated data symbols may be routed to a computer for further processing or to a computer terminal for immediate display. In summary, a digital radio receiver has been described. The digital receiver of the present invention contemplates an all digital radio receiver which operates on a received signal which is converted to a digital form after preselection at die output of the antenna. The receiver of the present invention comprises a preselector, a high-speed analog-to-digital (A/D) converter, a digitally implemented intermediate-frequency (IF) selectivity section having an output signal at substantially baseband frequencies, and general-purpose digital signal processor (DSP) integrated circuits performing demodulation and audio filtering. Other uses and modifications of the present invention will be obvious to one of ordinary skill in the art without departing from the spirit and scope of the present invention. We claim:

Claims: 1. An apparatus for substantially digitally processing a wide-band analog signal containing a desired narrow band analog signal, comprising: (a) means, including coupling means and filter means for receiving and filtering a wide-band analog signal containing a desired narrow-band analog signal; (b) digitizing means, coupled to said filter means, for periodically sampling and converting said wide-band analog signal to a sampled wide-band digital signal; (c) digital means, coupled to said digitizing means, for selecting the desired sampled narrow-band digital signal from the sampled wide-band digital signal; and (d) digital processing means for demodulating said sampled narrow-band digital signal. 2. The apparatus as recited in claim 1 wherein said digital means includes a digital oscllator means, a digital multiplier /mixer means, and a digital narrow-band filter means 38 3. A method for substantially digitally processing a wide-band analog signal containing a desired narrow-band analog signal, comprising the steps of: (a) receiving and filtering a wide-band analog signal containing a desired narrow-band analog signal; (b) periodically sampling and converting said wide-band analog signal to a sampled wide-band digital signal; (c) selecting the desired sampled narrow-band digital signal from the sampled wide-band digital signal; and (d) demodulating said sampled narrow-band digital signal. 4. The method as recited in claim 3 wherein said selecting step further comprises the steps of generating a digital local osciUator signal, multiplying the digital local oscillato s i gnal by the sampled wide-band digital signal to produce a sampled product signal and d i g i tal narrow-band filtering the sampled product signal to produce the sampled narrow-band digital signal. 5. A substantially digital apparatus for digitally processing a wide-band radio frequency (RF) signal containing a desired narrow-band signal, comprising: (a) means, including antenna means for receiving (RF) signals containing said wide-band (RF) signal; (b) filter means, coupled to said antenna means, for filtering said wide-band (RF) signal; (c) digitizing means, coupled to said filter means, for periodically sampling and converting said wide-band RF signal to a sampled wide-band digital signal; (d) digital means, coupled to said digitizing means, for selecting the desired sampled narrow-band digital signal from the sampled wide-band digital signal; and (e) digital processing means for demodulating said sampled narrow-band digital signal. 6. The substantially digital apparatus as recited in claim 5 wherein said digital means includes a digital quadrature osciUator, a digital quadrature multiplier/mixer, and a digital quadrature narrow-band low pass filter. 42 7. A method for substantially digitaUy processing a wide-band radio frequency (RF) signal containing a desired narrow-band signal, comprising me steps of: (a) receiving (RF) signals containing said wide-band RF signal; (b) filtering said wide-band RF signal; (c) periodically sampling and converting said filtered wide-band (RF) signal to a sampled wide-band digital signal; (c) selecting the desired sampled narrow-band digital signal from the sampled wide-band digital signal; and (d) digitally demodulating said sampled narrow-band digital signal. 8. The method as recited in claim 7 wherein said selecting step further includes the steps of generating a digital local osciUator signal, multiplying the digital local osc i Uator signal by the sampled wide-band digital signal to produce a sampled product signal, and digital narrow-band filtering the sampled product signal to produce the sampled narrow-band digital signal. 9. A method of digitally demodulating a received angle-modulated signal, said method comprising the steps of: - (a) inputting digitized quadrature samples of a signal centered approximately at zero frequency, said samples indicating a composite signal vector; (b) scaling said samples to a desired magnitude within a predetermined range; (c) calculating the nearest octant within which the scaled composite signal vector lies, said nearest octant comprising a coarse phase range value; (d) rotationally scaling the scaled composite signal vector to lie within a range between -τr /4 to +TT /4. (e) calculating a second value equal to the tangent of the phase of the rotationally scaled signal vector; (f) calculating a third value equal to the phase angle of said signal vector by deriving the arctangent of said second value, said third value comprising a fine phase angle value; (g) summing the fine phase angle and coarse phase angle values to produce a composite phase angle sample equivalent to the phase angle of the input signal vector; (h) filtering the sequence of phase angle samples to produce a sequence of demodulated message samples; and (i) outputting said demodulated message samples to an output register. 10. A digital demodulator apparatus having improved linearity, said apparatus comprising: (a) means for inputting a sampled input vector 5 comprising a quadrature signal centered approximately zero freαuencv: (b) sealer means for quantizing said inputted sampled quadratur ree ssiiggnal within a predetermined range; 0 (c) phase accumulator means for generating a current coarse phase value related to input vectors of the quadrature FM signal; 5 (d) vector rotation means for rotating said input vector to a quadrant within a range between -Tf /4 to + TT/4; (e) means for determining a fine phase value based o on said rotated input signal vector; (f) summing means for summing said fine and coarse phase values and outputting a composite phase value; and 5 (g) filtering means for filtering the sequence of phase angle samples to produce a sequence of demodulated message samples. 0 5 11. A method of digitally demodulating a received FM signal, said method comprising the steps of: (a) inputting digitized quadrature samples of a signal centered approximately ar zero frequency, said samples indicating a composite signal vector; (b) scaling said samples to a desired magnitude within a predetermined range; (c) calculating the nearest octant within which the scaled composite signal vector lies, said nearest octant comprising a coarse phase range value; (d) rotationally scaling the scaled composite signal vector to lie within a range between -τr/4 to +TT/4. (e) calculating a second value equal to the tangent of the phase of the rotationally scaled signal vector; (f) calculating a third value equal to the phase angle of said signal vector by deriving the arctangent of said second value, said third value comprising a fine phase angle value; (g) summing the fine phase angle and coarse phase angle values to produce a composite phase angle sample equivalent to the phase angle of the input signal vector; (h) subtracting the value of the previous composite phase angle sample from the value of the current composite phase angle sample to produce a demodulated message sample; and (i) outputting said demodulated message sample to an output register. 12. A digital FM demodulator apparatus having improved linearity, said apparatus comprising: (a) means for inputting a sampled input vector comprising a quadrature FM digital signal centered approximately zero frequency; (b) sealer means for quantizing said inputted sampled quadrature signal within a predetermined range; 0 (c) phase accumulator means for generating a current coarse phase value related to input vectors of the quadrature FM signal; 5 (d) vector rotation means for rotating said input vector to a quadrant within a range between -TT /4 to + TT/4; (e) means for determining a fine phase value based o on said rotated input signal vector; (f) summing means for summing said fine and coarse phase values and outputting a composite phase value; and 5 (g) filtering means for subtracting the value of the previous composite phase angle sample from the value of the current composite phase angle sample to produce a demodulated message sample. 0 5

Inventors: JANC ROBERT VINCENT, JASPER STEVEN CHARLES, LAMBERT KATHERINE HELEN, LILLIE ROSS JAMES, LONGLEY LESTER ANDERSON, TURNEY WILLIAM JOSEPH, JANC, ROBERT, VINCENT, JASPER, STEVEN, CHARLES, LAMBERT, KATHERINE, HELEN, LILLIE, ROSS, JAMES, LONGLEY, LESTER, ANDERSON, TURNEY, WILLIAM, JOSEPH
Applicants: MOTOROLA INC, MOTOROLA, INC.
Application year: 1986
Main classification: H03D1
IPC codes: H03D1, H03D3, H03H17, H04B1, H04B14