Patent Publication Number: US-8527283-B2

Title: Method and apparatus for estimating high-band energy in a bandwidth extension system

Description:
RELATED APPLICATIONS 
     This application is related to co-pending and co-owned U.S. patent application Ser. No. 11/946,978 filed on Nov. 29, 2007, which is incorporated by reference in its entirety herein. This application is additionally related to co-pending and co-owned U.S. patent application No. 12/024,620 filed Feb. 1, 2008, which is additionally incorporated by reference herein. This application is also related to co-pending and co-owned U.S. patent application Ser. No. 12/027,571, filed Feb. 07, 2008. 
     TECHNICAL FIELD 
     This invention relates generally to rendering audible content and more particularly to bandwidth extension techniques. 
     BACKGROUND 
     The audible rendering of audio content from a digital representation comprises a known area of endeavor. In some application settings the digital representation comprises a complete corresponding bandwidth as pertains to an original audio sample. In such a case, the audible rendering can comprise a highly accurate and natural sounding output. Such an approach, however, requires considerable overhead resources to accommodate the corresponding quantity of data. In many application settings, such as, for example, wireless communication settings, such a quantity of information cannot always be adequately supported. 
     To accommodate such a limitation, so-called narrow-band speech techniques can serve to limit the quantity of information by, in turn, limiting the representation to less than the complete corresponding bandwidth as pertains to an original audio sample. As but one example in this regard, while natural speech includes significant components up to 8 kHz (or higher), a narrow-band representation may only provide information regarding, say, the 300-3,400 Hz range. The resultant content, when rendered audible, is typically sufficiently intelligible to support the functional needs of speech-based communication. Unfortunately, however, narrow-band speech processing also tends to yield speech that sounds muffled and may even have reduced intelligibility as compared to full-band speech. 
     To meet this need, bandwidth extension techniques are sometimes employed. One artificially generates the missing information in the higher and/or lower bands based on the available narrow-band information as well as other information to select information that can be added to the narrow-band content to thereby synthesize a pseudo wide (or full) band signal. Using such techniques, for example, one can transform narrow-band speech in the 300-3400 Hz range to wide-band speech, say, in the 100-8000 Hz range. Towards this end, a critical piece of information that is required is the spectral envelope in the high-band (3400-8000 Hz). If the wide-band spectral envelope is estimated, the high-band spectral envelope can then usually be easily extracted from it. One can think of the high-band spectral envelope as comprised of a shape and a gain (or equivalently, energy). 
     By one approach, for example, the high-band spectral envelope shape is estimated by estimating the wideband spectral envelope from the narrow-band spectral envelope through codebook mapping. The high-band energy is then estimated by adjusting the energy within the narrow-band section of the wideband spectral envelope to match the energy of the narrow-band spectral envelope. In this approach, the high-band spectral envelope shape determines the high-band energy and any mistakes in estimating the shape will also correspondingly affect the estimates of the high-band energy. 
     In another approach, the high-band spectral envelope shape and the high-band energy are separately estimated, and the high-band spectral envelope that is finally used is adjusted to match the estimated high-band energy. By one related approach the estimated high-band energy is used, besides other parameters, to determine the high-band spectral envelope shape. However, the resulting high-band spectral envelope is not necessarily assured of having the appropriate high-band energy. An additional step is therefore required to adjust the energy of the high-band spectral envelope to the estimated value. Unless special care is taken, this approach will result in a discontinuity in the wideband spectral envelope at the boundary between the narrow-band and high-band. While the existing approaches to bandwidth extension, and, in particular, to high-band envelope estimation are reasonably successful, they do not necessarily yield resultant speech of suitable quality in at least some application settings. 
     In order to generate bandwidth extended speech of acceptable quality, the number of artifacts in such speech should be minimized. It is known that over-estimation of high-band energy results in annoying artifacts. Incorrect estimation of the high-band spectral envelope shape can also lead to artifacts but these artifacts are usually milder and are easily masked by the narrow-band speech. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above needs are at least partially met through provision of the method and apparatus for estimating high-band energy in a bandwidth extension system described in the following detailed description. The accompanying figures where like reference numerals refer to identical or functionally similar elements throughout the separate views and which together with the detailed description below are incorporated in and form part of the specification, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the present invention. 
         FIG. 1  comprises a flow diagram as configured in accordance with various embodiments of the invention; 
         FIG. 2  comprises a graph as configured in accordance with various embodiments of the invention; 
         FIG. 3  comprises a block diagram as configured in accordance with various embodiments of the invention; 
         FIG. 4  comprises a block diagram as configured in accordance with various embodiments of the invention; 
         FIG. 5  comprises a block diagram as configured in accordance with various embodiments of the invention; and 
         FIG. 6  comprises a graph as configured in accordance with various embodiments of the invention. 
     
    
    
     Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions and/or relative positioning of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of various embodiments of the present invention. Also, common but well-understood elements that are useful or necessary in a commercially feasible embodiment are often not depicted in order to facilitate a less obstructed view of these various embodiments of the present invention. It will further be appreciated that certain actions and/or steps may be described or depicted in a particular order of occurrence while those skilled in the art will understand that such specificity with respect to sequence is not actually required. It will also be understood that the terms and expressions used herein have the ordinary technical meaning as is accorded to such terms and expressions by persons skilled in the technical field as set forth above except where different specific meanings have otherwise been set forth herein. 
     DETAILED DESCRIPTION 
     Teachings discussed herein are directed to a cost-effective method and system for artificial bandwidth extension. According to such teachings, a narrow-band digital audio signal is received. The narrow-band digital audio signal may be a signal received via a mobile station in a cellular network, for example, and the narrow-band digital audio signal may include speech in the frequency range of 300-3400 Hz. Artificial bandwidth extension techniques are implemented to spread out the spectrum of the digital audio signal to include low-band frequencies such as 100-300 Hz and high-band frequencies such as 3400-8000 Hz. By utilizing artificial bandwidth extension to spread the spectrum to include low-band and high-band frequencies, a more natural-sounding digital audio signal is created that is more pleasing to a user of a mobile station implementing the technique. 
     In the artificial bandwidth extension techniques, the missing information in the higher (3400-8000 Hz) and lower (100-300 Hz) bands is artificially generated based on the available narrow-band information as well as apriori information derived and stored from a speech database and added to the narrow-band signal to synthesize a pseudo wide-band signal. Such a solution is quite attractive because it requires minimal changes to an existing transmission system. For example, no additional bit rate is needed. Artificial bandwidth extension can be incorporated into a post-processing element at the receiving end and is therefore independent of the speech coding technology used in the communication system or the nature of the communication system itself, e.g., analog, digital, land-line, or cellular. For example, the artificial bandwidth extension techniques may be implemented by a mobile station receiving a narrow-band digital audio signal, and the resultant wide-band signal is utilized to generate audio played to a user of the mobile station. 
     In determining the high-band information, the energy in the high-band is estimated first. A subset of the narrow-band signal is utilized to estimate the high-band energy. The subset of the narrow-band signal that is closest to the high-band frequencies generally has the highest correlation with the high-band signal. Accordingly, only a subset of the narrow-band, as opposed to the entire narrow-band, is utilized to estimate the high-band energy. The subset that is used is referred to as the “transition-band” and may include frequencies such as 2500-3400 Hz. More specifically, the transition-band is defined herein as a frequency band that is contained within the narrow-band and is close to the high-band, i.e., it serves as a transition to the high-band. This approach is in contrast with prior art bandwidth extension systems which estimate the high-band energy in terms of the energy in the entire narrow-band, typically as a ratio. 
     In order to estimate the high-band energy, the transition-band energy is first estimated via techniques discussed below with respect to  FIGS. 4 and 5 . For example, the transition-band energy of the transition-band may be calculated by first up-sampling an input narrow-band signal, computing the frequency spectrum of the up-sampled narrow-band signal, and then summing the energies of the spectral components within the transition-band. The estimated transition-band energy is subsequently inserted into a polynomial equation as an independent variable to estimate the high-band energy. The coefficients or weights of the different powers of the independent variable in the polynomial equation including that of the zeroth power, that is, the constant term, are selected to minimize the mean squared error between true and estimated values of the high-band energy over a large number of frames from a training speech database. The estimation accuracy may be further enhanced by conditioning the estimation on parameters derived from the narrow-band signal as well as parameters derived from the transition-band signal as is discussed in further detail below. After the high-band energy has been estimated, the high-band spectrum is estimated based on the high-band energy estimate. 
     By utilizing the transition-band in this manner, a robust bandwidth extension technique is provided that produces a corresponding audio signal of higher quality than would be possible if the energy in the entire narrow-band were used to estimate the high-band energy. Moreover, this technique may be utilized without unduly adversely affecting existing communication systems because the bandwidth extension techniques are applied to a narrow-band signal received via the communication system, i.e., existing communication systems may be utilized to send the narrow-band signals. 
       FIG. 1  illustrates a process  100  for generating a bandwidth extended digital audio signal in accordance with various embodiments of the invention. First, at operation  101 , a narrow-band digital audio signal is received. In a typical application setting, this will comprise providing a plurality of frames of such content. These teachings will readily accommodate processing each such frame as per the described steps. By one approach, for example, each such frame can correspond to 10-40 milliseconds of original audio content. 
     This can comprise, for example, providing a digital audio signal that comprises synthesized vocal content. Such is the case, for example, when employing these teachings in conjunction with received vo-coded speech content in a portable wireless communications device. Other possibilities exist as well, however, as will be well understood by those skilled in the art. For example, the digital audio signal might instead comprise an original speech signal or a re-sampled version of either an original speech signal or synthesized speech content. 
     Referring momentarily to  FIG. 2 , it will be understood that this digital audio signal pertains to some original audio signal  201  that has an original corresponding signal bandwidth  202 . This original corresponding signal bandwidth  202  will typically be larger than the aforementioned signal bandwidth as corresponds to the digital audio signal. This can occur, for example, when the digital audio signal represents only a portion  203  of the original audio signal  201  with other portions being left out-of-band. In the illustrative example shown, this includes a low-band portion  204  and a high-band portion  205 . Those skilled in the art will recognize that this example serves an illustrative purpose only and that the unrepresented portion may only comprise a low-band portion or a high-band portion. These teachings would also be applicable for use in an application setting where the unrepresented portion falls mid-band to two or more represented portions (not shown). 
     It will therefore be readily understood that the unrepresented portion(s) of the original audio signal  201  comprise content that these present teachings may reasonably seek to replace or otherwise represent in some reasonable and acceptable manner. It will also be understood this signal bandwidth occupies only a portion of the Nyquist bandwidth determined by the relevant sampling frequency. This, in turn, will be understood to further provide a frequency region in which to effect the desired bandwidth extension. 
     Referring back to  FIG. 1 , the input digital audio signal is processed to generate a processed digital audio signal at operation  102 . By one approach, the processing at operation  102  is an up-sampling operation. By another approach, it may be a simple unity gain system for which the output equals the input. At operation  103 , a high-band energy level corresponding to the input digital audio signal is estimated based on a transition-band of the processed digital audio signal within a predetermined upper frequency range of a narrow-band bandwidth. 
     By using the transition-band components as the basis for the estimate, a more accurate estimate is obtained than would generally be possible if all of the narrow-band components were collectively used to estimate the energy value of the high-band components. By one approach, the high-band energy value is used to access a look-up table that contains a plurality of corresponding candidate high-band spectral envelope shapes to determine the high-band spectral envelope, i.e. the appropriate high-band spectral envelope shape at the correct energy level. 
     At  104  the estimated high-band energy level is modified based on an estimation accuracy and/or narrow-band signal characteristics to reduce artifacts and thereby enhance the quality of the bandwidth extended audio signal. This will be described in detail below. Finally, at  105 , a high-band digital audio signal is optionally generated based on the modified estimate of the high-band energy level and an estimated high-band spectrum corresponding to the modified estimate of the high-band energy level. 
     This process  100  will then optionally accommodate combining the digital audio signal with high-band content corresponding to the estimated energy value and spectrum of the high-band components to provide a bandwidth extended version of the narrow-band digital audio signal to be rendered. Although the process shown in  FIG. 1  only illustrates adding the estimated high-band components, it should be appreciated that low-band components may also be estimated and combined with the narrow-band digital audio signal to generate a bandwidth extended wide-band signal. 
     The resultant bandwidth extended audio signal (obtained by combining the input digital audio signal with the artificially generated out-of-signal bandwidth content) has an improved audio quality versus the original narrow-band digital audio signal when rendered in audible form. By one approach, this can comprise combining two items that are mutually exclusive with respect to their spectral content. In such a case, such a combination can take the form, for example, of simply concatenating or otherwise joining the two (or more) segments together. By another approach, if desired, the high-band and/or low-band bandwidth content can have a portion that is within the corresponding signal bandwidth of the digital audio signal. Such an overlap can be useful in at least some application settings to smooth and/or feather the transition from one portion to the other by combining the overlapping portion of the high-band and/or low-band bandwidth content with the corresponding in-band portion of the digital audio signal. 
     Those skilled in the art will appreciate that the above-described processes are readily enabled using any of a wide variety of available and/or readily configured platforms, including partially or wholly programmable platforms as are known in the art or dedicated purpose platforms as may be desired for some applications. Referring now to  FIG. 3 , an illustrative approach to such a platform will now be provided. 
     In this illustrative example, in an apparatus  300  a processor  301  of choice operably couples to an input  302  that is configured and arranged to receive a digital audio signal having a corresponding signal bandwidth. When the apparatus  300  comprises a wireless two-way communications device, such a digital audio signal can be provided by a corresponding receiver  303  as is well known in the art. In such a case, for example, the digital audio signal can comprise synthesized vocal content formed as a function of received vo-coded speech content. 
     The processor  301 , in turn, can be configured and arranged (via, for example, corresponding programming when the processor  301  comprises a partially or wholly programmable platform as are known in the art) to carry out one or more of the steps or other functionality set forth herein. This can comprise, for example, estimating the high-band energy value from the transition-band energy and then using the high-band energy value and a set of energy-index shapes to determine the high-band spectral envelope. 
     As described above, by one approach, the aforementioned high-band energy value can serve to facilitate accessing a look-up table that contains a plurality of corresponding candidate spectral envelope shapes. To support such an approach, this apparatus can also comprise, if desired, one or more look-up tables  304  that are operably coupled to the processor  301 . So configured, the processor  301  can readily access the look-up table  304  as appropriate. 
     Those skilled in the art will recognize and understand that such an apparatus  300  may be comprised of a plurality of physically distinct elements as is suggested by the illustration shown in  FIG. 3 . It is also possible, however, to view this illustration as comprising a logical view, in which case one or more of these elements can be enabled and realized via a shared platform. It will also be understood that such a shared platform may comprise a wholly or at least partially programmable platform as are known in the art. 
     It should be appreciated the processing discussed above may be performed by a mobile station in wireless communication with a base station. For example, the base station may transmit the narrow-band digital audio signal via conventional means to the mobile station. Once received, processor(s) within the mobile station perform the requisite operations to generate a bandwidth extended version of the digital audio signal that is clearer and more audibly pleasing to a user of the mobile station. 
     Referring now to  FIG. 4 , input narrow-band speech s nb  sampled at 8 kHz is first up-sampled by 2 using a corresponding upsampler  401  to obtain up-sampled narrow-band speech ś nb  sampled at 16 kHz. This can comprise performing an 1:2 interpolation (for example, by inserting a zero-valued sample between each pair of original speech samples) followed by low-pass filtering using, for example, a low-pass filter (LPF) having a pass-band between 0 and 3400 Hz. 
     From s nb , the narrow-band linear predictive (LP) parameters, A nb ={1, α 1 , α 2 , . . . , α P } where P is the model order, are also computed using an LP analyzer  402  that employs well-known LP analysis techniques. (Other possibilities exist, of course; for example, the LP parameters can be computed from a 2:1 decimated version of Ś nb .) These LP parameters model the spectral envelope of the narrow-band input speech as 
     
       
         
           
             
               
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     In the equation above, the angular frequency ω radians/sample is given by ω=2πf/F s , where f is the signal frequency in Hz and F s , is the sampling frequency in Hz. For a sampling frequency F s , of 8 kHz, a suitable model order P, for example, is 10. 
     The LP parameters A nb  are then interpolated by 2 using an interpolation module  403  to obtain Á nb ={1, 0, α 1 , 0, α 2 , 0, . . . 0, α P }. Using Á nb , the up-sampled narrow-band speech ś nb  is inverse filtered using an analysis filter  404  to obtain the LP residual signal ŕ nb  (which is also sampled at 16 kHz). By one approach, this inverse (or analysis) filtering operation can be described by the equation
 
 ŕ   nb ( n )= ś   nb ( n )+α 1   ś   nb ( n −2)+α 2   ś   nb ( n −4)+ . . . +α P   ś   nb ( n −2 P )
 
     where n is the sample index. 
     In a typical application setting, the inverse filtering of ś nb  to obtain ŕ nb  can be done on a frame-by-frame basis where a frame is defined as a sequence of N consecutive samples over a duration of T seconds. For many speech signal applications, a good choice for T is about 20 ms with corresponding values for N of about 160 at 8 kHz and about 320 at 16 kHz sampling frequency. Successive frames may overlap each other, for example, by up to or around 50%, in which case, the second half of the samples in the current frame and the first half of the samples in the following frame are the same, and a new frame is processed every T/2 seconds. For a choice of T as 20 ms and 50% overlap, for example, the LP parameters A nb  are computed from 160 consecutive s nb  samples every 10 ms, and are used to inverse filter the middle  160  samples of the corresponding ś nb  frame of  320  samples to yield  160  samples of ŕ nb . 
     One may also compute the 2P-order LP parameters for the inverse filtering operation directly from the up-sampled narrow-band speech. This approach, however, may increase the complexity of both computing the LP parameters and the inverse filtering operation, without necessarily increasing performance under at least some operating conditions. 
     The LP residual signal ŕ nb  is next full-wave rectified using a full-wave rectifier  405  and high-pass filtering the result (using, for example, a high-pass filter (HPF)  406  with a pass-band between 3400 and 8000 Hz) to obtain the high-band rectified residual signal rr hb . In parallel, the output of a pseudo-random noise source  407  is also high-pass filtered  408  to obtain the high-band noise signal n hb . Alternately, a high-pass filtered noise sequence may be pre-stored in a buffer (such as, for example, a circular buffer) and accessed as required to generate n hb . The use of such a buffer eliminates the computations associated with high-pass filtering the pseudo-random noise samples in real time. These two signals, viz., rr hb  and n hb , are then mixed in a mixer  409  according to the voicing level v provided by an Estimation &amp; Control Module (ECM)  410  (which module will be described in more detail below). In this illustrative example, this voicing level v ranges from 0 to 1, with 0 indicating an unvoiced level and 1 indicating a fully-voiced level. The mixer  409  essentially forms a weighted sum of the two input signals at its output after ensuring that the two input signals are adjusted to have the same energy level. The mixer output signal m hb  is given by
 
 m   hb =( v ) rr   hb +(1 −v ) n   hb .
 
     Those skilled in the art will appreciate that other mixing rules are also possible. It is also possible to first mix the two signals, viz., the full-wave rectified LP residual signal and the pseudo-random noise signal, and then high-pass filter the mixed signal. In this case, the two high-pass filters  406  and  408  are replaced by a single high-pass filter placed at the output of the mixer  409 . 
     The resultant signal m hb  is then pre-processed using a high-band (HB) excitation preprocessor  411  to form the high-band excitation signal ex hb . The pre-processing steps can comprise: (i) scaling the mixer output signal m hb  to match the high-band energy level E hb , and (ii) optionally shaping the mixer output signal m hb  to match the high-band spectral envelope SE hb . Both E hb  and SE hb  are provided to the HB excitation pre-processor  411  by the ECM  410 . When employing this approach, it may be useful in many application settings to ensure that such shaping does not affect the phase spectrum of the mixer output signal m hb ; that is, the shaping may preferably be performed by a zero-phase response filter. 
     The up-sampled narrow-band speech signal ś nb  and the high-band excitation signal ex hb  are added together using a summer  412  to form the mixed-band signal ŝ mb . This resultant mixed-band signal ŝ mb  is input to an equalizer filter  413  that filters that input using wide-band spectral envelope information SE wb  provided by the ECM  410  to form the estimated wide-band signal ŝ wb . The equalizer filter  413  essentially imposes the wide-band spectral envelope SE wb  on the input signal ŝ mb  to form ŝ wb  (further discussion in this regard appears below). The resultant estimated wide-band signal ŝ wb  is high-pass filtered, e.g., using a high pass filter  414  having a pass-band from 3400 to 8000 Hz, and low-pass filtered, e.g., using a low pass filter  415  having a pass-band from 0 to 300 Hz, to obtain respectively the high-band signal ś hb  and the low-band signal ŝ lb . These signals ŝ hb , ŝ lb , and the up-sampled narrow-band signal ŝ nb  are added together in another summer  416  to form the bandwidth extended signal s bwe . 
     Those skilled in the art will appreciate that there are various other filter configurations possible to obtain the bandwidth extended signal s bwe . If the equalizer filter  413  accurately retains the spectral content of the up-sampled narrow-band speech signal ś nb  which is part of its input signal ŝ mb , then the estimated wide-band signal ŝ wb  can be directly output as the bandwidth extended signal s bwe  thereby eliminating the high-pass filter  414 , the low-pass filter  415 , and the summer  416 . Alternately, two equalizer filters can be used, one to recover the low frequency portion and another to recover the high-frequency portion, and the output of the former can be added to high-pass filtered output of the latter to obtain the bandwidth extended signal s bwe . 
     Those skilled in the art will understand and appreciate that, with this particular illustrative example, the high-band rectified residual excitation and the high-band noise excitation are mixed together according to the voicing level. When the voicing level is 0 indicating unvoiced speech, the noise excitation is exclusively used. Similarly, when the voicing level is 1 indicating voiced speech, the high-band rectified residual excitation is exclusively used. When the voicing level is in between 0 and 1 indicating mixed-voiced speech, the two excitations are mixed in appropriate proportion as determined by the voicing level and used. The mixed high-band excitation is thus suitable for voiced, unvoiced, and mixed-voiced sounds. 
     It will be further understood and appreciated that, in this illustrative example, an equalizer filter is used to synthesize ŝ wb . The equalizer filter considers the wide-band spectral envelope SE wb  provided by the ECM as the ideal envelope and corrects (or equalizes) the spectral envelope of its input signal s mb  to match the ideal. Since only magnitudes are involved in the spectral envelope equalization, the phase response of the equalizer filter is chosen to be zero. The magnitude response of the equalizer filter is specified by SE wb (ω)/SE mb (ω). The design and implementation of such an equalizer filter for a speech coding application comprises a well understood area of endeavor. Briefly, however, the equalizer filter operates as follows using overlap-add (OLA) analysis. 
     The input signal ŝ mb  is first divided into overlapping frames, e.g., 20 ms (320 samples at 16 kHz) frames with 50% overlap. Each frame of samples is then multiplied (point-wise) by a suitable window, e.g., a raised-cosine window with perfect reconstruction property. The windowed speech frame is next analyzed to estimate the LP parameters modeling its spectral envelope. The ideal wide-band spectral envelope for the frame is provided by the ECM. From the two spectral envelopes, the equalizer computes the filter magnitude response as SE wb (ω)/SE mb (ω) and sets the phase response to zero. The input frame is then equalized to obtain the corresponding output frame. The equalized output frames are finally overlap-added to synthesize the estimated wide-band speech ŝ wb . 
     Those skilled in the art will appreciate that besides LP analysis, there are other methods to obtain the spectral envelope of a given speech frame, e.g., cepstral analysis, piecewise linear or higher order curve fitting of spectral magnitude peaks, etc. 
     Those skilled in the art will also appreciate that instead of windowing the input signal ŝ mb  directly, one could have started with windowed versions of ś nb , rr hb , and n hb  to achieve the same result. It may also be convenient to keep the frame size and the percent overlap for the equalizer filter the same as those used in the analysis filter block used to obtain ŕ nb  from ś nb . 
     The described equalizer filter approach to synthesizing ŝ wb  offers a number of advantages: i) Since the phase response of the equalizer filter  413  is zero, the different frequency components of the equalizer output are time aligned with the corresponding components of the input. This can be useful for voiced speech because the high energy segments (such as glottal pulse segments) of the rectified residual high-band excitation ex hb  are time aligned with the corresponding high energy segments of the up-sampled narrow-band speech ś nb  at the equalizer input, and preservation of this time alignment at the equalizer output will often act to ensure good speech quality; ii) the input to the equalizer filter  413  does not need to have a flat spectrum as in the case of LP synthesis filter; iii) the equalizer filter  413  is specified in the frequency domain, and therefore a better and finer control over different parts of the spectrum is feasible; and iv) iterations are possible to improve the filtering effectiveness at the cost of additional complexity and delay (for example, the equalizer output can be fed back to the input to be equalized again and again to improve performance). 
     Some additional details regarding the described configuration will now be presented. 
     High-band excitation pre-processing: The magnitude response of the equalizer filter  413  is given by SE wb (ω)/SE mb (ω) and its phase response can be set to zero. The closer the input spectral envelope SE mb (ω) is to the ideal spectral envelope SE wb (ω), the easier it is for the equalizer to correct the input spectral envelope to match the ideal. At least one function of the high-band excitation pre-processor  411  is to move SE mb (ω) closer to SE wb (ω) and thus make the job of the equalizer filter  413  easier. First, this is done by scaling the mixer output signal m hb  to the correct high-band energy level E hb  provided by the ECM  410 . Second, the mixer output signal m hb  is optionally shaped so that its spectral envelope matches the high-band spectral envelope SE hb  provided by the ECM  410  without affecting its phase spectrum. A second step can comprise essentially a pre-equalization step. 
     Low-band excitation: Unlike the loss of information in the high-band caused by the band-width restriction imposed, at least in part, by the sampling frequency, the loss of information in the low-band (0-300 Hz) of the narrow-band signal is due, at least in large measure, to the band-limiting effect of the channel transfer function consisting of, for example, a microphone, amplifier, speech coder, transmission channel, or the like. Consequently, in a clean narrow-band signal, the low-band information is still present although at a very low level. This low-level information can be amplified in a straight-forward manner to restore the original signal. But care should be taken in this process since low level signals are easily corrupted by errors, noise, and distortions. An alternative is to synthesize a low-band excitation signal similar to the high-band excitation signal described earlier. That is, the low-band excitation signal can be formed by mixing the low-band rectified residual signal rr lb  and the low-band noise signal n lb  in a way similar to the formation of the high-band mixer output signal m hb . 
     Referring now to  FIG. 5 , Estimation and Control Module (ECM)  410  is shown comprising onset/plosive detector  503 , zero-crossings calculator  501 , transition-band slope estimator  505 , transition-band energy estimator  504 , narrow-band spectrum estimator  509 , low-band spectrum estimator  511 , wide-band spectrum estimator  512 , high-band spectrum estimator  510 , SS/Transition detector  513 , high-band energy estimator  506 , voicing level estimator  502 , energy adapter  514 , energy track smoother  507 , and energy adapter  508 . 
     ECM  410  takes as input the narrow-band speech s nb , the up-sampled narrow-band speech ś nb , and the narrow-band LP parameters A nb  and provides as output the voicing level v, the high-band energy E hb , the high-band spectral envelope SE hb , and the wide-band spectral envelope SE wb . 
     Voicing level estimation: To estimate the voicing level, a zero-crossing calculator  501  calculates the number of zero-crossings zc in each frame of the narrow-band speech s nb  as follows: 
     
       
         
           
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                         ) 
                       
                     
                   
                    
                 
               
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               Sgn 
               ⁡ 
               
                 ( 
                 
                   
                     s 
                     nb 
                   
                   ⁡ 
                   
                     ( 
                     n 
                     ) 
                   
                 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     1 
                   
                   
                     
                       
                         if 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             s 
                             nb 
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                       ≥ 
                       0 
                     
                   
                 
                 
                   
                     
                       - 
                       1 
                     
                   
                   
                     
                       
                         
                           if 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               s 
                               nb 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         &lt; 
                         0 
                       
                       , 
                     
                   
                 
               
             
           
         
       
     
     n is the sample index, and Nis the frame size in samples. It is convenient to keep the frame size and percent overlap used in the ECM  410  the same as those used in the equalizer filter  413  and the analysis filter blocks, e.g., T=20 ms, N=160 for 8 kHz sampling, N=320 for 16 kHz sampling, and 50% overlap with reference to the illustrative values presented earlier. The value of the zc parameter calculated as above ranges from 0 to 1. From the zc parameter, a voicing level estimator  502  can estimate the voicing level v as follows. 
     
       
         
           
             v 
             = 
             
               ( 
               
                 
                   
                     
                       
                         1 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         if 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         zc 
                       
                       &lt; 
                       
                         ZC 
                         low 
                       
                     
                   
                 
                 
                   
                     
                       
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         if 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         zc 
                       
                       &gt; 
                       
                         ZC 
                         high 
                       
                     
                   
                 
                 
                   
                     
                       1 
                       - 
                       
                         
                           [ 
                           
                             
                               zc 
                               - 
                               
                                 ZC 
                                 low 
                               
                             
                             
                               
                                 ZC 
                                 high 
                               
                               - 
                               
                                 ZC 
                                 low 
                               
                             
                           
                           ] 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         otherwise 
                       
                     
                   
                 
               
             
           
         
       
     
     where, ZC low  and ZC high  represent appropriately chosen low and high thresholds respectively, e.g., ZC low =0.40 and ZC high =0.45. The output d of an onset/plosive detector  503  can also be fed into the voicing level detector  502 . If a frame is flagged as containing an onset or a plosive with d=1, the voicing level of that frame as well as the following frame can be set to 1. Recall that, by one approach, when the voicing level is 1, the high-band rectified residual excitation is exclusively used. This is advantageous at an onset/plosive, compared to noise-only or mixed high-band excitation, because the rectified residual excitation closely follows the energy versus time contour of the up-sampled narrow-band speech thus reducing the possibility of pre-echo type artifacts due to time dispersion in the bandwidth extended signal. 
     In order to estimate the high-band energy, a transition-band energy estimator  504  estimates the transition-band energy from the up-sampled narrow-band speech signal ś nb . The transition-band is defined here as a frequency band that is contained within the narrow-band and close to the high-band, i.e., it serves as a transition to the high-band, (which, in this illustrative example, is about 2500-3400 Hz). Intuitively, one would expect the high-band energy to be well correlated with the transition-band energy, which is borne out in experiments. A simple way to calculate the transition-band energy E tb  is to compute the frequency spectrum of ś nb  (for example, through a Fast Fourier Transform (FFT)) and sum the energies of the spectral components within the transition-band. 
     From the transition-band energy E tb  in dB (decibels), the high-band energy E hb0  in dB is estimated as
 
 E   hb0   =αE   tb +β
 
     where, the coefficients α and β are selected to minimize the mean squared error between the true and estimated values of the high-band energy over a large number of frames from a training speech database. 
     The estimation accuracy can be further enhanced by exploiting contextual information from additional speech parameters such as the zero-crossing parameter zc and the transition-band spectral slope parameter sl as may be provided by a transition-band slope estimator  505 . The zero-crossing parameter, as discussed earlier, is indicative of the speech voicing level. The slope parameter indicates the rate of change of spectral energy within the transition-band. It can be estimated from the narrow-band LP parameters A nb  by approximating the spectral envelope (in dB) within the transition-band as a straight line, e.g., through linear regression, and computing its slope. The zc-sl parameter plane is then partitioned into a number of regions, and the coefficients α and β are separately selected for each region. For example, if the ranges of zc and sl parameters are each divided into 8 equal intervals, the zc-sl parameter plane is then partitioned into 64 regions, and 64 sets of α and β coefficients are selected, one for each region. 
     By another approach (not shown in  FIG. 5 ), further improvement in estimation accuracy is achieved as follows. Note that instead of the slope parameter sl (which is only a first order representation of the spectral envelope within the transition band), a higher resolution representation may be employed to enhance the performance of the high-band energy estimator. For example, a vector quantized representation of the transition band spectral envelope shapes (in dB) may be used. As one illustrative example, the vector quantizer (VQ) codebook consists of  64  shapes referred to as transition band spectral envelope shape parameters tbs that are computed from a large training database. One could replace the sl parameter in the zc-sl parameter plane with the tbs parameter to achieve improved performance. By another approach, however, a third parameter referred to as the spectral flatness measure sfm is introduced. The spectral flatness measure is defined as the ratio of the geometric mean to the arithmetic mean of the narrow-band spectral envelope (in dB) within an appropriate frequency range (such as, for example, 300-3400 Hz). The sfm parameter indicates how flat the spectral envelope is—ranging in this example from about 0 for a peaky envelope to 1 for a completely flat envelope. The sfm parameter is also related to the voicing level of speech but in a different way than zc. By one approach, the three dimensional zc-sfm-tbs parameter space is divided into a number of regions as follows. The zc-sfm plane is divided into 12 regions thereby giving rise to 12×64=768 possible regions in the three dimensional space. Not all of these regions, however, have sufficient data points from the training data base. So, for many application settings, the number of useful regions is limited to about 500, with a separate set of α and β coefficients being selected for each of these regions. 
     A high-band energy estimator  506  can provide additional improvement in estimation accuracy by using higher powers of E tb  in estimating E hb0 , e.g.,
 
 E   hb0 =α 4   E   tb   4 +α 3   E   tb   3 +α 2   E   tb   2 +α 1   E   tb +β.
 
     In this case, five different coefficients, viz., α 4 , α 3 , α 2 , α 1 , and β, are selected for each partition of the zc-sl parameter plane (or alternately, for each partition of the zc-sfm-tbs parameter space). Since the above equations (refer to paragraphs 70 and 75) for estimating E hb0  are non-linear, special care must be taken to adjust the estimated high-band energy as the input signal level, i.e, energy, changes. One way of achieving this is to estimate the input signal level in dB, adjust E tb  up or down to correspond to the nominal signal level, estimate E hb0 , and adjust E hb0  down or up to correspond to the actual signal level. 
     Estimation of the high-band energy is prone to errors. Since over-estimation leads to artifacts, the estimated high-band energy is biased to be lower by an amount proportional to the standard deviation of the the estimation of E hb0 . That is, the high-band energy is adapted in energy adapter 1 ( 514 ) as:
 
 E   hb1   =E   hb0 −λ·σ
 
where, E hb1  is the adapted high-band energy in dB, E hb0  is the estimated high-band energy in dB, λ≧0 is a proportionality factor, and σ is the standard deviation of the estimation error in dB. Thus, after receiving the input digital audio signal comprising the narrow-band signal, and determining the estimated high-band energy level from the corresponding digital audio signal, the estimated high-band energy level is modified based on an estimation accuracy of the estimated high-band energy. With reference to  FIG. 5 , high-band energy estimator  506  additionally determines a measure of unreliability in the estimation of the high-band energy level and energy adapter  514  biases the estimated high-band energy level to be lower by an amount proportional to the measure of unreliability. In one embodiment of the present invention the measure of unreliability comprises a standard deviation of the error in the estimated high-band energy level. Note that other measures of unreliability may as well be employed without departing from the scope of this invention.
 
     By “biasing down” the estimated high-band energy, the probability (or number of occurrences) of energy over-estimation is reduced, thereby reducing the number of artifacts. Also, the amount by which the estimated high-band energy is reduced is proportional to how good the estimate is—a more reliable (i.e., low σ value) estimate is reduced by a smaller amount than a less reliable estimate. While designing the high-band energy estimator, the σ value corresponding to each partition of the zc-sl parameter plane (or alternately, each partition of the zc-sfm-tbs parameter space) is computed from the training speech database and stored for later use in “biasing down” the estimated high-band energy. The σ value of the about 500 partitions of the zc-sfm-tbs parameter space, for example, ranges from about 3 dB to about 10 dB with an average value of about 5.8 dB. A suitable value of 2 for this high-band energy predictor, for example, is 1.5. 
     In a prior-art approach, over-estimation of high-band energy is handled by using an asymmetric cost function that penalizes over-estimated errors more than under-estimated errors in the design of the high-band energy estimator. Compared to this prior-art approach, the “bias down” approach described in this invention has the following advantages: (A) The design of the high-band energy estimator is simpler because it is based on the standard symmetric “squared error” cost function; (B) The “bias down” is done explicitly during the operational phase (and not implicitly during the design phase) and therefore the amount of “bias down” can be easily controlled as desired; and (C) The dependence of the amount of “bias down” to the reliability of the estimate is explicit and straightforward (instead of implicitly depending on the specific cost function used during the design phase). 
     Besides reducing the artifacts due to energy over-estimation, the “bias down” approach described above has an added benefit for voiced frames—namely that of masking any errors in high-band spectral envelope shape estimation and thereby reducing the resultant “noisy” artifacts. However, for unvoiced frames, if the reduction in the estimated high-band energy is too high, the bandwidth extended output speech no longer sounds like wideband speech. To counter this, the estimated high-band energy is further adapted in energy adapter 1 ( 514 ) depending on its voicing level as
 
 E   hb2   =E   hb1 +(1 −v )·δ 1   +v·δ   2  
 
     where, E hb2  is the voicing-level adapted high-band energy in dB, v is the voicing level ranging from 0 for unvoiced speech to 1 for voiced speech, and δ 1  and δ 2  (δ 1 &gt;δ 2 ) are constants in dB. The choice of δ 1  and β 2  depends on the value of λ used for the “bias down” and is determined empirically to yield the best-sounding output speech. For example, when λ is chosen as 1.5, δ 1  and δ 2  may be chosen as 7.6 and −0.3 respectively. Note that other choices for the value of λ may result in different choices for δ 1  and δ 2 —the values of δ 1  and δ 2  may both be positive or negative or of opposite signs. The increased energy level for unvoiced speech emphasizes such speech in the bandwidth extended output compared to the narrow-band input and also helps to select a more appropriate spectral envelope shape for such unvoiced segments. 
     With reference to  FIG. 5 , voicing level estimator outputs a voicing level to energy adapter 1 which further modifies the estimated high-band energy level based on narrow-band signal characteristics by further modifying the estimated high-band energy level based on a voicing level. The further modifying may comprise reducing the high-band energy level for substantially voiced speech and/or increasing the high-band energy level for substantially unvoiced speech. 
     While the high-band energy estimator  506  followed by energy adapter 1 ( 514 ) works quite well for most frames, occasionally there are frames for which the high-band energy is grossly under- or over-estimated. Such estimation errors can be at least partially corrected by means of an energy track smoother  507  that comprises a smoothing filter. Thus the step of modifying the estimated high-band energy level based on the narrow-band signal characteristics may comprise smoothing the estimated high-band energy level (which has been previously modified as described above based on the standard deviation of the estimation σ and the voicing level v), essentially reducing an energy difference between consecutive frames. 
     For example, the voicing-level adapted high-band energy E hb2  may be smoothed using a 3-point averaging filter as
 
 E   hb3   =[E   hb2 ( k −1)+ E   hb2 ( k )+ E   hb2 ( k +1)]/3
 
     where, E hb3  is the smoothed estimate and k is the frame index. Smoothing reduces the energy difference between consecutive frames, especially when an estimate is an “outlier”, that is, the high-band energy estimate of a frame is too high or too low compared to the estimates of the neighboring frames. Thus, smoothing helps to reduce the number of artifacts in the output bandwidth extended speech. The 3-point averaging filter introduces a delay of one frame. Other types of filters with or without delay can also be designed for smoothing the energy track. 
     The smoothed energy value E hb3  may be further adapted by energy adapter 2 ( 508 ) to obtain the final adapted high-band energy estimate E hb . This adaptation can involve either decreasing or increasing the smoothed energy value based on the ss parameter output by the steady-state/transition detector  513  and/or the d parameter output by the onset/plosive detector  503 . Thus, the step of modifying the estimated high-band energy level based on the narrow-band signal characteristics may comprise the step of modifying the estimated high-band energy level (or previously modified estimated high-band energy level) based on whether or not a frame is steady-state or transient. This may comprise reducing the high-band energy level for transient frames and/or increasing the high-band energy level for steady-state frames, and may further comprise modifying the estimated high-band energy level based on an occurrence of an onset/plosive. By one approach, adapting the high-band energy value changes not only the energy level but also the spectral envelope shape since the selection of the high-band spectrum can be tied to the estimated energy. 
     A frame is defined as a steady-state frame if it has sufficient energy (that is, it is a speech frame and not a silence frame) and it is close to each of its neighboring frames both in a spectral sense and in terms of energy. Two frames may be considered spectrally close if the Itakura distance between the two frames is below a specified threshold. Other types of spectral distance measures may also be used. Two frames are considered close in terms of energy if the difference in the narrow-band energies of the two frames is below a specified threshold. Any frame that is not a steady-state frame is considered a transition frame. A steady state frame is able to mask errors in high-band energy estimation much better than transient frames. Accordingly, the estimated high-band energy of a frame is adapted based on the ss parameter, that is, depending on whether it is a steady-state frame (ss=1) or transition frame (ss=0) as 
     
       
         
           
             
               E 
               
                 hb 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         E 
                         
                           hb 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                         
                       
                       + 
                       
                         μ 
                         1 
                       
                     
                   
                   
                     
                       for 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       steady 
                       ⁢ 
                       
                         - 
                       
                       ⁢ 
                       state 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       frames 
                     
                   
                 
                 
                   
                     
                       min 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               E 
                               
                                 hb 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 3 
                               
                             
                             - 
                             
                               μ 
                               2 
                             
                           
                           , 
                           
                             E 
                             
                               hb 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                         ) 
                       
                     
                   
                   
                     
                       for 
                       ⁢ 
                       
                         
                             
                         
                         ⁢ 
                         
                             
                         
                       
                       ⁢ 
                       transition 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       frames 
                     
                   
                 
               
             
           
         
       
     
     where, μ 2 &gt;μ 1 ≧0, are empirically chosen constants in dB to achieve good output speech quality. The values of μ 1  and μ 2  depend on the choice of the proportionality constant λ used for the “bias down”. For example, when λ is chosen as 1.5, δ 1  as 7.6, and δ 2  as −0.3, μ 1  and μ 2  may be chosen as 1.5 and 6.0 respectively. Notice that in this example we are slightly increasing the estimated high-band energy for steady-state frames and decreasing it significantly further for transition frames. Note that other choices for the values of λ, δ 1 , and δ 2  may result in different choices for μ 1  and  μ2 —the values of μ 1  and μ 2  may both be positive or negative or of opposite signs. Further, note that other criteria for identifying steady-state/transition frames may also be used. 
     Based on the onset/plosive detector output d, the estimate high-band energy level can be adjusted as follows: When d=1, it indicates that the corresponding frame contains an onset, for example, transition from silence to unvoiced or voiced sound, or a plosive sound. An onset/plosive is detected at the current frame if the narrow-band energy of the preceding frame is below a certain threshold and the energy difference between the current and preceding frames exceeds another threshold. Other methods for detecting an onset/plosive may also be employed. An onset/plosive presents a special problem because of the following reasons: A) Estimation of high-band energy near onset/plosive is difficult; B) Pre-echo type artifacts may occur in the output speech because of the typical block processing employed; and C) Plosive sounds (e.g., [p], [t], and [k]), after their initial energy burst, have characteristics similar to certain sibilants (e.g., [s], [∫], and [3]) in the narrow-band but quite different in the high-band leading to energy over-estimation and consequent artifacts. High-band energy adaptation for an onset/plosive (d=1) is done as follows: 
     
       
         
           
             
               
                 E 
                 hb 
               
               ⁡ 
               
                 ( 
                 k 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       E 
                       min 
                     
                   
                   
                     
                       
                         
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           k 
                         
                         = 
                         1 
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         K 
                         min 
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           E 
                           
                             hb 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       Δ 
                     
                   
                   
                     
                       
                         
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           k 
                         
                         = 
                         
                           
                             K 
                             min 
                           
                           + 
                           1 
                         
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         
                           
                             K 
                             T 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           if 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             v 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         &gt; 
                         
                           V 
                           1 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           E 
                           
                             hb 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       Δ 
                       + 
                       
                         
                           Δ 
                           T 
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             
                               K 
                               T 
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         
                           for 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           k 
                         
                         = 
                         
                           
                             K 
                             T 
                           
                           + 
                           1 
                         
                       
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       
                         
                           
                             K 
                             max 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           if 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             v 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                         &gt; 
                         
                           V 
                           1 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     where k is the frame index. For the first K min  frames starting with the frame (k=1) at which the onset/plosive is detected, the high-band energy is set to the lowest possible value E min . For example, E min  can be set to −∞ dB or to the energy of the high-band spectral envelope shape with the lowest energy. For the subsequent frames (i.e., for the range given by k=K min +1 to k=K max ), energy adaptation is done only as long as the voicing level v(k) of the frame exceeds the threshold V 1 . Whenever the voicing level of a frame within this range becomes less than or equal to V 1 , the onset energy adaptation is immediately stopped, that is, E hb (k) is set equal to E hb4 (k) until the next onset is detected. If the voicing level v(k) is greater than V 1 , then for k=K min +1 to k=K T , the high-band energy is decreased by a fixed amount Δ. For k=K T +1 to k=K max , the high-band energy is gradually increased from E hb4 (k)−Δ towards E hb4 (k) by means of the pre-specified sequence Δ T (k-K T ) and at k=K max +1, E hb (k) is set equal to E hb4 (k), and this continues until the next onset is detected. Typical values of the parameters used for onset/plosive based energy adaptation, for example, are K min =2, K T =5, K max 7, V 1 =0.4, Δ=−12 dB, Δ T  (1)=6 dB, and Δ T  (2)=9.5 dB. For d=0, no further adaptation of the energy is done, that is, E hb  is set equal to E hb4 . Thus, the step of modifying the estimated high-band energy level based on the narrow-band signal characteristics may comprise the step of modifying the estimated high-band energy level (or previously modified estimated high-band energy level) based on an occurrence of an onset/plosive. 
     The adaptation of the estimated high-band energy as outlined in paragraphs 77 through paragraph 95 helps to minimize the number of artifacts in the bandwidth extended output speech and thereby enhance its quality. Although the sequence of operations used to adapt the estimated high-band energy has been presented in a particular way, those skilled in the art will recognize that such specificity with respect to sequence is not actually required. Also, the operations described for modifying the high-band energy level may selectively be applied. 
     The estimation of the wide-band spectral envelope SE wb  is described next. To estimate SE wb , one can separately estimate the narrow-band spectral envelope SE nb , the high-band spectral envelope SE hb , and the low-band spectral envelope SE lb , and combine the three envelopes together. 
     A narrow-band spectrum estimator  509  can estimate the narrow-band spectral envelope SE nb  from the up-sampled narrow-band speech ś nb . From ś nb , the LP parameters, B nb ={1, b 1 , b 2 , . . . b Q } where Q is the model order, are first computed using well-known LP analysis techniques. For an up-sampled frequency of 16 kHz, a suitable model order Q, for example, is 20. The LP parameters B nb  model the spectral envelope of the up-sampled narrow-band speech as 
     
       
         
           
             
               
                 SE 
                 usnb 
               
               ⁡ 
               
                 ( 
                 ω 
                 ) 
               
             
             = 
             
               
                 1 
                 
                   1 
                   + 
                   
                     
                       b 
                       1 
                     
                     ⁢ 
                     
                       ⅇ 
                       
                         - 
                         jω 
                       
                     
                   
                   + 
                   
                     
                       b 
                       2 
                     
                     ⁢ 
                     
                       ⅇ 
                       
                         
                           - 
                           j 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         ω 
                       
                     
                   
                   + 
                   … 
                   + 
                   
                     
                       b 
                       Q 
                     
                     ⁢ 
                     
                       ⅇ 
                       
                         
                           - 
                           j 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Q 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                       
                     
                   
                 
               
               . 
             
           
         
       
     
     In the equation above, the angular frequency ω in radians/sample is given by ω=2πf/2F s , where f is the signal frequency in Hz and F s  is the sampling frequency in Hz. Notice that the spectral envelopes SE nbin  and SE usnb  are different since the former is derived from the narrow-band input speech and the latter from the up-sampled narrow-band speech. However, inside the pass-band of 300 to 3400 Hz, they are approximately related by SE nb  (ω)≈SE nbin  (2ω) to within a constant. Although the spectral envelope SE nsnb  is defined over the range 0-8000 (F s ) Hz, the useful portion lies within the pass-band (in this illustrative example, 300-3400 Hz). 
     As one illustrative example in this regard, the computation of SE usnb  is done using FFT as follows. First, the impulse response of the inverse filter B nb (z) is calculated to a suitable length, e.g., 1024, as {1, b 1 , b 2 , . . . , b Q , 0, 0, . . . , 0}. Then an FFT of the impulse response is taken, and magnitude spectral envelope SE usnb  is obtained by computing the inverse magnitude at each FFT index. For an FFT length of 1024, the frequency resolution of SE usnb  computed as above is 16000/1024=15.625 Hz. From SE usnb , the narrow-band spectral envelope SE nb  is estimated by simply extracting the spectral magnitudes from within the approximate range, 300-3400 Hz. 
     Those skilled in the art will appreciate that besides LP analysis, there are other methods to obtain the spectral envelope of a given speech frame, e.g., cepstral analysis, piecewise linear or higher order curve fitting of spectral magnitude peaks, etc. 
     A high-band spectrum estimator  510  takes an estimate of the high-band energy as input and selects a high-band spectral envelope shape that is consistent with the estimated high-band energy. A technique to come up with different high-band spectral envelope shapes corresponding to different high-band energies is described next. 
     Starting with a large training database of wide-band speech sampled at 16 kHz, the wide-band spectral magnitude envelope is computed for each speech frame using standard LP analysis or other techniques. From the wide-band spectral envelope of each frame, the high-band portion corresponding to 3400-8000 Hz is extracted and normalized by dividing through by the spectral magnitude at 3400 Hz. The resulting high-band spectral envelopes have thus a magnitude of 0 dB at 3400 Hz. The high-band energy corresponding to each normalized high-band envelope is computed next. The collection of high-band spectral envelopes is then partitioned based on the high-band energy, e.g., a sequence of nominal energy values differing by 1 dB is selected to cover the entire range and all envelopes with energy within 0.5 dB of a nominal value are grouped together. 
     For each group thus formed, the average high-band spectral envelope shape is computed and subsequently the corresponding high-band energy. In  FIG. 6 , a set of 60 high-band spectral envelope shapes  600  (with magnitude in dB versus frequency in Hz) at different energy levels is shown. Counting from the bottom of the figure, the 1 st , 10 th , 20 th , 30 th , 40 th , 50 th , and 60 th  shapes (referred to herein as pre-computed shapes) were obtained using a technique similar to the one described above. The remaining 53 shapes were obtained by simple linear interpolation (in the dB domain) between the nearest pre-computed shapes. 
     The energies of these shapes range from about 4.5 dB for the 1 st  shape to about 43.5 dB for the 60 th  shape. Given the high-band energy for a frame, it is a simple matter to select the closest matching high-band spectral envelope shape as will be described later in the document. The selected shape represents the estimated high-band spectral envelope SE hb  to within a constant. In  FIG. 6 , the average energy resolution is approximately 0.65 dB. Clearly, better resolution is possible by increasing the number of shapes. Given the shapes in  FIG. 6 , the selection of a shape for a particular energy is unique. One can also think of a situation where there is more than one shape for a given energy, e.g., 4 shapes per energy level, and in this case, additional information is needed to select one of the 4 shapes for each given energy level. Furthermore, one can have multiple sets of shapes each set indexed by the high-band energy, e.g., two sets of shapes selectable by the voicing parameter v, one for voiced frames and the other for unvoiced frames. For a mixed-voiced frame, the two shapes selected from the two sets can be appropriately combined. 
     The high-band spectrum estimation method described above offers some clear advantages. For example, this approach offers explicit control over the time evolution of the high-band spectrum estimates. A smooth evolution of the high-band spectrum estimates within distinct speech segments, e.g., voiced speech, unvoiced speech, and so forth is often important for artifact-free band-width extended speech. For the high-band spectrum estimation method described above, it is evident from  FIG. 6  that small changes in high-band energy result in small changes in the high-band spectral envelope shapes. Thus, smooth evolution of the high-band spectrum can be essentially assured by ensuring that the time evolution of the high-band energy within distinct speech segments is also smooth. This is explicitly accomplished by energy track smoothing as described earlier. 
     Note that distinct speech segments, within which energy smoothing is done, can be identified with even finer resolution, e.g., by tracking the change in the narrow-band speech spectrum or the up-sampled narrow-band speech spectrum from frame to frame using any one of the well known spectral distance measures such as the log spectral distortion or the LP-based Itakura distortion. Using this approach, a distinct speech segment can be defined as a sequence of frames within which the spectrum is evolving slowly and which is bracketed on each side by a frame at which the computed spectral change exceeds a fixed or an adaptive threshold thereby indicating the presence of a spectral transition on either side of the distinct speech segment. Smoothing of the energy track may then be done within the distinct speech segment, but not across segment boundaries. 
     Here, smooth evolution of the high-band energy track translates into a smooth evolution of the estimated high-band spectral envelope, which is a desirable characteristic within a distinct speech segment. Also note that this approach to ensuring a smooth evolution of the high-band spectral envelope within a distinct speech segment may also be applied as a post-processing step to a sequence of estimated high-band spectral envelopes obtained by prior-art methods. In that case, however, the high-band spectral envelopes may need to be explicitly smoothed within a distinct speech segment, unlike the straightforward energy track smoothing of the current teachings which automatically results in the smooth evolution of the high-band spectral envelope. 
     The loss of information of the narrow-band speech signal in the low-band (which, in this illustrative example, may be from 0-300 Hz) is not due to the bandwidth restriction imposed by the sampling frequency as in the case of the high-band but due to the band-limiting effect of the channel transfer function consisting of, for example, the microphone, amplifier, speech coder, transmission channel, and so forth. 
     A straight-forward approach to restore the low-band signal is then to counteract the effect of this channel transfer function within the range from 0 to 300 Hz. A simple way to do this is to use a low-band spectrum estimator  511  to estimate the channel transfer function in the frequency range from 0 to 300 Hz from available data, obtain its inverse, and use the inverse to boost the spectral envelope of the up-sampled narrow-band speech. That is, the low-band spectral envelope SE lb  is estimated as the sum of SE usnb  and a spectral envelope boost characteristic SE boost  designed from the inverse of the channel transfer function (assuming that spectral envelope magnitudes are expressed in log domain, e.g., dB). For many application settings, care should be exercised in the design of SE boost . Since the restoration of the low-band signal is essentially based on the amplification of a low level signal, it involves the danger of amplifying errors, noise, and distortions typically associated with low level signals. Depending on the quality of the low level signal, the maximum boost value should be restricted appropriately. Also, within the frequency range from 0 to about 60 Hz, it is desirable to design SE boost  to have low (or even negative, i.e., attenuating) values to avoid amplifying electrical hum and background noise. 
     A wide-band spectrum estimator  512  can then estimate the wide-band spectral envelope by combining the estimated spectral envelopes in the narrow-band, high-band, and low-band. One way of combining the three envelopes to estimate the wide-band spectral envelope is as follows. 
     The narrow-band spectral envelope SE nb  is estimated from ś nb  as described above and its values within the range from 400 to 3200 Hz are used without any change in the wide-band spectral envelope estimate SE wb . To select the appropriate high-band shape, the high-band energy and the starting magnitude value at 3400 Hz are needed. The high-band energy E hb  in dB is estimated as described earlier. The starting magnitude value at 3400 Hz is estimated by modeling the FFT magnitude spectrum of ś nb  in dB within the transition-band, viz., 2500-3400 Hz, by means of a straight line through linear regression and finding the value of the straight line at 3400 Hz. Let this magnitude value by denoted by M 3400  in dB. The high-band spectral envelope shape is then selected as the one among many values, e.g., as shown in  FIG. 6 , that has an energy value closest to E hb -M 3400 . Let this shape be denoted by SE closest . Then the high-band spectral envelope estimate SE hb  and therefore the wide-band spectral envelope SE wb  within the range from 3400 to 8000 Hz are estimated as SE closest +M 3400 . 
     Between 3200 and 3400 Hz, SE wb  is estimated as the linearly interpolated value in dB between SE nb  and a straight line joining the SE nb  at 3200 Hz and M 3400  at 3400 Hz. The interpolation factor itself is changed linearly such that the estimated SE wb  moves gradually from SE nb  at 3200 Hz to M 3400  at 3400 Hz. Between 0 to 400 Hz, the low-band spectral envelope SE lb  and the wide-band spectral envelope SE wb  are estimated as SE nb +SE boost , where SE boost  represents an appropriately designed boost characteristic from the inverse of the channel transfer function as described earlier. 
     As alluded to earlier, frames containing onsets and/or plosives may benefit from special handling to avoid occasional artifacts in the band-width extended speech. Such frames can be identified by the sudden increase in their energy relative to the preceding frames. The onset/plosive detector  503  output d for a frame is set to 1 whenever the energy of the preceding frame is low, i.e., below a certain threshold, e.g., −50 dB, and the increase in energy of the current frame relative to the preceding frame exceeds another threshold, e.g., 15 dB. Otherwise, the detector output d is set to 0. The frame energy itself is computed from the energy of the FFT magnitude spectrum of the up-sampled narrow-band speech ś nb  within the narrow-band, i.e., 300-3400 Hz. As noted above, the output of the onset/plosive detector  503  d is fed into the voicing level estimator  502  and the energy adapter  508 . As described earlier, whenever a frame is flagged as containing an onset or a plosive with d=1, the voicing level v of that frame as well as the following frame is set to 1. Also, the high-band energy value of that frame as well as the following frames is modified as described earlier. 
     Those skilled in the art will appreciate that the described high-band energy estimation techniques may be used in conjunction with other prior-art bandwidth extension systems to scale the artificially generated high-band signal content for such systems to an appropriate energy level. Furthermore, note that although the energy estimation technique has been described with reference to the high frequency band, (for example, 3400-8000 Hz), it can also be applied to estimate the energy in any other band by appropriately redefining the transition band. For example, to estimate the energy in a low-band context, such as 0-300 Hz, the transition band may be redefined as the 300-600 Hz band. Those skilled in the art will also recognize that the high-band energy estimation techniques described herein may be employed for speech/audio coding purposes. Likewise, the techniques described herein for estimating the high-band spectral envelope and high-band excitation may also be used in the context of speech/audio coding. 
     Note that techniques other than the ones described in this invention may be used for estimating the high-band energy level. It is also possible for the bandwidth extension system to receive an estimate of the high-band energy level transmitted from elsewhere. The high-band energy level may also be implicitly estimated, e.g., one could estimate the energy level of the wideband signal instead, and from this estimate and other known information, the high-band energy level can be extracted. 
     Note that while the estimation of parameters such as spectral envelope, zero crossings, LP coefficients, band energies, and so forth has been described in the specific examples previously given as being done from the narrow-band speech in some cases and the up-sampled narrow-band speech in other cases, it will be appreciated by those skilled in the art that the estimation of the respective parameters and their subsequent use and application, may be modified to be done from the either of those two signals (narrow-band speech or the up-sampled narrow-band speech), without departing from the spirit and the scope of the described teachings. 
     Those skilled in the art will recognize that a wide variety of modifications, alterations, and combinations can be made with respect to the above described embodiments without departing from the spirit and scope of the invention, and that such modifications, alterations, and combinations are to be viewed as being within the ambit of the inventive concept.