Abstract:
An efficient approach for estimating scalefactors for use in the quantization of audio signal spectrum values is described. The scalefactor estimation approach can be implemented in multiple stages. A first stage estimates a distortion level for a selected scalefactor band spectrum value based on a received maximum tolerant distortion threshold and the spectrum values in the scalefactor band. A second stage determines an interim process value based on the previously estimated distortion level and generates a scalefactor for a selected scalefactor band spectrum value based on the generated interim process value and a statistically predetermined fraction. A third stage generates a scalefactor that applies to the whole scalefactor band based on the scalefactor generated for the selected scalefactor band spectrum value. The approach provides a performance gain of 40% over previous techniques, thereby reducing device power requirements and audio encoder bottlenecks.

Description:
INCORPORATION BY REFERENCE 
     This application claims the benefit of U.S. Provisional Application No. 61/118,811, “EFFICIENT SCALEFACTOR ESTIMATION ALGORITHM IN AAC LC ENCODER,” filed by Lijie Tang and Ke Ding on Dec. 1, 2008, which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Adaptive quantization is used by frequency-domain audio encoders, such as the advance audio coding (AAC) and MP3 encoder, to reduce the number of bits required to store encoded audio data, while maintaining a desired audio quality. 
     Adaptive quantization transforms time-domain digital audio signals into frequency-domain signals and groups the respective frequency-domain spectrum data into frequency bands, or scalefactor bands. In this manner, the techniques used to eliminate redundant data, i.e., inaudible data, and the techniques used to efficiently quantize and encode the remaining data, can be tailored based on the frequency and/or other characteristics associated with the respective scalefactor bands, such as the perception of the frequencies in the respective scalefactor bands by the human ear. 
     For example, in advance audio coding, the interval, or scalefactor, used to quantize each respective scalefactor band can be individually determined for each scalefactor band. Selection of a scalefactor for each scalefactor band allows the advance audio coding process to use scalefactors to quantize the signal in certain spectral regions (the scalefactor bands) to leverage the compression ratio and the signal-to-noise ratio in those bands. Thus scalefactors implicitly modify the bit-allocation over frequency since higher spectral values usually need more bits to be encoded. The use of larger scalefactors reduces the number of bits required to encode a scalefactor band, however, the use of larger scalefactors introduces an increase amount of distortion to the encoded signal. The use of smaller scalefactors decreases the amount of distortion introduced to the final encoded signal, however, the use of smaller scalefactors also increases the number of bits required to encode a scalefactor band. 
     In order to achieve improved sound quality as well as improved compression, selection of an appropriate scalefactor for each scalefactor band is an important process. Unfortunately, current approaches for selecting a scalefactor for a scalefactor band are computationally complex and processor cycle intensive. 
     The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure. 
     SUMMARY 
     An efficient approach for estimating scalefactors for use in the quantization of audio signal spectrum data is described. The scalefactor estimation approach can be implemented in multiple stages. A first stage estimates a distortion level for a selected scalefactor band spectrum value based on a received maximum tolerant distortion threshold and the spectrum values in the scalefactor band. A second stage determines an interim process value based on the previously estimated distortion level and generates a scalefactor for a selected scalefactor band spectrum value based on the generated interim process value and a statistically predetermined fraction. A third stage generates a scalefactor that applies to the whole scalefactor band based on the scalefactor generated for the selected scalefactor band spectrum value. The approach provides a performance gain of 40% over previous techniques, thereby reducing device power requirements and audio encoder bottlenecks. 
     In one example embodiment, an audio encoder is described that includes a scalefactor estimation module that includes, a difference generating module that can determine a distortion level, for a spectrum value selected from a set of spectrum values in a scalefactor band, based on a maximum tolerant distortion threshold for the scalefactor band, and the set of spectrum values within the scalefactor band, a spectrum value scalefactor generating module that can generate a scalefactor for the selected spectrum value based in part on the determined distortion level and the selected spectrum value, and a spectrum band scalefactor generating module that can generate a scalefactor for the scalefactor band based on the scalefactor generated for the selected spectrum value. 
     In a second example embodiment, a method of generating a scalefactor for a scalefactor band is described that includes, generating a distortion level for a spectrum value selected from a set of spectrum values in the scalefactor band, based on a maximum tolerant distortion threshold for the scalefactor band and the set of spectrum values within the scalefactor band, generating a scalefactor for the selected spectrum value based in part on the distortion level and the selected spectrum value, and generating the scalefactor for the scalefactor band based on the scalefactor generated for the selected spectrum value. 
     In a third example embodiment, an audio encoder is described that generates a scalefactor for a scalefactor band using a method that includes, generating a distortion level for a spectrum value selected from a set of spectrum values in the scalefactor band, based on a maximum tolerant distortion threshold for the scalefactor band and the set of spectrum values within the scalefactor band, generating a scalefactor for the selected spectrum value based in part on the distortion level and the selected spectrum value, and generating the scalefactor for the scalefactor band based on the scalefactor generated for the selected spectrum value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Example embodiments of an efficient approach for estimating scalefactors for use in the quantization of audio signal spectrum data will be described with reference to the following drawings, wherein like numerals designate like elements, and wherein: 
         FIG. 1  is a block diagram of an example audio signal encoder architecture that includes example embodiments of the described scalefactor estimation approach; 
         FIG. 2  is an embodiment of a quantization and encoding module shown in  FIG. 1  that includes example embodiments of the described scalefactor estimation approach; 
         FIG. 3  is an embodiment of a scalefactor estimation module shown in  FIG. 2  that includes example embodiments of the described scalefactor estimation approach; 
         FIG. 4  is a flow-chart of an example quantization and encoding process that uses an example embodiment of the described scalefactor estimation approach; 
         FIG. 5  is a flow-chart of a process that uses an example embodiment of the described scalefactor estimation approach; 
         FIG. 6  is a plot of calculated real distortion levels introduced to a stream of encoded audio spectrum values as a result of quantizing the audio spectrum values with scalefactors selected from a set of linearly increasing scalefactors; 
         FIG. 7  is a plot of the calculated real distortion levels shown in  FIG. 6 , and a plot of estimated distortion levels determined using aspects of the described scalefactor estimation approach; 
         FIG. 8  is a plot of scalefactors estimated using aspects of the described scalefactor estimation approach based on real distortion levels calculated for audio spectrum values quantized using scalefactors selected from a set of linearly increasing scalefactors; and 
         FIG. 9  includes a plot of calculated real distortion levels introduced to a stream of encoded audio spectrum values as a result of quantizing the audio spectrum values with a set of linearly increasing scalefactors, a plot of a target distortion threshold to be met by audio spectrum values quantized with an estimated scalefactor, and a plot of a scalefactor selected using the described scalefactor estimation approach. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       FIG. 1  is a block diagram of an example audio signal encoder architecture that includes example embodiments of the described scalefactor estimation approach. As shown in  FIG. 1 , audio signal encoder  100  can include a frequency domain transformation module  102 , a psychoacoustic module  104 , an advanced audio coding encoding module  106 , and a bitstream packing module  108 . As further shown in  FIG. 1 , AAC encoding module  106  can include a signal processing toolset module  110  and a quantization and encoding module  112 . 
     In operation, frequency domain transformation module  102  receives digital, time-domain based, audio signal samples, e.g., pulse-code modulation (PCM) samples, and performs a time-domain to frequency domain transformation, e.g., a Modified Discrete Cosine Transform (MDCT), that results in digital, frequency-based audio signal samples, or audio signal spectrum values, or spectrum values. Frequency domain transformation module  102  arranges these spectrum values into frequency bands, or scalefactor bands, that roughly reflect the Bark scale of the human auditory system. For example, the Bark scale defines 24 critical bands of hearing with frequency band edges located at 20 Hz, 100 Hz, 200 Hz, 300 Hz, 400 Hz, 510 Hz, 630 Hz, 770 Hz, 920 Hz, 1080 Hz, 1270 Hz, 1480 Hz, 1720 Hz, 2000 Hz, 2320 Hz, 2700 Hz, 3150 Hz, 3700 Hz, 4400 Hz, 5300 Hz, 6400 Hz, 7700 Hz, 9500 Hz, 12000 Hz, 18500 Hz. Frequency domain transformation module  102  can group the generated spectrum values in scalefactor bands with similar frequency band edges. 
     Psychoacoustic module  104  receives spectrum values from the frequency domain transformation module  102 , e.g., grouped in scalefactor bands, and processes the respective scalefactor bands based on a psychoacoustic model of human hearing. For example, psychoacoustic module  104  can assess the intensity of the spectrum values within the respective scalefactor bands to determine a maximum level of distortion, or maximum tolerant distortion threshold, that can be introduced to the spectrum values in a scalefactor band by the quantization process without significantly degrading the sound quality of the quantized audio signal. As described below, the maximum tolerant distortion threshold produced by psychoacoustic module  104  for each scalefactor band is used by quantization and encoding module  112  as a control parameter to control aspects of the quantization and encoding process. Further, psychoacoustic module  104  can process the received spectrum values and can remove, e.g., set to 0, spectrum values from the respective scalefactor bands with frequencies and intensities known, based on the psychoacoustic model of human hearing, to be inaudible to the human ear. Such an approach allows psychoacoustic module  104  to improve the data compression that can be achieved by subsequent spectrum values processing, quantization and encoding processes without significantly impacting the quality of the audio signal. 
     Signal processing toolset module  110  receives scalefactor band spectrum values from frequency domain transformation module  102  and receives a maximum tolerant distortion threshold from psychoacoustic module  104  for each received set of scalefactor band spectrum values and provides additional tools that can be used to further process scalefactor band spectrum values to further increase compression efficiency. For example, signal processing toolset module  110  may be configured with tools such as mid-side stereo coding, temporal noise shaping, perceptual noise substitution, and others, that may be combined to produce different encoding profiles based, for example, on the nature and/or characteristics of the received audio signal and a desired audio quality and desired final compression size. For example, in one example embodiment, the signal processing toolset module  110  is configured with a low complexity (LC) toolset, resulting in audio signal encoder  100  being configured as an advanced audio coding low complexity (AAC LC) audio signal encoder. However, signal processing toolset module  110  may be statically or dynamically configured with other signal processing profiles. Such profiles may include additional signal processing tools and/or control parameters to support additional and/or different processing than that supported by the low complexity (LC) toolset. 
     Quantization and encoding module  112  quantizes and encodes received scalefactor band spectrum values based on the maximum tolerant distortion threshold associated with the scalefactor band. Quantization and encoding module  112  can receive scalefactor band spectrum values and maximum tolerant distortion thresholds either directly from frequency domain transformation module  102  and psychoacoustic module  104 , respectively, or can receive scalefactor band spectrum values and maximum tolerant distortion thresholds from signal processing toolset module  110  that have been further processed and modified by one or more signal processing toolsets, as described above. Details related to quantization and encoding module  112  are described in greater detail below with respect to  FIG. 2  and  FIG. 3 . For example, as described below with respect to  FIG. 4 , the quantization and encoding process performed by quantization and encoding module  112  may be performed under the control of a double control processing loop until the resulting encoded data meets the maximum tolerant distortion threshold and target compression size set for the scalefactor band. 
     Bitstream packing module  108  receives control parameters from psychoacoustic module  104  and signal processing toolset module  110  and receives control parameters and encoded data from quantization and encoding module  112  and packs the encoded data, scalefactor bands scalefactors and/or other header/control data within AAC compatible frames. For example, the control parameters and encoded data received from psychoacoustic module  104 , signal processing toolset module  110  and quantization and encoding module  112  may be processed to form a set of predefined syntax elements that are included within each AAC frame. Details related to an example AAC frame format is addressed in detail in ISO/IEC 14496-3:2005 (MPEG-4 Audio). 
       FIG. 2  is one embodiment of quantization and encoding module  112  described above with respect to  FIG. 1 . As shown in  FIG. 2 , quantization and encoding module  112  can include a quantization and encoding controller  202 , a scalefactor estimation module  204 , a quantization module  206 , an encoding module  208 , a distortion threshold constraint module  210  and a bit rate constraint module  212 . As described above with respect to  FIG. 1 , quantization and encoding module  112  quantizes and encodes received scalefactor band spectrum values based on the maximum tolerant distortion threshold associated with the scalefactor band. Details related to operation of quantization and encoding module  112  operating under the control of quantization and encoding controller  202  are described below with respect to  FIG. 4  and  FIG. 5 . 
     In operation, quantization and encoding controller  202  maintains a set of static and/or dynamically updated control parameters that can be used by quantization and encoding controller  202  to invoke the other modules included in quantization and encoding module  112  to perform operations. Examples of such operations, performed in accordance with the control parameters and a set of predetermined process flows, are described below with respect to  FIG. 4  and  FIG. 5 . Quantization and encoding controller  202  may communicate with and receive status updates from the respective modules within quantization and encoding module  112  to allow quantization and encoding controller  202  to control operation of the respective process flows. 
     Scalefactor estimation module  204  can be invoked by quantization and encoding controller  202  to estimate a scalefactor for use in quantizing a received set of scalefactor band spectrum values. The process used by scalefactor estimation module  204  to estimate a scalefactor is described in greater detail at least with respect to  FIG. 5 . As described, scalefactor estimation module  204  is able to efficiently estimate a scalefactor based on a received set of scalefactor band spectrum values and the received scalefactor band maximum tolerant distortion threshold. Quantization is the most performance consuming part in an AAC encoder. Since an AAC encoder uses loss quantization, the quantization increment, i.e., the scalefactor, is crucial to the overall encoding quality. The scalefactor estimation process used by scalefactor estimation module  204  is applied at the scalefactor band level. Therefore the scalefactor estimation process used by scalefactor estimation module  204  is applied multiple times for each channel per frame. As described below, the scalefactor estimation process used by scalefactor estimation module  204  results in approximately a 40% performance improvement over other scalefactor estimation algorithms and yet is capable of consistently producing quantized scalefactor band values with a noise level within the tolerance prescribed by the scalefactor band maximum tolerant distortion threshold associated with the respective scalefactor band values. 
     Quantization module  206  can be invoked by quantization and encoding controller  202  to perform adaptive quantization of scalefactor band spectrum values. Quantization module  206  uses the scalefactor generated by scalefactor estimation module  204  to quantize the received scalefactor band spectrum values in a manner consistent with the maximum tolerant distortion threshold assigned to the scalefactor band. By quantizing each scalefactor band based on a scalefactor specifically selected based on the spectrum values within the scalefactor band and a maximum tolerant distortion threshold selected for the scalefactor band based on an analysis of the spectrum values within the scalefactor band with a psychoacoustic model of human hearing, quantization module  206  is able to tailor the quantization process for each scalefactor band resulting in efficient compression and optimized audio quality at any specified bit rate. 
     Encoding module  208  can be invoked by quantization and encoding controller  202  to apply a predetermined coding scheme to quantized scalefactor band spectrum values to produce encoded scalefactor data. 
     Distortion threshold constrain module  210  can be invoked by quantization and encoding controller  202  to validate whether quantized data produced by quantization module  206  complies with the maximum tolerant distortion threshold imposed by either an external control parameter that reflects an end-user requirement, the psychoacoustic module  104 , or one or more of the signal processing tools included in the encoding profile implemented by signal processing toolset module  110 . If the maximum tolerant distortion threshold is not met, e.g., as described below, additional signal processing by tools within signal processing toolset module  110  may be performed and the quantization process for the set of scalefactor spectrum values is repeated using adjusted control parameters, such as an adjusted global scalefactor, an adjusted maximum tolerant distortion threshold and/or a new estimated scalefactor. 
     Bit rate constraint module  212  can be invoked by quantization and encoding controller  202  to validate whether encoded data produced by encoding module  208  complies with a bit constraint imposed by either an external control parameter that reflects an end-user requirement, or a bit constraint imposed by one or more of the signal processing tools included in the encoding profile implemented by signal processing toolset module  110 . If a bit constraint is not met, e.g., as described below, additional signal processing by tools within signal processing toolset module  110  may be performed and the quantization process and the encoding process for the set of scalefactor spectrum values is repeated using adjusted control parameters, such as an adjusted global scalefactor, an adjusted maximum tolerant distortion threshold and/or a new estimated scalefactor. 
       FIG. 3  is one embodiment of the scalefactor estimation module  204  shown in  FIG. 2 . The scalefactor estimation module  204  is used to implement embodiments of the described scalefactor estimation approach, detail of which are described below with respect to equation [1] through equation [4] and with respect to  FIG. 4  and  FIG. 5 . As shown in  FIG. 3 , scalefactor estimation module  204  can include a scalefactor estimation controller  302 , a spectrum difference generating module  304 , a temporary value generating module  306 , a spectrum value scalefactor generating module  308 , and a spectrum band scalefactor generating module  310 . 
     In operation, scalefactor estimation controller  302  maintains a set of static and/or dynamically updated control parameters that can be used by scalefactor estimation controller  302  to invoke the other modules included in scalefactor estimation module  204  to perform operations, as described below, in accordance with the control parameters and predetermined process flows, such as the example process flow described below with respect to  FIG. 5 . Scalefactor estimation controller  302  may communicate with quantization and encoding controller  202 , described above, to receive control parameters and to report status. Further, scalefactor estimation controller  302  may communicate with and receive status updates from the respective modules of scalefactor estimation module  204  to allow scalefactor estimation controller  302  to control operation of the scalefactor estimation process. As described below with respect to equations [1] through [4], the scalefactor estimation process can be implemented in multiple stages, each stage relying upon an output generated by a previous stage. In  FIG. 3  and  FIG. 5 , the scalefactor estimation process is described as a 4-stage process; however, different embodiments may implement the scalefactor estimation process with any number of stages consistent with the described approach, for example, by combining multiple stages into a single stage, or by splitting a single stage into multiple stages. 
     Spectrum difference generating module  304  can be invoked by scalefactor estimation controller  302  to perform a first stage of the scalefactor estimation process in which a distortion level, or difference Diff k , for a selected scalefactor band spectrum value is determined based on a received maximum tolerant distortion threshold and a sum of the spectrum values in the scalefactor band. For example, an equation that may be implemented by spectrum difference generating module  304  to achieve such a result based on such input values is represented at equation [1] below. 
                       Diff   k   2     =       Distortion   sfb     *              X   ⁡     (   k   )              1   2       /       ∑     k   =   1     n     ⁢            X   ⁡     (   k   )              1   2               ⁢     
     ⁢       X   ⁡     (   k   )       ≠   0             [     EQ   .           ⁢   1     ]               
A derivation and further explanation of equation [1] is provided with respect to the derivation of equation [24] below.
 
     Temporary value generating module  306  can be invoked by scalefactor estimation controller  302  to initiate a second stage of the scalefactor estimation process by generating an interim process value based on the difference generated by the spectrum difference generating module  304 , as described above, and based on the selected scalefactor band spectrum value for which the difference was obtained. For example, an equation that may be implemented by temporary value generating module  306  to achieve such a result based on such input values is represented at equation [2] below. 
                   a   =     3   *     (         (     1   +     0.5   *       Diff   k            X   ⁡     (   k   )                  )       1   2       -   1     )               [     Eq   .           ⁢   2     ]               
A derivation and further explanation of equation [2] is provided with respect to the derivation of equation [17] below.
 
     Spectrum value scalefactor generating module  308  can be invoked by scalefactor estimation controller  302  to complete the second stage of the scalefactor estimation process by generating a scalefactor for the selected scalefactor band spectrum value based on the interim process value generated by the temporary value generating module  306 , as described above, and based on a predetermined fraction. In one embodiment, this predetermined fraction, for example, may be a common predetermined fraction associated with each of the scalefactor band spectrum values in a scalefactor band. In another embodiment, the predetermined fraction may be a value which has been statistically pre-determined based on the scalefactor band spectrum values themselves and/or can be a predetermined value associated with the scalefactor band by the AAC encoding profile being implemented. For example, an equation that may be implemented by spectrum value scalefactor generating module  308  to achieve such a result based on such input values is represented at equation [3] below. 
                     Scf   ⁢           ⁢   1     =            X   ⁡     (   k   )            *       (     a   fraction     )       4   3                 [     EQ   .           ⁢   3     ]               
A derivation and further explanation of equation [3] is provided with respect to equation [16] below.
 
     Spectrum band scalefactor generating module  310  can be invoked by scalefactor estimation controller  302  to perform a third stage of the scalefactor estimation process in which a scalefactor for a scalefactor band is generated based on the scalefactor generated by spectrum value scalefactor generating module  308  for the selected scalefactor band spectrum value. For example, an equation that may be implemented by spectrum band scalefactor generating module  310  to achieve such a result based on such an input value is represented at equation [4] below.
 
 Scf= 4*log 2 ( Scf 1)  [EQ. 4]
 
A derivation and further explanation of equation [4] is provided with respect to the derivation of equation [7] below.
 
       FIG. 4  is a flow-chart of an example quantization and encoding process that may be implemented by audio signal encoder  100  with the support of quantization and encoding module  112  and scalefactor estimation module  204 , as described above with respect to  FIG. 1  through  FIG. 3 . As shown in  FIG. 4 , operation of process  400  begins at S 402  and proceeds to S 404 . 
     At S 404 , frequency domain transformation module  102  receives digital, time-domain based, audio signal samples, e.g., pulse-code modulation samples, and operation of the process continues at S 406 . 
     At S 406 , frequency domain transformation module  102  performs a time-domain to frequency-domain transformation, e.g., a modified discrete cosine transform, on the received digital, time-domain based, audio signal samples that results in digital, frequency-based audio signal samples, or audio signal spectrum values, or spectrum values, and operation of the process continues at S 408 . 
     At S 408 , frequency domain transformation module  102  arranges the spectrum values into frequency bands, or scalefactor bands, that reflect the Bark scale of the human auditory system, and operation of the process continues at S 410 . 
     At S 410 , psychoacoustic module  104  receives/selects a first/next set of scalefactor band spectrum values from frequency domain transformation module  102 , and operation of the process continues at S 412 . 
     At S 412 , psychoacoustic module  104  processes the set of scalefactor band spectrum values to eliminate inaudible data and to generate a maximum tolerant distortion threshold for the scalefactor band based on a psychoacoustic model of human hearing, and operation of the process continues at S 414 . 
     At S 414 , signal processing toolset module  110  can apply one or more signal processing techniques associated with a selected AAC encoding profile, e.g., the AAC low complexity profile, to support further compression of the scalefactor band spectrum values and/or to further refine the maximum tolerant distortion threshold for the scalefactor band, and operation of the process continues at S 416 . 
     At S 416 , scalefactor estimation module  204  can be invoked by quantization and encoding module  112  to generate an estimated scalefactor for the currently selected scalefactor band based on received scalefactor band spectrum values and the associated scalefactor band maximum tolerant distortion threshold, as described above with respect to  FIG. 3 , and operation of the process continues at S 418 . 
     At S 418 , quantization module  206  can be invoked by quantization and encoding module  112  to quantize the scalefactor band spectrum values associated with the currently selected scalefactor band based on the estimated scalefactor generated at S 416 , and operation of the process continues at S 420 . 
     At S 420 , distortion threshold constraint module  210  can be invoked by quantization and encoding module  112  to determine whether the quantized scalefactor band spectrum values have introduced a level of distortion that exceeds the maximum tolerant distortion threshold for the scalefactor band. For example, distortion threshold constraint module  210  may generate a difference between an inverse quantized spectrum value and a corresponding quantized spectrum value produced by quantization module  206  at S 418 , above, e.g., as described below with respect to equation [25] through [27]. If the maximum tolerant distortion threshold is met, operation of the process continues at S 422 ; otherwise, operation of the process continues at S 414 . 
     At S 422 , encoding module  208  can be invoked by quantization and encoding module  112  to encode the quantized scalefactor band spectrum values generated by quantization module  206  at S 418 , and operation of the process continues at S 424 . 
     At S 424 , bit rate constraint module  212  can be invoked by quantization and encoding module  112  to determine whether the encoded, quantized scalefactor band spectrum values meet a bit rate constraint imposed on the scalefactor band by, for example, an external control parameter that reflects an end-user requirement, or a bit constraint imposed by one or more of the signal processing tools included in the encoding profile implemented by signal processing toolset module  110 . If the bit constrain is met, operation of the process continues at S 426 ; otherwise, operation of the process continues at S 414 . 
     At S 426 , if the last scalefactor band generated by frequency domain transformation module  102  at S 408  has been quantized and encoded, operation of the process terminates at S 428 ; otherwise, operation of the process continues at S 410 . 
       FIG. 5  is a flow-chart of an example scalefactor estimation process that may be implemented by scalefactor estimation module  204 , as described above with respect to  FIG. 3 . As shown in  FIG. 5 , operation of process  500  begins at S 502  and proceeds to S 504 . 
     At S 504 , scalefactor estimation controller  302  receives from quantization and encoding controller  202 , scalefactor band spectrum values and a maximum tolerant distortion threshold for the scalefactor band, and operation of the process continues at S 506 . 
     At S 506 , scalefactor estimation controller  302  selects a scalefactor band spectrum value from the set of received scalefactor band spectrum values, and operation of the process continues at S 508 . 
     At S 508 , spectrum difference generating module  304  is invoked by scalefactor estimation controller  302  to perform a first stage of the scalefactor estimation process in which a distortion level, or difference, for the selected scalefactor band spectrum value is determined based on the received maximum tolerant distortion threshold and a sum of the spectrum values in the scalefactor band, as described above with respect to  FIG. 3 , and operation of the process continues at S 510 . 
     At S 510 , temporary value generating module  306  can be invoked by scalefactor estimation controller  302  to initiate a second stage of the scalefactor estimation process by generating an interim process value based on the difference generated at S 508 , and as described above with respect to  FIG. 3 , and operation of the process continues at S 512 . 
     At S 512 , spectrum value scalefactor generating module  308  is invoked by scalefactor estimation controller  302  to complete the second stage of the scalefactor estimation process by generating a scalefactor for the selected scalefactor band spectrum value based on the interim process value generated at S 510 , and as described above with respect to  FIG. 3 , and operation of the process continues at S 514 . 
     At S 514 , spectrum band scalefactor generating module  310  is invoked by scalefactor estimation controller  302  to perform a third stage of the scalefactor estimation process in which a scalefactor for the scalefactor band is generated based on the scalefactor generated for the selected scalefactor band spectrum value at S 512 , and as described above with respect to  FIG. 3 , and operation of the process terminates at S 516 . 
     The derivation of equations [1] through equation [4] described above with respect to  FIG. 3  and  FIG. 5  is described below with respect to equation [5] to equation [27]. The derivation of equations [1] through equation [4] are based on algorithms defined in advance audio coding (AAC) ISO/IEC 14496-3, which states that the quantization and inverse quantization formulas used by an AAC encoder can be simplified to equation [5] and equation [6], provided below. 
     
       
         
           
             
               
                 
                   
                     
                       X 
                       quant 
                     
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                     . 
                     
                         
                     
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                     5 
                   
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     Where X quant (k) is the quantized spectrum; and,
         MAGIC_NUMBER=0.4054       

     
       
         
           
             
               
                 
                   
                     
                       X 
                       invquant 
                     
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                       k 
                       ) 
                     
                   
                   = 
                   
                     
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     Where X invquant (k) is the reconstructed spectrum. 
     To begin the derivation process, the scalefactor band spectrum values are limited to positive values, and the relationship between the scalefactor for a spectrum value within a scalefactor band and the scalefactor for the scalefactor band as a whole is assumed to be provided by equation [7] below. 
     
       
         
           
             
               
                 
                   
                     Scf 
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                       ⁢ 
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                       ⁢ 
                       is 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       equivalent 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       to 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Scf 
                     
                     = 
                     
                       4 
                       * 
                       
                         
                           log 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           
                             Scf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     Where Scf1 is the scalefactor for a selected spectrum value within the scalefactor band; and, 
     Scf is the scalefactor for the scalefactor band as a whole 
     In this case, equations [5] and [6] above may be rewritten as equations [8] and [9] below. 
     
       
         
           
             
               
                 
                   
                     
                       X 
                       quant 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     int 
                     ⁢ 
                     
                       { 
                       
                         
                           
                             ( 
                             
                               
                                 
                                   X 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 / 
                                 Scf 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             ) 
                           
                           
                             3 
                             4 
                           
                         
                         + 
                         MAGIC_NUMBER 
                       
                       } 
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       X 
                       invquant 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             X 
                             quant 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         ) 
                       
                       
                         4 
                         3 
                       
                     
                     * 
                     Scf 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
     Because int(x+MAGIC_NUMBER)=x+fraction, equation [8] can be rewritten as is changed to 
     
       
         
           
             
               
                 
                   
                     
                       X 
                       quant 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               X 
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             / 
                             Scf 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         ) 
                       
                       
                         3 
                         4 
                       
                     
                     + 
                     fraction 
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
     Further, by defining Diff as the difference between X invquant (k) and X(k), based on equation [8] and [9], Diff may be written in equation form as shown below in equation [11]. 
     
       
         
           
             
               
                 
                   Diff 
                   = 
                   
                     
                        
                       
                         
                           
                             X 
                             invquant 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         - 
                         
                           X 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                        
                     
                     = 
                     
                       
                          
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     X 
                                     quant 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ) 
                               
                               
                                 4 
                                 3 
                               
                             
                             * 
                             Scf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           - 
                           
                             X 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                          
                       
                       = 
                       
                          
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           
                                             X 
                                             ⁡ 
                                             
                                               ( 
                                               k 
                                               ) 
                                             
                                           
                                           / 
                                           Scf 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         1 
                                       
                                       ) 
                                     
                                     
                                       3 
                                       4 
                                     
                                   
                                   + 
                                   fraction 
                                 
                                 ) 
                               
                               
                                 4 
                                 3 
                               
                             
                             * 
                             Scf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           - 
                           
                             X 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                          
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     Newton&#39;s generalized binomial theorem is presented at equation [12] below. 
                       (     a   +   1     )       4   3       =         (     a   +   1     )     *       (     a   +   1     )       1   3         =       (     a   +   1     )     *     (     1   +       1   3     ⁢   a     -       1   9     ⁢     a   2       +       5   81     ⁢     a   3       -       10   243     ⁢     a   4       +   …     ⁢           )                 [     EQ   .           ⁢   12     ]               
If |a|&lt;1, the high exponent items can be truncated, and an approximation of equation [12] is
 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         a 
                         + 
                         1 
                       
                       ) 
                     
                     
                       4 
                       3 
                     
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         4 
                         3 
                       
                       ⁢ 
                       a 
                     
                     + 
                     
                       
                         2 
                         9 
                       
                       ⁢ 
                       
                         a 
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
     Therefore, the Diff calculation in equation [11] can be transformed to 
     
       
         
           
             
               
                 
                   Diff 
                   = 
                   
                     
                       
                         
                           X 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         * 
                         
                           
                             ( 
                             
                               1 
                               + 
                               a 
                             
                             ) 
                           
                           
                             4 
                             3 
                           
                         
                       
                       - 
                       
                         X 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     = 
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       * 
                       
                         ( 
                         
                           
                             
                               4 
                               3 
                             
                             ⁢ 
                             a 
                           
                           + 
                           
                             
                               2 
                               9 
                             
                             ⁢ 
                             
                               a 
                               2 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     Where 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     a 
                   
                   &gt; 
                   0 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         2 
                         9 
                       
                       ⁢ 
                       
                         a 
                         2 
                       
                     
                     + 
                     
                       
                         4 
                         3 
                       
                       ⁢ 
                       a 
                     
                     - 
                     
                       Diff 
                       
                         X 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                   = 
                   0 
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     Where 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     a 
                   
                   = 
                   
                     fraction 
                     * 
                     
                       
                         ( 
                         
                           Scf 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             1 
                             / 
                             
                               X 
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                       
                         3 
                         4 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
     Since |fraction|&lt;1, if a positive fraction is chosen and 0&lt;Scf1/X(k)&lt;1, 0&lt;a&lt;1 is fulfilled. Therefore, the positive root of equation [15] is 
     
       
         
           
             
               
                 
                   a 
                   = 
                   
                     3 
                     * 
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 0.5 
                                 * 
                                 
                                   Diff 
                                   
                                     X 
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ) 
                           
                           
                             1 
                             2 
                           
                         
                         - 
                         1 
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     17 
                   
                   ] 
                 
               
             
           
         
       
     
     Therefore, based on equation [17] if we know Diff for a spectrum value X(k), we can determine a based on equation [17], and further, we can determine a scalefactor for the spectrum value X(k) based on equation [16] by equation [7], 
     
       
         
           
             
               Scf 
               ⁢ 
               
                   
               
               ⁢ 
               1 
             
             = 
             
               
                 2 
                 
                   Scf 
                   4 
                 
               
               . 
             
           
         
       
     
     From the description above with respect to equations [5]-[17] the mathematical relationship between Diff and a scalefactor for a spectrum value X(k) within a scalefactor band is described. Equations [18]-[24] describe how to determine the Diff for each spectrum value based on the scalefactor band maximum tolerant distortion threshold, Distortion sfb . For example, for each scalefactor band, the following two constrains are always true: 
     
       
         
           
             
               
                 
                   
                     
                       1 
                       ) 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       Distortion 
                       
                         
                             
                         
                         ⁢ 
                         sfb 
                       
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         n 
                       
                       ⁢ 
                       
                         Distortion 
                         
                           
                               
                           
                           ⁢ 
                           k 
                         
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         n 
                       
                       ⁢ 
                       
                         Diff 
                         k 
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ] 
                 
               
             
           
         
       
     
     Where Distortion sfb  is the scalefactor band maximum tolerant distortion threshold for the whole scalefactor band; 
     Distortion k  is the distortion at each spectrum value X(k); and 
     n is the number of spectrum values in the scalefactor band. 
     A second constraint assumes that for all spectrum values in a common scalefactor band, a single uniform scalefactor is used, as shown in equation [19] below
 
2)  Scf   1   =Scf   2   = . . . =Scf   n   [EQ. 19]
 
     Therefore, based on equation [19], i.e., constraint #2, and equation [7], i.e., 
                 Scf   ⁢           ⁢   1     =     2     Scf   4         ,         
above, we have Scf1 1 =Scf1 2 = . . . =Scf1 n , which states that the scalefactor for each scalefactor band value within a scalefactor band can be assumed to be the same.
 
     Assuming that that the parameter fraction is the same value for all spectrum values and is chosen based on statistical analysis, as described above, equation [14] can be rewritten as 
     
       
         
           
             
               
                 
                   
                     Diff 
                     k 
                   
                   = 
                   
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       * 
                       
                         4 
                         3 
                       
                       * 
                       a 
                     
                     = 
                     
                       
                         
                           X 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         * 
                         
                           4 
                           3 
                         
                         * 
                         fraction 
                         * 
                         
                           
                             ( 
                             
                               Scf 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 1 
                                 / 
                                 
                                   X 
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                           
                             3 
                             4 
                           
                         
                       
                       = 
                       
                         
                           4 
                           3 
                         
                         ⁢ 
                         fraction 
                         * 
                         Scf 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           1 
                           
                             3 
                             4 
                           
                         
                         * 
                         
                           
                             X 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           
                             1 
                             4 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ] 
                 
               
             
           
         
       
     
     Assuming 
               Coeff   =       4   3     ⁢   fraction   *   Scf   ⁢           ⁢     1     3   4           ,         
equation [20] can be rewritten as
 
                     Diff   k     =     coeff   *       X   ⁡     (   k   )         1   4                 [     EQ   .           ⁢   21     ]               
Where
 
               Coeff   =       4   3     ⁢   fraction   *   Scf   ⁢           ⁢     1     3   4           ,         
for all spectrum Coeff 1 =Coeff 2 = . . . =Coeff n =Coeff
 
     According to equation [18], above, 
                 Distortion   sfb     =       ∑     k   =   1     n     ⁢     Diff   k   2         ,         
therefore,
 
                     Distortion   sfb     =         ∑     k   =   1     n     ⁢     Diff   k   2       =         ∑     k   =   1     n     ⁢       coeff   k   2     *       X   ⁡     (   k   )         1   2           =       Coeff   2     *       ∑     k   =   1     n     ⁢       X   ⁡     (   k   )         1   2                       [     EQ   .           ⁢   22     ]               
And hence,
 
     
       
         
           
             
               
                 
                   
                     Coeff 
                     2 
                   
                   = 
                   
                     
                       Distortion 
                       sfb 
                     
                     / 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         n 
                       
                       ⁢ 
                       
                         
                           X 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         
                           1 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   ] 
                 
               
             
           
         
       
     
     From equation [20] and equation [23], above, 
     
       
         
           
             
               
                 
                   
                     Diff 
                     k 
                     2 
                   
                   = 
                   
                     
                       
                         Coeff 
                         2 
                       
                       * 
                       
                         
                           X 
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         
                           1 
                           2 
                         
                       
                     
                     = 
                     
                       
                         Distortion 
                         sfb 
                       
                       * 
                       
                         
                           
                             X 
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           
                             1 
                             2 
                           
                         
                         / 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               1 
                             
                             n 
                           
                           ⁢ 
                           
                             
                               X 
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             
                               1 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     24 
                   
                   ] 
                 
               
             
           
         
       
     
     Since the right side parameters for equation [24] are all known, if we chose a non-zero spectrum value X(k), Diff k  can be calculated. By combining equation [24] with equation [17], [16], and [7], as described above with respect to equation [1] through equation [4], and the final scalefactor for the scalefactor band can be determined. 
     In the equations above, the spectrum values X(k) are assumed to be positive numbers. However, if the spectrum values X(k) are negative, equation [5] and [6] can be rewritten as equation [25] and equation [26], below. 
     
       
         
           
             
               
                 
                   
                     
                       X 
                       quant 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         int 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               ( 
                               
                                 
                                   
                                      
                                     
                                       X 
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                   
                                   / 
                                   Scf 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                               ) 
                             
                             
                               3 
                               4 
                             
                           
                           + 
                           MAGIC_NUMBER 
                         
                         } 
                       
                     
                     = 
                     
                       - 
                       
                         
                           X 
                           quant 
                           ′ 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     25 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     
                       X 
                       inquant 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             ( 
                             
                                
                               
                                 
                                   X 
                                   quant 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             ) 
                           
                           
                             4 
                             3 
                           
                         
                       
                       * 
                       Scf 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                     = 
                     
                       
                         
                           - 
                           
                             
                               ( 
                               
                                  
                                 
                                   
                                     X 
                                     quant 
                                     ′ 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                  
                               
                               ) 
                             
                             
                               4 
                               3 
                             
                           
                         
                         * 
                         Scf 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                       = 
                       
                         - 
                         
                           
                             X 
                             inquant 
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     EQ 
                     . 
                     
                         
                     
                     ⁢ 
                     26 
                   
                   ] 
                 
               
             
           
         
       
     
     Where X′ quant (k) is the quantization result for X′(k)=abs(X(k)), and
         X′ invquant (k) is the inverse quantization result for X′(k)=abs(X(k)).       

     Based on equation [11] we know that Diff=|X invquant (k)−X(k)|, therefore,
 
Diff=| X   invquant ( k )− X ( k )|=|− X′   invquant ( k )−(− X ′( k ))|=| X′   invquant ( k )− X ′( k )|  [EQ. 27]
 
and it follows the mathematic model is also suitable for all negative spectrum value X(k). Therefore, abs(X(k)) may be used to replace X(k) in all equations.
 
       FIG. 6  is a plot of real distortion levels  602  introduced to a stream of encoded audio spectrum values as a result of quantizing the audio spectrum values with scalefactors selected from a set of linearly increasing scalefactors. As shown in  FIG. 6 , distortion levels (represented on the y-axis) in quantized data increases when larger scalefactors (represented on the x-axis) are used in the quantization process. 
       FIG. 7  is a plot of the real distortion levels  602  shown in  FIG. 6 , and a plot of estimated distortion levels  702  determined using aspects of the described scalefactor estimation approach. For example, the estimated distortion levels show at  702  may be estimated based on equation [14], described above. 
       FIG. 8  is a plot of estimated scalefactors  802  (represented on the y-axis), estimated using aspects of the described scalefactor estimation approach based on distortion levels calculated for audio spectrum values quantized using scalefactors (represented on the x-axis) selected from a set of linearly increasing scalefactors  804 . As demonstrated in  FIG. 8 , scalefactors can be effectively estimated from distortion levels, as described above with respect to equation [1] through equation [4]. 
       FIG. 9  includes a plot of calculated real distortion levels  902  introduced to a stream of encoded audio spectrum values as a result of quantizing the audio spectrum values with a set of linearly increasing scalefactors, a plot of a target distortion threshold  904  to be met by audio spectrum values quantized with an estimated scalefactor, and a plot of an estimated scalefactor  906  determined using the described scalefactor estimation approach. As shown in  FIG. 9 , an estimated scalefactor, estimated using the described approach and shown in  FIG. 9  as a single point at  906 , will introduce a level of distortion to quantized data that is below the prescribed maximum tolerant distortion threshold  904 . 
     It is noted that the scalefactor estimation approach, described above, can be used by a wide range of frequency-domain audio encoders, such as the advance audio coding (AAC) encoder and the MP3 encoder. 
     For purposes of explanation in the above description, numerous specific details are set forth in order to provide a thorough understanding of the described embodiments of an efficient approach for estimating scalefactors for use in the quantization of audio signal spectrum values. It will be apparent, however, to one skilled in the art based on the disclosure and teachings provided herein that the described embodiments may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to avoid obscuring the features of the described embodiments. 
     While the embodiments of an efficient approach for estimating scalefactors for use in the quantization of audio signal spectrum values have been described in conjunction with the specific embodiments thereof, it is evident that many alternatives, modifications, and variations will be apparent to those skilled in the art. Accordingly, the described embodiments, as set forth herein, are intended to be illustrative, not limiting. There are changes that may be made without departing from the spirit and scope of the invention.