JP2016024450A - Arithmetic device and sound encoding system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an arithmetic device capable of doing high-accuracy approximation when an arithmetic for approximating a logarithmic function is included in an arithmetic process, and a sound encoding system using this arithmetic device.SOLUTION: The present invention is an arithmetic device including an arithmetic unit for performing arithmetic on a function that approximates a function, as the object of approximation, that includes a logarithmic function. The arithmetic unit approximates a function that is the object of approximation by a diode function that does not exceed a function value connecting a plurality of points on said function with a line segment and constituting the object of approximation. The arithmetic unit finds a plurality of points at which an approximation error derived by subtracting, from the function that is the object of approximation, the diode function obtained by connecting a plurality of points on said function is minimum, and finds a diode function that does not exceed the plurality of points as the end points of the respective line segment of the diode function.SELECTED DRAWING: Figure 4

Description

  The present invention relates to an arithmetic device that approximates and calculates a function including a logarithmic function, and a sound encoding system that uses adaptive differential pulse code modulation (ADPCM) to which the arithmetic device is applied.

  When transmitting sound, such as a mobile phone or a wireless microphone, a method is adopted in which analog sound is digitized and compressed into a digital sound signal for transmission. As a digital audio signal compression method, many methods utilizing the property of high correlation between adjacent samples of digital audio have been proposed, such as DPCM (Differential Pulse Code Modulation) method and ADPCM method. It has been known.

  In the case of a speech encoding system using any method, a speech encoding device that encodes input speech and a speech decoding device that decodes the encoded speech are provided. In any of the methods, in the speech coding apparatus, a prediction error is obtained by the difference between the sampled actual digital speech and the predicted value, and the prediction error is quantized and encoded, and then the speech decoding apparatus via the transmission path. Transmit to. In the speech decoding apparatus, the input speech is reproduced by adding the speech obtained by decoding the encoded signal and the predicted value of the sampled actual digital speech. As described above, each of the systems transmits only difference information and restores the input voice at the transmission destination. Therefore, there is an advantage that the amount of information to be transmitted can be reduced.

  On the other hand, there are the following differences between the DPCM method and the ADPCM method. That is, in the DPCM method, the prediction error is a difference between the sampled sample value at the current time and the previous sample value. This difference value is quantized in a certain quantization unit. The speech decoding apparatus reproduces speech by adding digital speech delayed by one sample time from the current time to the transmitted and decoded prediction error.

  On the other hand, in the ADPCM system, ITU-T G.I. As represented by 726, since the level of the audio signal fluctuates with time, it is more adaptive while changing the step size according to the level of the audio level, rather than quantizing with a constant quantization unit when quantizing. Quantize. That is, a speech signal with a large level is roughly quantized with a large step size, and a speech signal with a small level is finely quantized with a small step size. By doing so, it is possible to reduce the quantization error that occurs at the time of quantization, and it is possible to reproduce the voice more accurately.

JP-A-11-150480 International Publication No. 2004/112256

By the way, ITU-TG In a speech encoding system using a conventional ADPCM method represented by 726, the absolute value x of the prediction error is logarithmized when the prediction error is encoded. At that time, degrades the logarithm to the integer part x _e and fraction x _m. That _{is, log 2 x = x e + x} m, seeking an integer part _{x e} and fraction _{x m.} Here, the integer part x _e is ^obtained by comparing the magnitudes of x and 2 ^k from k = 0 and obtaining the maximum exponent k by 2 ^{k that} does not exceed x. On the other hand, the decimal part x _m is obtained by approximating x _m = log ₂ (1 + x _m ) from the viewpoint of reducing the amount of calculation.

  However, since this approximation is made from the viewpoint of reducing the amount of calculation, it is not always accurate. Therefore, in a speech encoding system using the conventional ADPCM method, there is a possibility that the sound quality of the reproducible speech may be deteriorated.

  Further, such approximation with poor accuracy is not limited to the above approximation method, and can be similarly performed for a general arithmetic device that approximates a logarithmic function in an arithmetic process.

  The present invention has been made in order to solve the above-described problems. When the calculation process includes an operation for approximating a logarithmic function, an arithmetic device capable of approximating with high accuracy and the arithmetic device are used. It is to provide a sound encoding system.

An arithmetic device of the present invention is an arithmetic device including an arithmetic unit that approximates and calculates a function including a logarithmic function, and has the following configuration.
(1) The calculation unit approximates the function to be approximated by a line function that does not exceed the function value to be approximated by connecting a plurality of points on the function by line segments.

Moreover, you may make it provide the following structure.
(2) The calculation unit obtains a plurality of points where the approximation error is minimized by subtracting a polygonal line function obtained by connecting a plurality of points on the function with line segments from the function to be approximated, Find a line function that does not exceed a point as the end point of each line segment of the line function.

An arithmetic device of the present invention is an arithmetic device including an arithmetic unit that approximates and calculates a function including a logarithmic function, and has the following configuration.
(3) The calculation unit approximates the function to be approximated by a line function that does not fall below the function value to be approximated by connecting a plurality of points on the function with line segments.

Moreover, you may make it provide the following structure.
(4) A polygonal line function that does not fall is a tangent line in which each line segment has a contact point with the function to be approximated as the plurality of points within the domain of definition, and the calculation unit defines the contact point as a line segment on which the contact point is placed. Find the approximation error with the function to be approximated by the two adjacent line segments.

An arithmetic device of the present invention is an arithmetic device including an arithmetic unit that approximates and calculates a function including a logarithmic function, and has the following configuration.
(5) The calculation unit approximates the function to be approximated by a polygonal line function including a line segment that intersects with the function, and the polygonal line function includes the end points (x _n , y _n ) and (x _{n + 1} , y _{n + 1).} a line segment _{S n} with) represented by the formula (31), the division error evaluation function _{E S} according to the line segment _{S n} when expressed in equation (32), minimizes the error evaluation function E of equation (33) What you get when you do.

Furthermore, the sound encoding system of the present invention is characterized by having the following configuration.
(6) An encoding device that encodes the input sound, a decoding device that decodes the input sound code, and a transmission medium that transmits the sound code output by the encoding device to the decoding device. The encoding device and the decoding device each include an arithmetic device having any one of the configurations (1) to (5).

Moreover, you may make it provide the following structure.
(7) The encoding device and the decoding device, as an arithmetic device having any one of the configurations (1) to (5) described above, a prediction error that is a difference between the sound information and a predicted value of the sound information, and the prediction An adaptive normalization unit that obtains a normalized prediction error obtained by normalizing the prediction error based on the prediction value of the error, and the adaptive normalization unit uses a logarithm of the absolute value of the prediction error as a function for obtaining the normalized prediction error. Including functions.

  According to the present invention, it is possible to obtain an arithmetic device capable of improving the approximation accuracy and a sound encoding system to which the arithmetic device is applied.

It is a figure which shows the whole structure of the sound coding system which concerns on 1st Embodiment. It is a figure which shows schematic structure of the encoder and decoder which concern on 1st Embodiment. It is a figure which shows the adaptive normalization part which concerns on 1st Embodiment. It is a graph for demonstrating the broken line approximation which does not exceed. It is a graph for demonstrating the broken line approximation which is not less than. It is the graph which plotted the square mean value of the approximation error with respect to the number of line segments or the number of nodes on the logarithmic axis. It is an operation | movement flowchart of an encoding apparatus. It is an operation | movement flowchart of a decoding apparatus.

  Hereinafter, a sound encoding system according to an embodiment of the present invention will be described with reference to the drawings.

[1. First Embodiment]
[1-1. Schematic configuration]
FIG. 1 is a diagram showing an overall configuration of a sound encoding system according to the present embodiment. The present sound encoding system includes an encoding device 10, a decoding device 20, and a transmission medium 30 for transmitting encoded sound information.

  The encoding device 10 encodes a sound or a digital signal that is an analog signal input from the outside of the system, and outputs it as information including a sound code. The encoding device 10 and the decoding device 20 are connected via a transmission medium 30, and the transmission medium 30 transmits information including a sound code output from the encoding device 10 to the decoding device 20. The decoding device 20 decodes information including the sound code transmitted from the encoding device 10 into an analog signal and outputs the analog signal to the outside of the system. The present sound encoding system can be used for a wireless microphone system, for example.

[1-2. Configuration of each part]
(Encoding device)
The encoding device 10 includes a user interface UI11, an external connection I / F 12, a control unit 13, a storage unit 14, a sound input I / F 15, an encoder 16, and a code output I / F 17.

  The user interface UI11 has an operation input unit and a status output unit (not shown), and provides an interface between the system and the user. The operation input unit detects an operation requested by the user with a detector such as a switch or a motion sensor, and transmits the operation to the control unit 13. The status output unit outputs the internal status of the apparatus by a display device such as an LED or LCD, vibration by a vibrator, sound output by a speaker, and the like, and gives feedback to the user.

  As an output of the internal state, for example, a parameter used for driving an encoder 16 described later can be displayed on a display. In addition, when changing to a parameter suitable for the sound source according to a user's request because the sound source input to the system is changed, the operation input unit accepts a user desired parameter and sends it to the control unit 13 as a control signal. The parameters of each part of the system are changed by the control unit 13 triggered by the input of the signal to the control unit 13. Note that only one of the operation input unit or the state output unit may be mounted on the user interface UI11. Further, the operation input unit may include a touch panel and a display, display a plurality of parameters stored in the storage unit 14, and accept a parameter selection by the user, or drive the encoder 16 on the display. The parameters used may also be displayed. The parameter may be displayed by displaying an identifier that uniquely corresponds to the parameter, or by dividing the display into each processing unit in the encoder 16.

  The external connection I / F 12 provides an interface with an external connection device. A connection medium between the external connection I / F 12 and the external connection device is wired or wireless. An external connection device that can acquire the internal state of the system via the external connection I / F 12 and can perform operation control is used. Examples of the external connection device include a computer and a mobile terminal. The external connection device may have parameters used in the processing unit inside the encoder 16, and the parameters may be input and stored in the storage unit 13 via the external connection I / F 12. Note that the external connection device may hold the parameter in advance, or may be generated separately from the acquired internal state of the system. Further, the external connection device may acquire parameters of the processing unit in the encoder 16, and may further hold the parameters and use them for input to the storage unit 13.

  The control unit 13 is connected to the user interface UI11, the external connection I / F 12, the storage unit 14, the sound input I / F 15, the encoder 16, and the code output I / F 17, and functions as a control unit. That is, the control unit 13 performs management of the internal state of the system, operation control of each unit, and communication with the external connection I / F 12, the sound input I / F 15, and the code output I / F 17.

  The control unit 13 resets the internal state of each part of the system at startup. Further, the internal state designated in advance may be reset by a request from each unit or detection of a specific internal state, and the entire system or a predetermined part may be restarted. Further, a predetermined parameter may be dynamically updated by referring to a predetermined parameter from the storage unit 14 based on a request from each unit or detection of a specific internal state. The request from each unit includes at least one of a request from the user via the user interface UI11, a request from the external connection device, and a request from the processing unit. Further, it is confirmed whether the parameters including the parameters dynamically input from the outside are valid, or whether the parameters common to the encoder 16 and the decoder 26 described later are consistent, and the confirmation result is notified to each unit. May be.

  The control unit 13 generates a periodic timing for each unit to input and output sound, sound information, and sound code, and gives the timing to each unit. Alternatively, in addition to the periodic timing, a predetermined timing necessary for the operation of each unit may be generated. The control unit 13 accumulates general information such as sound information and sound codes in the storage unit 14 and transfers the accumulated information from the storage unit 14 to each unit.

  The storage unit 14 stores a plurality of types of parameters that determine the internal state and the operation of each unit, and refers to and updates the information via the control unit 13 or directly. The plurality of types of parameters correspond to a plurality of sound sources, and at least one of these parameters is processed by the processing unit of the encoder 16 and the decoder 26, which will be described later, such as sound information and sound code. Used for. The storage unit 14 may individually refer to and update the parameters, or may store an identification value that uniquely identifies each parameter in association with each parameter. In addition, state change history, sound information, and sound codes may be accumulated and stored.

  The sound input I / F 15 inputs the sound of the sound source outside the system at a predetermined timing, converts it into time-series sound information, and outputs it. The sound input I / F 15 has an acoustic transducer such as a microphone, for example, converts an incoming sound into an electrical signal according to a predetermined parameter, and outputs it as sound information. This sound information is output to the encoder 16 and / or the control unit 13. Note that the sound input I / F 15 may convert sound information by pre-emphasis processing or the like, or may directly input / output sound information from an external connection device.

  The encoder 16 converts the input sound information and outputs it as a sound code. That is, the sound information input from the sound input I / F 15 is quantized and encoded, and is output to the code output I / F 17 and the control unit 13 as a sound code. The detailed configuration of the encoder 16 will be described later.

  The code output I / F 17 outputs the sound code input from the encoder 16 to the transmission medium 30 at a predetermined timing. Note that the code output I / F 17 may output information for synchronizing with the output timing of the sound code, for example, a frame synchronization signal in the case of outputting the sound code after framing to the control unit 13. The code output I / F 17 may also output information related to or independent from the sound code, and the sound code stored in the storage unit 14 via the control unit 13 may be output via the control unit 13. It may be output at a predetermined timing.

(Transmission medium)
The transmission medium 30 outputs information including a sound code output from the code output I / F 17 of the encoding device 10 to a code input I / F 25 described later of the decoding device 20. The transmission medium 30 may be wired or wireless. Further, the transmission of the transmission medium 30 may be a real-time transmission format in which transmission is performed sequentially, or may be a storage format in which data stored in a storage device or the like is transmitted sequentially.

(Decryption device)
The decoding device 20 includes a user interface UI21, an external connection I / F22, a control unit 23, a storage unit 24, a code input I / F25, a decoder 26, and a sound output I / F27. The user interface UI21, the external connection I / F 22, the control unit 23, and the storage unit 24 have the same configurations as the user interface UI11, the external connection I / F 12, the control unit 13, and the storage unit 14 of the encoding device 10, respectively. Therefore, the description thereof is omitted.

  The code input I / F 25 inputs information including a sound code from the transmission medium 30 at a predetermined timing, and outputs the information to the decoder 26 and / or the control unit 23. The code input I / F 25 may output a timing synchronization signal with a sound code included in the input information to the control unit 23, or may include information related to or independent of the sound code included in the input information. You may make it output to the control part 23. FIG. The code input I / F 25 inputs information including a sound code from the transmission medium 30 sequentially at a predetermined timing when the transmission medium 30 is in the storage format.

  The decoder 26 converts the input sound code and outputs it as sound information to the sound output I / F 27. The detailed configuration of the decoder 26 will be described later.

  The sound output I / F 27 converts the time-series sound information input from the decoder 26 into sound outside the system at a predetermined timing and outputs the sound. The sound output I / F 27 includes, for example, an acoustic transducer such as a speaker, and converts sound information into sound according to a predetermined parameter and outputs the sound. Note that the sound output I / F 27 may convert the sound information by de-emphasis processing or the like, or may directly input the input sound information to the external connection device.

[1-3. Detailed configuration of encoder and decoder]
(Encoder)
As shown in FIG. 2, the encoder 16 includes a preprocessing unit 41, an adder 42, an adaptive normalization unit 43, an optimal quantization unit 44, an optimal inverse quantization unit 45, an adaptive prediction unit 46, an adder 47, and a post-processing unit. A processing unit 48 is included.

  Each of these processing units has operation control I / Fs 41p, 43p to 46p, and 48p, and parameters necessary for processing of each processing unit are temporarily stored and / or stored in advance. The operation control I / Fs 41p, 43p to 46p, and 48p temporarily store parameters used for processing of the processing unit provided with the operation control I / Fs 41p, 43p to 46p, and 48p. Each of these processing units performs various processes based on the parameters in response to a request from the control unit 13. The operation control I / Fs 41p, 43p to 46p, and 48p can also be referred to as storage means because they store parameters.

  The parameters are optimally designed for a plurality of types of sound sources such as voices of various people (not only men and women of all ages but specific persons) and sounds of musical instruments. As each parameter, a parameter that dynamically refers to a parameter stored in the storage unit 14 in response to a request from the control unit 13 may be used. More specifically, the operation control I / Fs 41p, 43p to 46p, and 48p are controls for updating parameters used in the processing unit according to sound information or a sound code input to the processing unit provided with the operation control I / F 41p, 43p to 46p, 48p. The signal is output to the control unit 13. And the control part 13 can update the parameter used with a process part with reference to the parameter corresponding to the said control signal from the parameters memorize | stored in the memory | storage part 14. FIG.

  As the updated parameters, those stored in advance in the operation control I / Fs 41p, 43p to 46p, and 48p may be used. Furthermore, the input from the user via the user interface UIs 11 and 12 or the input from the external connection device via the external connection I / Fs 12 and 22 may be used.

  As described above, each part of the encoder 16 has a variable parameter according to the sound source, and can be dynamic or static according to the sound source, so that the quantization error can be reduced and it is suitable for the sound source. The codec can be configured to obtain sound with good sound quality.

  The pre-processing unit 41 performs a predetermined process on the sound information input from the sound input I / F 17 or the control unit 13 and outputs the processed sound information to the adder 42. As the predetermined processing, for example, processing may be performed according to predetermined parameters, or input sound information may be output as it is. Further, the amplitude of the input sound information may be scaled and output, or if the amplitude is excessive, it may be output after clipping.

  The adder 42 is connected to the preprocessing unit 41, the adaptive normalization unit 43, and the adaptive prediction unit 46. The difference between the sound information input from the preprocessing unit 41 and the predicted value of the sound information input from the adaptive prediction unit 46 is calculated, and this difference is output to the adaptive normalization unit 43 as a prediction error.

  The adaptive normalization unit 43 calculates a normalized prediction error normalized based on the input prediction error and its predicted value. Specifically, the adaptive normalization unit 43 is connected to the optimal quantization unit 44, obtains a normalization prediction error from the prediction error input from the adder 42 using a normalization function, and obtains an optimal quantization unit 44, The data is output to the adaptive prediction unit 46 and the adder 47.

  The normalization function is a function of the prediction error and its predicted value. The normalization function will be described later in detail, and is, for example, an expression (2) or an expression (3) described later. The normalization function is stored in the operation control I / F 43p. When a plurality of normalization functions are stored as parameters in the operation control I / F 43p, a desired function can be selected by parameter control from the control unit 13.

  The adaptive normalization unit 43 sets a prediction value of a prediction error (hereinafter also referred to as a normalization coefficient) according to a quantum normalization prediction error described later including the past, as in Expression (11) described later. Update with prediction error prediction function. The normalization function normalizes the prediction error according to a predetermined parameter and a normalization coefficient. In addition, including the above-described prediction error prediction function, “including the past” in this specification refers to a time before the next time to be updated, and includes the current time and a time before the current time. .

  On the other hand, the adaptive normalization unit 43 is also connected to the optimum inverse quantization unit 45, and a later-described quantum normalized prediction error input from the optimum inverse quantization unit 45 and an inverse normalization function corresponding to the normalization. The normalization is solved, and the function value is output to the adaptive prediction unit 46 and the adder 47 as a quantized prediction error. The inverse normalization function is an inverse function of the normalization function and solves the normalization of the input value according to a predetermined parameter and a normalization coefficient. The normalization coefficient is the same for the normalization function and the denormalization function.

  The normalization coefficient has a synchronous convergence structure. In other words, normalization coefficients having different initial values converge to the same value when update is sequentially performed under the same conditions. Details of the synchronous convergence structure will be described later.

  The adaptive normalization unit 43 has an abnormality control function. For example, when a predetermined threshold value is stored in advance in the operation control I / F 43p and an input of a prediction error that is not normal or an input of a quantum normalized prediction error is detected, this is a function that quickly eliminates the propagation of an abnormal value. Will be described later.

  The optimal quantization unit 44 quantizes the normalized prediction error input from the adaptive normalization unit 43 and obtains a corresponding phonetic code. The optimum quantization unit 44 is connected to the optimum inverse quantization unit 45 and the post-processing unit 48, and outputs the obtained sound code to these. More specifically, the optimum quantization unit 44 quantizes the parameters stored in the operation control I / F 44p and optimally designed, and outputs the quantization level corresponding to the quantum normalized prediction error as a sound code. This quantization range is not updated adaptively and is constant when the codec is driven. Note that the phonogram may be a value for representing an abnormality other than the value corresponding to the quantum normalized prediction error.

  The optimal inverse quantization unit 45 outputs a quantization value corresponding to the phone code input from the optimal quantization unit 44, that is, a quantum normalized prediction error. More specifically, the optimal inverse quantization unit 45 performs inverse quantization using the optimally designed parameters stored in the operation control I / F 45 p and outputs a quantum normalized prediction error to the adaptive normalization unit 43.

  The adder 47 is connected to the adaptive normalization unit 43 and the adaptive prediction unit 46. The adder 47 adds the quantized prediction error from the adaptive normalization unit 43 and the predicted value from the adaptive prediction unit 46, and outputs the obtained sound information to the adaptive prediction unit 46. Note that the sound information obtained by the addition is the same as the sound information finally output from the decoder 26.

  The adaptive prediction unit 46 drives an adaptive prediction model (described later) defined by a predetermined parameter from the quantized prediction error and past decoded sound information including the past, and predicts sound information to be input next. A value is obtained and output to the adders 42 and 47. The sum of the output prediction value and the previous quantization prediction error becomes decoded sound information. The adaptive prediction model is adapted to the input sound information sequence by sequentially updating the prediction coefficient. The prediction coefficient has a synchronous convergence structure. That is, prediction coefficients having different initial values converge to the same value when update is performed sequentially under the same conditions.

  The adaptive prediction unit 46 has an abnormality control function. For example, a predetermined threshold value is stored in advance in the operation control I / F 46p, and when the predicted value is obtained beyond the expected amplitude range of the sound information, it is a function of clipping to the same range, which will be described in detail later. .

  The post-processing unit 48 processes the input sound code in accordance with predetermined parameters stored in advance in the operation control I / F 48p, and outputs the processed sound code to the code output I / F 17. Examples of the process include a process of outputting the input phonetic as it is, a process of inverting the sign of the input phonetic.

(decoder)
As shown in FIG. 2, the decoder 26 includes a preprocessing unit 51, an optimal inverse quantization unit 55, an adaptive normalization unit 53, an adaptive prediction unit 56, an adder 57, and a postprocessing unit 58. Each of these units has operation control I / Fs 51p, 53p, 55p, 56p, and 58p, and stores parameters corresponding to various processes. The operation control I / Fs 51p, 53p, 55p, 56p, and 58p can also be referred to as storage means because they store parameters. Since the adaptive normalization unit 53, the optimal inverse quantization unit 55, and the adaptive prediction unit 56 have the same configuration as the adaptive normalization unit 43, the optimal inverse quantization unit 45, and the adaptive prediction unit 46 of the encoder 16, the description thereof will be given. Omitted.

  The preprocessing unit 51 processes the sound code input from the code input I / F 25 or the control unit 23 according to a predetermined parameter stored in advance in the operation control I / F 51p, and optimizes the processed sound code The result is output to the inverse quantization unit 55. As this process, for example, an input phonetic code is output as it is. In addition, for example, when the input sound code is a value indicating an abnormality stored in advance in the operation control I / F 51p, the preprocessing unit 51 notifies the control unit 23 to that effect, and the operation control I / F 51p. May be output in place of normal phonetic symbols designated by parameters stored in advance.

  The post-processing unit 58 processes the decoded sound information input from the adder 57 in accordance with a predetermined parameter stored in advance in the operation control I / F 58p, and the processed decoded sound information is output to the sound output I / F 27. Output to. As this process, for example, an input phonetic code is output as it is. The post-processing unit 58 stores, for example, a predetermined threshold value in the operation control I / F 58p in advance, and when the input decoded sound information is obtained beyond the expected amplitude range of the sound information, You may make it output by clipping to.

[1-3. Action]
Next, the sound encoding and decoding operations of the present system having the above configuration will be described. The behavior and characteristics of this system are controlled by various parameters stored in each operation control I / F of the encoder 16 and the decoder 26. Here, the following points are assumed.
• All parameters are optimally designed to meet the desired system performance.
The encoder 16 and the decoder 26 input and output sound information according to a sampling frequency and sound information amount designed in advance.
In order to handle sound information in time series, the sample number is represented by k, and the instantaneous information of the time series information s sampled at a certain moment k is represented as s (k).

[Prediction error]
When the prediction value p (k) of the adaptive prediction unit 46 with respect to the sound information s _i (k) output from the preprocessing unit 41 of the encoder 16 is given, the prediction error d (k) is as shown in Equation (1). I can express.

  If the adaptive prediction model of the adaptive prediction unit 46 is ideally driven, the prediction error is whitened and there is no room for further prediction. Therefore, in this case, the quantization procedure should be immediately followed. However, in reality, the input sound information is non-stationary and therefore cannot be predicted, and the color remains. Moreover, depending on the time series of sound information, quasi-periodicity is also exhibited.

[Adaptive normalization]
Therefore, in this system, the prediction error is also predicted, the prediction divergence d _d (k) of the prediction error is obtained, and the time series information that has been whitened is quantized. Here, when the prediction value of the prediction error d (k) adaptively predicted is p _d (k), and the function for obtaining the prediction divergence d _d (k) is represented by f _d (), the prediction divergence d For example, _d (k) is obtained by dividing the prediction error by the predicted value as shown in Equation (2). A method of predicting p _d (k) will be described later. If the fluctuation of the prediction error can be predicted ideally, the expected value E [f _d (d (k), p _d (k))] of the prediction divergence degree. Becomes 1.

Alternatively, the prediction divergence degree d _d (k) is expressed by a _function that predicts _d (k) in the logarithmic domain and outputs f _d () as a function having a ratio r and a prediction error code s as a component. You may obtain | require as 3).
sgn (x) is a sign function that outputs 1 when x ≧ 0 and −1 when x <0. The structure of the function f _d () may be stored in advance in the operation control I / F 43 p, or the structure of the function f _d () may be used as a parameter from the control unit 13 to the adaptive normalization unit 43. The adaptive normalization unit 43 may be dynamically constructed.

The adaptive normalization unit 43 outputs the prediction divergence degree to the optimal quantization unit 44 in the subsequent stage, but the quantization structure is not updated adaptively and is constant when the codec is driven. That is, the list of quantization thresholds in the optimum quantization unit 44 is given as a parameter from the control unit 13, and is constant when the system is driven. Therefore, since the prediction error is converted by normalization so that the fluctuating prediction error value falls within a specified range, whitening by obtaining the prediction divergence is referred to as normalization. That is, the prediction divergence degree d _d (k) is a normalized prediction error, and the predicted value p _d (k) is a normalization coefficient.

  As described above, the adaptive normalization unit 43 normalizes the prediction error, whereby the variance of the prediction error can be reduced. As a result, the normalized prediction error (normalized prediction error = prediction divergence) can be kept within a specified range, so that the quantum error can be reduced. As a result, sound quality can be improved and sound reproducibility can be improved.

[Optimum quantization]
Next, the normalized prediction error is quantized to obtain a corresponding phonetic code. In this quantization, the quantization level L is set in advance. Since the sound code is finally input to the decoder 26 via the transmission medium 30, it is desirable to design the quantization level L = 2 ^m (m is a natural number) for the purpose of maximizing the amount of information. The list of quantization thresholds is given from the control unit 13 as a parameter. The quantization threshold values are arranged in ascending order, and the i-th threshold value is represented by q _th (i).

If the quantization interval is continuous in the quantization range, the phonetic code c (x) can be obtained as shown in Equation (4).

  Since the input to the phoneme c (x) is a normalized prediction error, the quantization threshold domain is designed in conformity with the domain of the adaptive normalization unit 43.

When the adaptive normalization unit 43 is driven in the logarithmic domain and Expression (3) is input to x of the sound code c (x), the sound code can be obtained as Expression (5). Where x. m represents the m component of the vector x.

  On the other hand, the quantization interval may be discontinuous. In this case, the quantization threshold specifies values at both ends of the target section. Note that the search time may be reduced by using a binary search for the search of the quantization interval.

Further, an anomaly level independent of quantization may be defined as in equation (6) so that each part of the encoding device 10 and the decoding device 20 can also detect an anomaly. In Expression (6), c (x) = 0 corresponds to the abnormal level.

  As described above, the sound code quantized and encoded by the optimal quantization unit 44 is output to the optimal inverse quantization unit 45 and the post-processing unit 48 and finally input to the decoder 26.

[Optimum inverse quantization]
The optimum inverse quantization unit 45 obtains a quantization value corresponding to the sound code input from the optimum quantization unit 44, that is, a quantum normalized prediction error, and outputs the quantization value to the adaptive normalization unit 43. Here, the list of quantization values is given as a parameter by the optimal design from the control unit 13 and corresponds to the quantization threshold. The quantized values are arranged in ascending order, and the i-th quantized value is represented by q (i).

If the quantum normalized prediction error is Q [d _d (k)] and the quantization error is e _q (k), the quantum normalized prediction error Q [d _d (k)] and the normalized prediction error d _d (k) ) Is expressed by Equation (7).

It can be seen that the quantization error can be minimized by minimizing the quantization interval. In order to reduce the quantization interval, the quantization level may be increased or the quantization range may be decreased. That is, the variance of the normalized prediction error d _d (k) input to the optimal quantization unit 44 may be reduced. For this reason, the quantum normalization prediction error Q [d _d (k)] is fed back to the adaptive normalization unit 43.

[Adaptive denormalization]
The adaptive normalization unit 43 uses the normalization coefficient p _d (k) used to normalize the quantum normalized prediction error Q [d _d (k)] and the prediction error d (k) input from the optimal inverse quantization unit 45. ) And the function value is output to the adaptive prediction unit 46 as a quantized prediction error. Since this function solves the normalization of the normalization function, it can be considered as an inverse function f _d ⁻¹ () of the normalization function f _d ().

Here, when the normalized prediction error is represented by Equation (2), the quantization prediction error Q [d (k)] is represented as Equation (8).

On the other hand, when the normalized prediction error is the logarithmic domain of Equation (3), the quantized prediction error Q [d (k)] is expressed as Equation (9) using the sound code.

Here, the error between the quantization prediction error and the prediction error is verified. For this purpose, the expression (8) is expanded as the following expression (10).

As is clear from the equation (10), the prediction error is converted into e _q (k) p _d (k) through the normalization, quantization, inverse quantization, and inverse normalization processes. It can be seen that only noise is added. It can also be seen that in order to minimize this noise, the quantization error e _q (k) and the normalization coefficient p _d (k) may be minimized.

As described above, in order to reduce the quantization error e _q (k), it is better that the variance of the normalized prediction error d _d (k) is smaller under a condition where the quantization level is constant. In order to minimize the normalization coefficient p _d (k), in addition to minimizing the prediction error, it is sufficient that the prediction error can be predicted ideally.

  In order to realize these optimizations, the adaptive normalization unit 43 needs to adaptively predict the input prediction error d (k). Here, since the sound code is input to the decoder 26, if the prediction structure of the prediction error d (k) is not subjected to synchronous convergence control, the internal state of the encoder 16 and the decoder 26 proceeds with a mismatch, and as expected. Sound will not be restored.

Therefore, it is necessary to provide a synchronous convergence structure as a prediction structure of the prediction error d (k). Therefore, as described above, since the predicted value of the prediction error d (k) is the normalized coefficient p _d (k), a synchronous convergence structure is given to the normalized coefficient p _d (k).

That is, the normalization coefficient p _d (k + 1) is obtained from the quantum normalization prediction error Q [d _d (k)] including the past and the normalization coefficient p _d (k) in the form of a prediction error prediction function of the formula (11). Updated with P _d ().

The prediction error prediction function P _d () has a synchronous convergence structure, and can be expressed as, for example, a linear combination of a quantum normalized prediction error Q [d _d (k)] and a normalization coefficient p _d (k). When the same input is given to a plurality of systems having the same structure with different internal states in time series, the function P _d () synchronizes the internal states of all the systems according to the system time constant and converges to the same state. Control structure. Note that the initial values of the quantum normalization prediction error and the normalization coefficient are set in advance.

More specifically, the prediction error prediction function P _d () has the following characteristics.
(i) Consists of gain and attenuation terms.
(ii) The gain term differs depending on whether the quantum normalization prediction error is positive or negative.
(iii) The gain term differs depending on the quantum normalized prediction error including the past.
(iv) Gain factor proportional to the quantum normalized prediction error including the past
(v) The gain term differs depending on the amount of change in the quantum normalization prediction error including the past.
(vi) Gain factor proportional to the amount of change in the quantum normalized prediction error including the past
(vii) Decay rate proportional to the normalization factor including the past
(viii) A lower threshold is set for the quantum normalized prediction error.
(ix) Proportional coefficient and threshold are used as parameters.

FIG. 3 shows a block diagram of the function P _d (). That is, the adaptive normalization unit 43 includes a normalization coefficient update unit that functions as the function P _d (). The normalization coefficient updating unit includes a plurality of gain term calculation units 431, a gain term selection condition unit 432, a switching unit 433, and an attenuation term calculation unit 434.

  The gain term selection condition unit 432 selects which gain term to calculate the normalization coefficient update among the plurality of gain term calculation units 431 according to the quantum normalization prediction error including the past input directly or via the delay element 432a. It is selected whether to use the calculation unit 431, and the switching signal is output to the switching unit 433. The switching unit 433 receives the signal from the gain term selection condition unit 432 and switches to the gain term calculation unit 431 used to calculate the normalization coefficient update.

Each gain term calculation unit 431 includes a plurality of coefficient control condition units 4310 to 431n, which are coefficients k _i (a gain factor according to a quantum normalized prediction error input directly or via the delay element 431a). i = 1, 2,... n) is determined. Also, the coefficient control condition units 4310 to 431n are coefficients k _i (i = 1, 2,... N) that are gain rates according to the amount of change of the quantum normalization prediction error input directly or via the delay element 431a. May be determined. The gain term calculation unit 431 linearly combines this coefficient and the quantum normalized prediction error by the adder 431b to calculate the gain term. The attenuation term calculation unit 434 includes a plurality of delay elements 434a, coefficients a _i (i = 1, 2,...) That are attenuation factors, and an adder 434b. From the normalization coefficients for the past, the delay elements 434a and An attenuation term is calculated by linear combination based on the coefficient a _i . As described above, the normalization coefficient update unit obtains the next normalization coefficient from the obtained gain term and attenuation term. Note that the switching of the gain term calculation unit 431 by the gain term selection condition unit 432 and the switching unit 433 may be performed in parallel with the calculation of the gain term by the gain term calculation unit 431.

As described in (ix) above, the coefficient used by the prediction error prediction function P _d () is used as a parameter, but this function itself may be used as a parameter. For example, it may be stored in advance in the operation control I / F 43p, or may be stored in advance in the storage unit 14 and acquired via the control unit 13. Further, by providing a lower limit value for the quantized normalized prediction error as in (viii) above, the quantization error can be reduced.

As described above, the adaptive normalization unit 43 uses the quantum normalized prediction error Q [d _d (k)] including the past and the normalization coefficient p _d (k) as drive sources, and these are used as the prediction error prediction function P. By substituting for _d (), the normalization coefficient is updated. Thus, the adaptive normalization unit 43 updates the prediction value p _d (k) of the prediction error d (k) and predicts the prediction error d (k), and thus has a function as a prediction error prediction unit. It can be said that The updated normalization coefficient is used for the next normalization, inverse quantization, and the next update of the normalization coefficient.

[Adaptive prediction]
From the quantization prediction error Q [d (k)] of the adaptive normalization unit 43 and the prediction value p (k) of the adaptive prediction unit 46, the input sound information s _i (k) is expressed by using the equation (1). It is restored as s _o (k) as in equation (12). The decoder 26 finally outputs the sound information s _o (k). Note that in expressing the equation (12), regarding the equations (8) and (10), the error between the quantized prediction error Q [d (k)] and the prediction error d (k) is assumed to be e (k), and the relationship between the two. Is generalized as shown in equation (13).

  Although it can be seen from equation (12) that errors due to normalization and quantization are included in the output sound, the source of this error is the prediction error. Therefore, even if the adaptive normalization unit 43 can predict the prediction error ideally, if the variance of the prediction error itself is large, the quantization error becomes large.

  Therefore, the adaptive prediction unit 46 determines the next input sound information from the restored sound information including the past and the quantized prediction error input from the adaptive normalization unit 43 so that the variance of the prediction error is minimized. Predict and output. For this prediction, a prediction model capable of well describing the space of time-series sound information input to the system is used.

  As described above, the prediction model adaptively updates the prediction coefficient, and the behavior is controlled by the prediction coefficient. As a method for adaptively updating the prediction coefficient, a method for adjusting the prediction error so as to minimize the prediction error can be used. For example, a least square method or a steepest descent method can be employed. Note that the prediction model itself may be used as a parameter.

When the input space is speech, a multipole model is suitable as the prediction model. This system is practical in that the third-order or higher-order pole is approximated by a large number of zero models as shown in Equation (14) due to the problem of stability conditions. In this case, a quantum normalized prediction error is used as a drive source. a _i and b _i are prediction coefficients. M is an integer of 2 or more.

  Since the order of the zero model is related to the spectral distribution of the input space and affects the prediction error, it is necessary to design an optimal order for the input space in advance. This order may be given as a parameter.

The zero model approximation requires a large number of orders and performs the same number of multiplications, which increases the computational scale. In order to avoid this, approximation may be performed as in Expression (15). According to this, it becomes possible to predict with higher accuracy than Expression (14).

  As described above, the adaptive prediction unit 46 obtains the prediction value of the sound information so that the variance of the prediction error is minimized. However, the adaptive prediction units 46 and 56 may be driven asynchronously by the encoder 16 and the decoder 26 in the same manner as the adaptive normalization units 43 and 53. For this reason, the prediction coefficient update formula must have a synchronous convergence control structure at the same time.

[Synchronous convergence control]
Next, synchronous convergence control will be described. In the present system, the adaptive normalization units 43 and 53 and the adaptive prediction units 46 and 56 are feedback adaptive formats in which past output values are input. In this case, the internal state of the same adaptor (adaptive system) such as adaptive parameters must be synchronized between the encoder 16 and the decoder 26. This is because unintended sound information is output from the decoder 26 in the asynchronous state.

  However, the encoder 16 and the decoder 26 generally start driving asynchronously. For this reason, it is desirable to quickly resolve this asynchronous state and converge to a synchronized state. Therefore, in this system, the adaptive normalization units 43 and 53 and the adaptive prediction units 46 and 56 have a synchronous convergence control structure.

In order to converge from the asynchronous state to the synchronous state, the adaptive system, that is, the adaptive normalization units 43 and 53 and the adaptive prediction units 46 and 56 must satisfy the following conditions (1) to (5). You may make it satisfy 6) and (7). In other words, satisfying the following conditions (1) to (5) has a synchronous convergence structure, and on the premise that the conditions (1) to (5) are satisfied, the conditions (6), ( 7) may be satisfied. In the conditions (1) to (4) and (6), the system refers to a target to be synchronized and converged, for example, a pair of adaptive normalization units 43 and 53 and a pair of adaptive prediction units 46 and 56. . The control formula is, for example, the above formulas (11), (14), and (15).
(1) The relationship between system input and output is expressed by a control equation.
(2) The system input consists of a simple input with no internal state and a system output.
(3) The simple inputs and control expressions between the synchronization target systems (for example, the adaptive normalization unit 43 and the adaptive normalization unit 53) are the same.
(4) The control expression includes the input and internal state, and the input system output is included in the internal state.
(5) The term including the internal state of the control equation is updated so that the absolute value decreases at an arbitrary speed (time constant). This speed is determined by the convergence time constant.
(6) Past system output may be input.
(7) The term including the internal state of the control equation can be quantized to a level well below the rate of decrease.

  The convergence time constant may be used as a parameter. As a result, the convergence speed can be controlled. The synchronous convergence speed is related to the spectral distribution of the input space and affects the prediction error. Therefore, it is necessary to design an optimal convergence time constant for the input space in advance.

  As described above, since the adaptive system has the synchronous convergence structure, it is possible to achieve the synchronous convergence regardless of the start timing of the encoder 16 and the decoder 26 and improve the sound reproducibility. In particular, since the adaptive normalization units 43 and 53 have a synchronous convergence structure, prediction errors can be predicted more accurately. Since the adaptive prediction units 46 and 56 have a synchronous convergence structure, sound information can be predicted more accurately.

[Abnormal control]
Since this system has a closed-loop structure based on external input and feedback of the internal state in prediction, there is a possibility that the system may fall into an unrecoverable state due to the occurrence of an abnormality. Examples of the abnormal state include that each part of the system is in an asynchronous state and that an input to each part of the system exceeds an expected range. As a factor of this abnormal state, there is a failure of the transmission medium 30 as a communication path. In this system, the following method can be adopted in order to avoid a situation in which the system cannot recover due to such an abnormality. Note that only one of the following methods may be performed, or two or more methods may be combined.

(1) When a value outside the expected range is input to each processing unit of the encoder 16 and / or the decoder 26, clipping is performed to the boundary value of the range. For example, a predetermined threshold value or range is stored in the operation control I / F 41p of the preprocessing unit 41, and compared with the sound information input to the preprocessing unit 41 based on the threshold value or range, whether or not there is an abnormality is determined. To do. If it is abnormal, clipping is performed.

(2) The pre-processing unit 51 of the decoder 26 compares the input sound code with a predetermined threshold value stored in advance in the operation control I / F 51p, and determines that the input sound code exceeds the threshold value and is abnormal. If so, the control unit 53 is notified accordingly. In this case, for example, under the control of the control unit 53, the user is notified of the abnormality via the user interface UI21, or the sound information specified by the parameter is output from the sound output I / F 27.

  According to the above method, abnormal sound information or sound code can be converted into normal sound information or sound code. However, the input sequence to the adaptive normalization units 43 and 53 and the internal state thereof differ between the encoder 16 and the decoder 26 until the period until the convergence converges. Furthermore, since the output of the adaptive normalization unit 43 of the encoder 16 is used as the input of the decoder 26, there is a possibility that unintended sound information such as output diverges from the decoder 26 at an excessive level until the synchronous convergence occurs. There is. Therefore, in this system, the following measures are taken as an early recovery procedure for synchronization.

(Early recovery of synchronization)
(a) The decoder 26 is stopped during the abnormal sound code input period. For example, a detection unit is provided that detects an abnormality of the sound code input to the preprocessing unit 51 of the decoder 26. The detection unit is preset with a predetermined threshold value or range for determining whether or not the input sound code is abnormal, and by comparing the input sound code with the predetermined threshold value or range. Determine if it is abnormal. The predetermined threshold value or range may be stored in advance in the operation control I / F 51p so that the operation control I / F 51p functions as a detection unit. As described above, by stopping the decoder 26, the internal state at the time of detecting the abnormal input can be maintained, so that the progress of desynchronization can be minimized. Therefore, the asynchronous problem between the encoder 16 and the decoder 26 can be solved early.

(b) The internal state of the decoder 26 is shifted in the direction of the initial state from the internal state when it is determined as abnormal. That is, it has been found that the unintentional generation of sound information until synchronous convergence is caused by the influence of an abnormal sound code remaining in the decoder 26 when the abnormal input is resolved. That is, since the state variable indicating the internal state of the decoder 26 is changed by the abnormal sound code input from the abnormality detection time point to the abnormality resolving time point, the internal state of the decoder 26 is changed, and the state from the initial state is changed. The degree of transition increases. As described above, since the influence of the abnormal sound code remains as past accumulated information in the internal state of the decoder 26 at the time of eliminating the abnormal input, there is a possibility of causing an unexpected action. Therefore, by causing the internal state of the decoder 26 to transition toward the initial state when the abnormal input is resolved, the generation of abnormal noise can be suppressed and the speed of synchronization convergence can be increased. The transition of the internal state in the direction of the initial state may be performed from the internal state at the time of eliminating the abnormal input. More preferably, a transition is made from the internal state at the start of abnormal input detection toward the initial state. The transition of the internal state of the decoder 26 includes adjusting the normalization coefficient according to the current value and resetting the internal state. Both the adjustment of the normalization coefficient and the reset of the internal state may be performed.

(c) The above processes (a) and (b) may be combined. For example, the decoder 26 may be stopped during the abnormal input period, the abnormality of the transmission medium 30 or the like is resolved, and the normalization coefficient may be adjusted and / or the internal state may be reset when the decoder 26 is activated again.

(d) Among the parameters related to synchronous convergence, the gain of the parameter related to the time constant is temporarily increased until the synchronous convergence. Thereby, for example, when the abnormal input is resolved and the decoder 26 is restarted, the synchronization convergence can be accelerated. Moreover, sound quality deterioration can be suppressed by keeping it for a short time until the convergence is completed, and restoring it after the period.

  On the other hand, even if the above-described measures are taken due to the occurrence of an abnormality, the information is missing as long as the abnormality is not resolved, so that the sound information encoded by the encoder 16 cannot often be restored as expected. In this regard, the flow of sound information is non-stationary, but if the sound information is not noise, it can be regarded as a sequence in which a short-term steady sound information segment transitions. In this segment, it can be interpreted that the sound amplitude waveform repeats at a constant pitch. Therefore, when sound information cannot be restored normally due to missing information, the following interpolation processing can be performed.

  In other words, under the condition that the abnormal input period is shorter than the sound information segment, the missing sound information is extracted from the sound information segment that was most recently output, and the missing information is interpolated and reproduced to output more reliable sound information. can do. The extraction of the sound information to be interpolated requires the pitch estimation of the sound information segment associated with the missing part.

For the pitch estimation, a short-term autocorrelation function of the sound information flow can be used. If the instantaneous value of the sound information sampled at time n is s [n], the short-term autocorrelation function R _s (n, m) at the lag m can be expressed by equation (16). However, k _l and k _g may be parameters related to the stationary period of the sound information segment, and the degree of influence before the target segment may be controlled.

Using an arbitrary short-term autocorrelation function R _s (n, m) in the time-series sound information s [n], the pitch p _s [n] at the time n is estimated as in Expression (17).

The pitch _p s [n] of the estimated abnormal input detection time _{n a} output sound information, from the output sound information sequence _s of the decoder _{26 [n a -p s [n} a] +1] to s _{[n a]} The sound information may be output by repeatedly playing until the abnormal input is resolved.

  This pitch estimation may be performed all the time or only when an abnormal input is detected. Also, the amplitude of the reproduced sound information may be gradually reduced to fade out. The sound information decoded from the abnormal input resolution time point and the reproduced sound information may be blended by a cross fade for a certain period and output.

  By the way, in the adaptive prediction unit 56 of the decoder 26, when the prediction model includes a closed-loop structure, the prediction value may exceed the amplitude range of the sound information because the prediction coefficient is arranged and updated near the stable region boundary. . In this case, the predicted value may be clipped within the amplitude range. Further, the prediction coefficient may be rearranged in a more stable region.

[Approximate solution of logarithmic and exponential functions]
The adaptive normalization units 43 and 53 may use a logarithmic function for normalizing a prediction error and an exponential function for denormalization. In this case, both of these functions should be implemented efficiently from the viewpoint of calculation cost and accuracy while satisfying the requirements of the problem to be applied. Below, the approximate solution method of the logarithmic function and exponential function in this system is demonstrated. Therefore, first, the basic part of the approximate solution and the conventional G.P. The error analysis at 726 and the conditions that the system should satisfy will be described.

  The approximate solution is implemented by the adaptive normalization units 43 and 53, but is not limited thereto. That is, the approximate solution of the logarithmic function and exponential function of the present system can also be applied to a general arithmetic unit including a CPU that uses a logarithmic function or an exponential function.

(Basic of approximate solution)
Consider representing an arbitrary positive number x using a radix b. If x ′ _m is a real number greater than or equal to 1 and less than b and x _e is an integer, this x can be uniquely expressed as in equation (18).

Using Equation (18), the logarithm of x with b as the base can be obtained as Equation (19). Here, x _m = log _b x ′ _m .
Since x _m is a real number from 0 to less than 1, the formula (19), by definition of formula (18) can be obtained by dividing the logarithm of x to the integer and fractional parts.

On the other hand, exponential function of base b to index the y = x e ₊ x _m b ^y also y as any real number, for exponential function is an inverse function of the logarithmic function, x the definition _'m is b of x _Since it is the _m- th power, it can be obtained as x as in equation (18). Further, practically, because the value to be logarithmically converted no problem even considered bounded, may be considered an integral part x _e logarithm is also bounded. However, fractional part x _m is required to obtain approximately by some solution.

In the following, the approximate solution of the logarithmic function and the exponential function defined by the equations (18) and (19) will be considered, but the radix b is fixed to 2 in order to facilitate the calculation by the CPU based on the general binary calculation. There is no problem. This is because it can be converted into an arbitrary radix by multiplying by a coefficient related to the constant log ₂ b as shown in equations (20) and (21).

  Furthermore, since the exponential function is an inverse function of the logarithmic function, an approximate solution method of the logarithmic function will be described below.

(G.726 implementation and error analysis)
ITU-TG using the conventional ADPCM method. In 726, although logarithmic absolute value x of the prediction error, the integer part x _e of the logarithm, and compares the x and 2 ^k from k = 0, as an index k by maximum 2 ^k that does not exceed x Seeking. The amount of calculation by this method is Ο (k). Fractional part _{x m} the formula (18) x 'a 1 + _{x m} Distant _m, as _{x m = log 2 (1 +} x m), are obtained by preferentially approximating the amount of calculation. The error due to this approximation exceeds 0.05 on average.

(Polynomial approximation)
G. In order to reduce the approximation error in the implementation of 726, it is also conceivable that log ₂ x ′ _m is polynomial approximated in the interval where x ′ _m is [1, _2] . Therefore, this n-th order polynomial is defined as f _PL (x, n) in Expression (22).

In order to optimally approximate log ₂ x with an n-order polynomial f _PL (x, n), the mean square error of f _PL (x, n) −log ₂ x may be minimized. For that purpose, the n-ary simultaneous equations of Expression (23) may be solved.

However, even if it can be accurately approximated by a quadratic polynomial, if an approximate expression of an exponential function that is its inverse function is analytically obtained, it becomes a function including the square root of x, and the exponential function is efficiently I can't solve it. This is especially true at the third order and higher. Naturally, if the exponential function 2 ^x , which is the inverse function of log ₂ x, is approximated by a polynomial expression using the same approach as the equation (23), it can be approximated with the same degree of accuracy. However, according to this approach, the approximate polynomials are not inversely related to each other.

(Requirements for conversion of the adaptive normalization unit)
If the logarithmic function approximation formula and the exponential function approximation formula, which are inverse functions of the logarithmic function approximation formula, do not become inverse functions of each other, even if the number is logarithmically converted using both approximation formulas, The number cannot be restored, and double approximation errors other than calculation errors are included. The quantization error of the prediction error in the adaptive normalization units 43 and 53 is propagated to the adaptive prediction units 46 and 56 of the encoder 16 and the decoder 26. In addition to this, the identity conversion error in the logarithm-exponential transformation is also propagated. As a result, there is a possibility that the prediction error increases, and consequently the quality of the decoded sound information of the decoder 26 is deteriorated.

Moreover, it must be possible to approximate over the entire domain of definition or value range. That is, G. As in 726, when 0 ≦ x _m ≦ 1, the condition is such that the entire range of 0 ≦ log ₂ (1 + x _m ) ≈x _m ≦ 1 can be approximated. However, even if the polynomial approximation is optimal, even if it is a quadratic polynomial, this condition cannot be satisfied and the conversion area is limited, which may lead to performance degradation.

  Furthermore, with regard to the approximation accuracy, if the degree of the polynomial is increased, the accuracy is improved, but the amount of calculation including multiplication is increased, which is not desirable. In order to solve the problems caused by these polynomial approximations, we propose an optimal polyline approximation of both functions and its optimization method.

[Basics of broken line approximation]
The approximation method of this system is a method of approximating a function to be approximated by a broken line obtained by connecting a plurality of points on the function with line segments. The polygonal line function used in this polygonal line approximation is a connection of line segments represented by piecewise linear equations. Therefore, the inverse function is also a line segment represented by a linear expression, and the inverse function can be easily obtained analytically. For this reason, there is an advantage that an identity conversion error such as polynomial approximation is not included.

  In addition, the amount of computation by line-line approximation is only a comparison of the number of times proportional to the logarithm of the line segment, multiplication and addition, and even if the number of line segments is increased and the approximation accuracy is improved, the amount of arithmetic operation is Has the advantage of being constant.

A polygonal line function f _BL (x, N) by an N line segment having end points (x _n , y _n ) and (x _{n + 1} , y _{n + 1} ) can be expressed as in Expression (24). Note that in the approximation of the logarithmic function, x _{n + 1} = x _n does not occur.
In the following, the following three methods are described: a polygonal line approximation that does not exceed, a polygonal line approximation that does not fall below, and an unconstrained polygonal line approximation, but any method may be used. These broken line approximations are used when the logarithmic function of the absolute value of the prediction error is included in the function for obtaining the normalized prediction error in the adaptive normalization units 43 and 53 as shown in Expression (3), for example. it can.

[Linear approximation not exceeding]
First, let us consider a polygonal line approximation in the case of only a negative error to which a condition not exceeding the function value to be approximated is attached. The number of line segments is a power of 2. Even in this way, generality is not lost.

^First , an approximation with the line number 21 is obtained. The end points (x ₀ ⁽¹⁾ , y ₀ ⁽¹⁾ ) = (1, 0), (x ₂ ⁽¹⁾ , y ₂ ⁽¹⁾ ) = (2, 1) are determined by the conditions of the domain and range Therefore, (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ) is a problem to be obtained. Here, the position of the end point n when the number of line segments is 2 ^m is represented as (x _n ^(m) , y _n ^(m) ).

In order to minimize the approximation error, all end points of the polygonal line function must be placed on the logarithmic function to be approximated. Then, y ₁ ⁽¹⁾ can be expressed as y ₁ ⁽¹⁾ = log ₂ x ₁ ⁽¹⁾ , resulting in a problem of finding x ₁ ⁽¹⁾ that minimizes the approximation error.

To obtain x ₁ ⁽¹ ), consider an error curve log ₂ x− (x−1) as shown in FIG. However, 1 ≦ x ≦ 2. The error curve is polygonal line approximation in the line number 2 ^0, i.e. G. An error in approximation similar to 726 is represented. Approximation error in the case of the line segment number 2 ¹ here is the shaded region in FIG. In order to minimize this region, triangles (x ₀ ⁽¹⁾ , y ₀ ⁽¹⁾ ), (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ), (x ₂ ⁽¹⁾ , y ₂ ⁽¹⁾ It can be seen that the area of) should be maximized.

That is, (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ) may be arranged at the maximum point of this error curve. This is to obtain x ₁ ⁽¹⁾ that satisfies Expression (25). In this case, it is determined in the range of x ₀ ⁽⁰⁾ <x ₁ ⁽¹⁾ <x ₁ ⁽⁰⁾ .
Any endpoints of formula (25) in case of the line segment number ^{_{2 m (x n (m)}} , y n (m)) , and end point when the update to the segment number ^{_{2 m + 1 (x 2n (}} m + 1), y 2n ^{(M + 1)} ) and the same.

In this way an approximation optimized endpoint group in line number 2 ¹ obtained, to inherit the polygonal line function of segment number 2 ^2. Similarly, approximate optimization is performed on the endpoints that are not associated by inheritance using Expression (25). Similarly, the end point group approximated and optimized in the line segment 2 ^m is inherited to the polygonal line function having the line number 2 ^{m + 1} and further approximated to optimize the line function with only the negative error having the desired approximation accuracy. Can be sought.

[Linear approximation not lower]
Next, let us consider a polygonal line approximation in the case of only a positive error to which a condition not lower than the function value to be approximated is attached.

^First , an approximation with the line number 21 is obtained. The end points (x ₀ ⁽¹⁾ , y ₀ ⁽¹⁾ ), (x ₂ ⁽¹⁾ , y ₂ ⁽¹⁾ ) are similar to the polygonal line approximation that does not exceed, but each line segment is subject to the condition that it does not fall below the function to be approximated. One of the conditions for minimizing the approximation error is to be the tangent of the approximation target function having a contact in the domain.

The end points (x ₀ ⁽¹⁾ , y ₀ ⁽¹⁾ ), (x ₂ ⁽¹⁾ , y ₂ ⁽¹⁾ ) are contact points because they are on the approximation target function, and the two line segments having both end points are Each tangent passing through is fixed. Therefore, (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ) has no degree of freedom and can be uniquely obtained as the intersection of both line segments.

The polygonal line approximation which is not less than this, because the polygonal line function of segment number 2 ¹ shown in FIG. 5 is a basic state of the approximation, the polygonal line approximation is not exceeded to change the representation of the end points, the number of line segments is determined by 2 ^m +1 Shall. The position of the end point n in this case is represented as (x _n ^(m) , y _n ^(m) ). 0 ≦ m is the same. Therefore, the end point (x ₀ ⁽¹⁾ , y ₀ ⁽¹⁾ ) is re-expressed as the end point (x ₀ ⁽⁰⁾ , y ₀ ⁽⁰⁾ ) in the line number 2 ⁰ +1. Similarly for the remaining two end points (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ), (x ₂ ⁽¹⁾ , y ₂ ⁽¹⁾ ), (x ₁ ⁽⁰⁾ , y ₁ ⁽⁰⁾ ), ( x ₂ ⁽⁰⁾ , y ₂ ⁽⁰⁾ ).

Subsequently, an approximation with a line number 2 ¹ +1 is obtained. This is a problem of finding both end points that minimize the approximation error for one line segment increased from the number of line segments 2 ⁰ +1 in the basic state. Here, the line number ² m +1, end point _{^{(x n (m), y}} n (m)) and _{^{(x n + 1 (m)}} , y n + 1 (m)) segment _S ^{n (m)} having the formula ( 26).

Further, the tangent line T of the approximation target function can be expressed as in Expression (27) if the point of contact is (x _T , y _T = log ₂ (x _T )).
Further, a contact belonging to the line segment S _n ^(m ) is represented as (u _n ^(m) , v _n ^(m) ).

According to the above notation, the leftmost end point (x ₀ ⁽¹⁾ , y ₀ ⁽¹⁾ ) and the rightmost end point (x ₃ ⁽¹⁾ , y ₃ ⁽¹⁾ ) that have already been determined are (u ₀ ^{(1 )} , V ₀ ⁽¹⁾ ), (u ₂ ⁽¹⁾ , v ₂ ⁽¹⁾ ). On the other hand, (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ), (x ₂ ⁽¹⁾ , y ₂ ⁽¹⁾ ) and (u ₁ ⁽¹⁾ , v ₁ ⁽¹⁾ ) are undecided.

This (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ) is the intersection of tangents T (x, u ₀ ⁽¹⁾ ) and T (x, u ₁ ⁽¹⁾ ), and (x ₂ ⁽¹⁾ , y ₂ ⁽¹⁾ ) is the intersection of tangents T (x, u ₁ ⁽¹⁾ ) and T (x, u ₂ ⁽¹⁾ ), T (x, u ₀ ⁽¹⁾ ) and T Since (x, u ₂ ⁽¹⁾ ) has already been determined, if (u ₁ ⁽¹⁾ , v ₁ ⁽¹⁾ ) is defined, (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ) and (x ₂ ^It can be seen that ⁽¹⁾ , y ₂ ⁽¹⁾ ) are also determined.

In this regard, the contact point (u ₁ ⁽¹⁾ , v ₁ ⁽¹⁾ ) has the smallest approximate error due to the line segment S ₁ ^{(1) on which} it is placed and the adjacent line segments S ₀ ⁽¹⁾ , S ₂ ^(1). What is necessary is just to ask. For this purpose, the section error evaluation function E _S () of the equation (28) can be used. This function obtains the mean square of the approximation error in the interval [a, b] by the tangent line T (x, x _T ).

On the other hand, in order to minimize the approximation error, (x ₁ ⁽¹⁾ , y ₁ ⁽¹⁾ ), (x ₂ ⁽¹⁾ , y ₂ ^{( )} determined by the contacts (u ₁ ⁽¹⁾ , v ₁ ⁽¹⁾ ) ⁾ . It is also possible to minimize Eq. (29) as E (1, 1) using Eq. (28) together with ¹⁾ ). In this ^{_{case, E (1,1) = E S}} (u 0 (1), 1, x 1 (1)) + E S (u 1 (1), x 1 (1), x 2 (1)) + E S (U ₂ ⁽¹⁾ , x ₂ ⁽¹⁾ , 2).

E (m, n) in equation (29) is a function of u _n ^(m) . Therefore, for minimization, u _n ^(m) with a derivative of 0 may be obtained analytically as shown in equation (30), or E (m, n) is obtained by solving a nonlinear optimization problem. The minimum u _n ^(m) may be obtained. In the former case, since it is analytical, it can be minimized without error.

The contact (u ₁ ⁽¹⁾ , v ₁ ⁽¹⁾ ) that minimizes the approximation error is obtained by the method described above. The obtained contact points and end points are inherited and used when optimizing the broken line approximation with the line number 2 ² +1. At that time, the contact points (u _n ^(m) , v _n ^(m) ) are associated with (u _2n ^{(m + 1)} , v _2n ^{(m + 1)} ) to be the same point.

In the line number 2 ² +1, the optimum contact (u ₁ ⁽²⁾ , v ₁ ⁽ from the tangents T (x, u ₀ ⁽²⁾ ) and T (x, u ₂ ⁽²⁾ ) is used to minimize the approximation error. ²⁾ ), and the optimum contact (u ₃ ⁽²⁾ , v ₃ ^{( 2)} ) is obtained from the tangents T (x, u ₂ ⁽²⁾ ) and T (x, u ₄ ⁽²⁾ ). Tangent T in this manner sequentially adjacent (x, u _{n over ^{1 (m)), T (}} x, u n + 1 (m)) contacts which minimizes the approximation error involved from _{^{(u n (m), v}} n ( ^m) )

Similarly, in the line segment 2 ^m +1, the contact group determined by the approximation optimization is inherited to the line function of the line segment number 2 ^{m + 1} +1, and further approximate optimization is performed so that only a positive error having a desired approximation accuracy can be obtained. Can be obtained.

[Linear approximation without constraints]
Consider a polygonal line approximation that has no constraints on end points, such as a polyline approximation that does not exceed, and no restrictions on line segments, such as a polyline approximation that does not fall below. That is, for the end points other than (1, 0) and (2, 1), the end points that exceed the points on the approximation target function at the same x coordinate value and the end points that fall below the points on the approximation target function at the same x coordinate value. Including. In other words, the unrestricted broken line approximation function is a broken line approximation function including a line segment that intersects the approximation target function, a line segment that exceeds the approximation target function, a line segment that falls below, a line segment that touches the approximation target function, and at least One end point may include at least one of the line segments on the approximation target function. Since there is no need to improve the approximation error while increasing the number of broken lines sequentially and inheriting the immediately preceding optimization information as in the conventional broken line approximation, the end point is expressed as (x _n , y _n ). Also, the line segment _{S n} with the end points _(x n, _{y n)} and a _{(x n + 1, y n} + 1) expressed as equation (31).

Classification error evaluation function _{E S} according to the _{S n} also using equation (32).

Overall error evaluation function E if the number of segments N can be expressed as Equation (33) using E _S.

  When the simultaneous equations having the partial derivatives of all the end points of Equation (33) as 0 can be solved analytically, the end point groups obtained thereby constitute the optimum approximation with the minimum approximation error. If this simultaneous equation cannot be solved analytically, the equation (33) may be minimized by a nonlinear optimization method or the like. If the end point group which is the optimal solution in each approximation is set as an initial state, a favorable optimal solution can be obtained.

(Comparison)
FIG. 6 shows a graph in which the mean square values of approximation errors with respect to the number of line segments or the number of nodes of these three types of broken line approximation are plotted on the logarithmic axis. The horizontal axis is the number of nodes only for the polygonal line approximation that does not fall below. Conventional G.M. While the mean square error of 726 is about 0.004, as shown in FIG. 6, this approximation method can obtain an approximation result that is better by one digit or more. Note that the integer part at the time of logarithm is the amount of computation of O (log ₂ k) according to the binary search. Since the calculation amount O (k) is less than 726, it can be obtained at a higher speed than the conventional method.

[1-4. Operation]
The operation of this system will be described with reference to FIGS. FIG. 7 is an operation flowchart of the encoding apparatus 10. FIG. 8 is an operation flowchart of the decoding device 20. Note that these are examples of operations and are not limited to the order.

  As a prerequisite for the operation of this system, the parameters are designed to satisfy the desired system characteristics, but when measuring or adjusting the correspondence between parameters and system characteristics during operation, Use the adjusted parameters.

[Initialize]
As shown in FIGS. 7 and 8, first, as initial settings at the start of operation, the parameters of each unit are set for both the encoding device 10 and the decoding device 20 (step S01). That is, parameters stored in advance in the storage units 14 and 24 of the devices 10 and 20 or parameters input via the user interface UIs 11 and 21 or the external connection I / Fs 12 and 22 are input to the units of the devices 10 and 20. Set.

  The control units 13 and 23 determine whether or not the parameter set using the parameter identification value is applicable. If the parameter is not applicable, the user interface UI11 or 21 or the external connection I / F 12 is displayed on the display. The notification may be notified to the outside via 22 and this operation may be suspended.

  Next, each device 10 and 20 resets an internal state such as a state variable to an initial state (step S02). This is to prevent an unintended sound from being output due to an undefined state variable before the start of operation.

[Information input and output]
The encoding device 10 inputs sound or sound information from the outside through the sound input I / F 15 or the like according to the set parameters, or inputs sound information stored in the storage unit 14 to the encoder 16 (step S03). The encoder 16 encodes the sound code according to the set parameter (step S04), and encodes the sound code encoded according to the set parameter, such as a synchronization signal, information necessary for reproduction thereof, and the sound code stored in the storage unit 14. The data is output to the decryption device 20 (step S05). Information necessary for reproduction of the encoded sound code includes a parameter identification value.

  The decoding apparatus 20 receives the sound code input from the transmission medium 30 according to the set parameters and information necessary for reproduction thereof (step S06). Here, the parameters common to the encoder 16 and the decoder 26 must be the same. In particular, in this system, since the parameters are variable, the consistency of the parameters is confirmed prior to the decoding of the sound code.

  That is, the control unit 23 of the decoding device 20 collates the parameter identification value included in the input information with the parameter identification value currently set in the decoding device 20 (step S07). If they match (YES in step S07), decoding of the input sound code is permitted, decoding is performed according to the set parameters, and decoded into sound information (step S08). Further, the decoded sound information is output to the outside of the decoding device 20 via the sound output I / F 27 (step S09).

  On the other hand, if the parameter identification values do not match (NO in step S07), inconsistency processing is performed (step S10). That is, inconsistency is notified to the outside via the user interface UI 21 and the external connection I / F 22 and decoding is not permitted. If the parameter corresponding to the parameter identification value input from the encoding device 10 is included in the storage unit 24 or the operation control I / F of each unit, the parameter is switched to that parameter for matching. Note that the parameters of the encoder 16 may be matched with the parameters of the decoder 26.

  After step S05 or step S09, the control units 13 and 23 confirm the reset request from the user or the external connection device and the reset request from the part where the abnormality is detected in the encoder 16 or the decoder 26 (step S11). If there is a reset request (YES in step S11), the process returns to step S02. On the other hand, if there is no reset request (NO in step S11), the process proceeds to step S12. If there is a request for parameter setting change via the user interface UI11, 12 or the external connection I / F 12, 22 by the user or the like during operation of this system (YES in step S12), the process returns to step S01 and the requested parameter is updated. To do. In this case, if necessary, the devices 10 and 20 may be temporarily stopped and reset before the update, and restarted after the update. If there is no request for parameter setting change (NO in step S12), the process returns to step S03 for sound input, step S06 for code input (NO in step S13), or ends (YES in step S13).

  Note that steps S01, S02, S11, and S12 may be performed in parallel by the encoding device 10 and the decoding device 20, or may be performed independently of each other, and before and after that are arbitrary. Further, only one of them may be performed.

[1-5. effect]
(1) The sound encoding system according to the present embodiment includes adaptive normalization units 43 and 53 serving as calculation units for calculating a function approximate to a function including a logarithmic function as an approximation target. Nos. 43 and 53 approximate the function to be approximated by a line function that does not exceed the function value to be approximated by connecting a plurality of points on the function with line segments. In particular, the adaptive normalization units 43 and 53 obtain a plurality of points that minimize the approximation error of a function to be approximated by subtracting a polygonal line function obtained by connecting a plurality of points on the function with line segments. Then, a line function that does not exceed these multiple points as the end points of each line segment of the line function is obtained.

  As a result, ITU-T G.I. Approximation accuracy can be improved as compared with the conventional ADPCM method represented by 726. For example, the mean square error is ITU-T GG. An approximation result that is one digit or more better than 726 can be obtained. Therefore, sound quality can be improved and sound reproducibility can be improved.

(2) The adaptive normalization units 43 and 53 approximate the function to be approximated by a polyline function that does not fall below the function value to be approximated by connecting a plurality of points on the function with line segments. In particular, a polygonal line function that does not fall is a tangent line in which each line segment has a contact point with a function to be approximated as a plurality of points within the domain of definition, and the adaptive normalization units 43 and 53 ride on the contact point. The approximation error between the line segment and the function to be approximated by both adjacent line segments is determined to be minimum.

  As a result, ITU-T G.I. Approximation accuracy can be improved as compared with the conventional ADPCM method represented by 726. For example, the mean square error is ITU-T GG. An approximation result that is one digit or more better than 726 can be obtained. Furthermore, the approximation accuracy can be improved as compared with the broken line approximation that does not fall below. Therefore, sound quality can be further improved, and sound reproducibility can be further improved.

(3) The adaptive normalization units 43 and 53 approximate the function to be approximated by a polygonal line function including a line segment intersecting with the function, and the polygonal line function is expressed by the end points (x _n , y _n ) and ( when representing the _{x n + 1, y n +} 1) line _{S n} with expressed by equation (31), the division error evaluation function _{E S} according to the line segment _{S n} in formula (32), the error evaluation of the expression (33) It was obtained when function E was minimized. As a result, ITU-T G. The approximation accuracy can be improved as compared with the conventional ADPCM method represented by 726, and the approximation accuracy can be further improved than the above-described broken line approximation and the broken line approximation not below.

[2. Other Embodiments]
The present invention is not limited to the above-described embodiments as they are, and can be embodied by modifying the constituent elements without departing from the scope of the invention in the implementation stage. In addition, various inventions can be formed by appropriately combining a plurality of components disclosed in the embodiment. For example, some components may be deleted from all the components shown in the embodiment. The following is an example.

(1) In the sound encoding system according to the first embodiment, the parameter setting has been described based on the user's request, but the present invention is not limited to this. The parameters used in the encoding device 10 and the decoding device 20 may be configured to be automatically changed when triggered by input to the devices 10 and 20 such as sound, sound information, and sound code. For example, when the input to the sound input I / F 15 of the encoding device 10 is switched from a male voice to a musical instrument sound, the probability distribution of the prediction error changes, so that the sound signal level, frequency characteristics, etc. change. And the parameters of the operation control I / F of the encoder 16 and the decoder 26 may be changed to parameters suitable for the sound of the instrument. As a method for determining an input change, for example, a threshold or a range for determining an input change is set in the operation control I / F of each part of the encoder 16 and the decoder 26.

(2) In the sound encoding system of the first embodiment, the encoder 16 and the decoder 26 are configured as separate bodies, but may be configured as a system in which these are integrated. Further, the system may be configured as a single device on which an encoder that outputs sound information decoded by the adaptive prediction unit 56 is mounted. In this case, it is useful for obtaining the correspondence between the setting parameter and the system characteristic.

(3) In the sound encoding system according to the first embodiment, the operation control I / F provided in the processing units of the encoder 16 and the decoder 26 is used according to the sound information or the sound code input to the processing unit. Although a control signal for parameter update is output to the control units 13 and 23 and the parameters are updated by the control units 13 and 23, the present invention is not limited to this, and the reverse relationship may be used. That is, the operation control I / F detects a predetermined internal state in which the operation control I / F is provided and notifies the control units 13 and 23, and the control units 13 and 23 are notified of each processing unit. A control signal for updating the parameter according to the internal state may be output to each processing unit, and the operation control I / F may update the parameter used in the processing unit based on the control signal.

10 Encoder 11 User interface UI
12 External connection I / F
13 Control unit 14 Storage unit 15 Sound input I / F
16 Encoder 17 Code output I / F
20 Decoding Device 21 User Interface UI
22 External connection I / F
23 Control unit 24 Storage unit 25 Code input I / F
26 Decoder 27 Sound output I / F
30 Transmission medium 41, 51 Preprocessing unit 42 Adder 43, 53 Adaptive normalization unit 44 Optimal quantization unit 45, 55 Optimal inverse quantization unit 46, 56 Adaptive prediction unit 47, 57 Adder 48, 58 Post processing unit 41p 43p-46p, 48p Operation control I / F
51p, 53p, 55p, 56p, 58p Operation control I / F
431 Gain term calculation unit 431a Delay element 431b Adder 4310 to 431n Coefficient control condition unit 432 Gain term selection condition unit 432a Delay element 433 Switching unit 434 Attenuation term calculation unit 434a Delay element 434b Adder

Claims (7)

An arithmetic unit including a calculation unit that calculates a function that approximates a function including a logarithmic function as an approximation target,
The calculation unit approximates the function to be approximated by a line function that does not exceed the function value to be approximated by connecting a plurality of points on the function with line segments,
An arithmetic unit characterized by the above. The calculation unit obtains the plurality of points where the approximation error is minimized by subtracting a polygonal line function obtained by connecting a plurality of points on the function with line segments from the function to be approximated. Obtaining a line function that does not exceed the point with the point as the end point of each line segment of the line function,
The arithmetic unit according to claim 1, wherein: An arithmetic unit including a calculation unit that calculates a function that approximates a function including a logarithmic function as an approximation target,
The calculation unit approximates the function to be approximated by a line function that is not lower than the function value to be approximated by connecting a plurality of points on the function with line segments,
An arithmetic unit characterized by the above. The non-lower polygonal line function is a tangent line in which each line segment has a point of contact with the function to be approximated as the plurality of points within the domain,
The computing unit determines the contact point such that an approximation error between the line segment on which the contact point is placed and the function to be approximated by both line segments adjacent thereto is minimized;
The arithmetic unit according to claim 3. An arithmetic unit including a calculation unit that calculates a function that approximates a function including a logarithmic function as an approximation target,
The calculation unit approximates a function to be approximated by a line function including a line segment intersecting with the function,
The polygonal line function, end point _(x n, _{y n)} and _{(x n + 1, y n} + 1) expressed by equation (1) the line segment _{S n} with the formula a classification error evaluation function _{E S} by the line segment _{S n} ( 2), it is obtained when the error evaluation function E of Equation (3) is minimized.
An arithmetic unit characterized by the above.
N: number of line segments, x: x coordinate on the line segment, y: y coordinate on the line segment
An encoding device for encoding the input sound;
A decoding device for decoding the input sound code;
A transmission medium for transmitting the sound code output by the encoding device to the decoding device;
With
The encoding device and the decoding device each include the arithmetic device according to any one of claims 1 to 5,
A sound coding system characterized by. The encoding device and the decoding device, as the arithmetic device according to any one of claims 1 to 5, include a prediction error that is a difference between sound information and a prediction value of the sound information, and a prediction value of the prediction error. An adaptive normalization unit for obtaining a normalized prediction error obtained by normalizing the prediction error based on
The adaptive normalization unit includes a logarithmic function of an absolute value of the prediction error in a function for obtaining the normalized prediction error;
The sound encoding system according to claim 6.