KR101089724B1 - Method for designing qmf filters, analyzing and synthesizing channel using the filters - Google Patents

Abstract

PURPOSE: A method for designing a QMF(Quadrature Mirror Filter), a channel separating method, and a channel synthesizing method are provided to reduce errors by improving the filtering efficiency of pixel values in a boundary of an image. CONSTITUTION: A QMF bank system sets a low pass filter and a high pass filter(110). A system sets a half-band product filter to a z polynomial(120). The system converts the set half-band product filter to the product of the symmetric polynomial and the square of the low pass filter(130). The system calculates a second polynomial by the conversion of the set half-band product filter(140). The system determines a high pass filter(150).

Description

ForＭＦ （ｑｕａｄｒａｔｕｒｅ ｉｉｒｒｏｒ ｆｉｌｔｅｒ） Filter design method, channel separation and synthesis method using the filter {Method for designing QMF filters, analyzing and synthesizing channel using the filters}

The present invention relates to a method for designing a QMF filter, a method for channel separation and synthesis using the filter, and more particularly, to a filter design method for determining filter coefficients used for encoding and decoding in a QMF filter bank for band division coding. The present invention relates to a method for separating an input signal into two channels using a filter designed through the above method, and a method for recovering an original input signal by synthesizing the separated channel signal.

The Joint Photographic Experts Group (JEPG) International Standardization Group recently released JPEG2000, which employs waveform conversion using a two-channel Quadrature Mirror Filter (QMF) banking system for high-quality image compression, and is widely used in medical imaging and many applications.

The two-channel QMF bank system uses a tree structure to split the input video signal into several successive frequency bands, and aliasing bands between adjacent bands represented by using non-ideal filters. The QMF filters that are 'alias-free' and used have a linear phase and are fully reproducible if the frequency response characteristic of the system function satisfies '1'.

The technical problem to be solved by the present invention is to solve the problem of QMF filter distortion and QMF quantization distortion in the QMF bank system, and to filter the pixel values existing at the boundary of the image. In order to overcome the limitation that the filtering efficiency of the boundary region pixels is degraded due to the use of unrelated correlated pixels, a method of designing a QMF filter and a channel separation and synthesis method using the filter are provided.

In order to solve the above technical problem, a design method of a quadrature mirror filter (QMF) filter for band division coding according to the present invention, a low-pass filter of a linear phase in which the order of the filter is p + 1 (p is a positive integer) setting a lowpass filter and a highpass filter of linear phase of order 3p + 1; Setting a half-band product filter corresponding to the product of the low pass filter and the high pass filter to a z polynomial having an order of 4p + 2; Converting the set inverse product filter to a product of a square of the low pass filter and a symmetric polynomial, and calculating a first polynomial using the low pass filter determined as a predetermined integer filter; Converting the set inverse product filter to produce a second polynomial having (1 + z ⁻¹ ) ² as a factor; And calculating the symmetric polynomial by comparing the calculated coefficients of the first polynomial and the calculated second polynomial, and determining a high pass filter from the product of the low pass filter and the calculated symmetric polynomial.

On the other hand, the following provides a computer readable recording medium having recorded thereon a program for executing a method of designing a QMF filter for band division coding described above on a computer.

In order to solve the above other technical problem, the channel separation method using the QMF filter according to the present invention, the first band signal is separated from the input signal through a first pass filter, and the second pass filter from the input signal through the second pass filter; Separating the two band signals; And decimating the separated first band signal and the separated second band signal in half, wherein the first pass filter is a low pass filter determined as a predetermined integer filter, and the reduced signal The channel synthesis stage restores a signal corresponding to the input signal through a reconstruction filter corresponding to the first pass filter and the second pass filter, respectively, and the reconstruction filter corresponding to the first pass filter is the order of the filter. Sets a low pass filter of linear phase where p + 1 (p is a positive integer) and a high pass filter of linear phase whose order is 3p + 1, and corresponds to the product of the low pass filter and the high pass filter Set an inverse product filter to a z polynomial having an order of 4p + 2, convert the set inverse product filter to the product of the square of the low pass filter and the symmetric polynomial, and A first polynomial is calculated using the low pass filter determined as an integer filter, and the set inverse product filter is converted to calculate a second polynomial having (1 + z ⁻¹ ) ² as an argument, and the calculated second Comparing coefficients of one polynomial and the calculated second polynomial yields the symmetric polynomial, and is obtained from the product of the low pass filter and the calculated symmetric polynomial.

In order to solve the other technical problem, the channel synthesis method using a QMF filter according to the present invention, the step of interpolating (doubled) receiving the first band signal and the second band signal; Reconstructing a signal corresponding to the original input signal at the channel separation stage through a reconstruction filter corresponding to each of the interpolated signals; And combining the reconstructed two signals to generate one signal, wherein the first band signal is separated from the original input signal through a low pass filter determined as a predetermined integer filter at the channel separation stage. The reconstruction filter corresponding to the first band signal includes a low pass filter of a linear phase in which the order of the filter is p + 1 (p is a positive integer) and a high pass of the linear phase in which the order of the filter is 3p + 1. A filter is set, a counterpass product filter corresponding to the product of the lowpass filter and the highpass filter is set to a z polynomial having an order of 4p + 2, and the set counterpass product filter is squared of the lowpass filter And a first polynomial using the low pass filter determined as a predetermined integer filter, and converting the set inverse product filter to (1 + z). ^{1) 2} to produce a second polynomial having as an argument, and wherein the output of the first polynomial and by comparing the coefficients of the second polynomial the calculated and calculating the symmetrical polynomial, the low-pass filter and the calculated symmetric polynomial Is obtained from the product of.

The low pass filter H ₀ (z) determined as the predetermined integer filter in the design method of the QMF filter and the channel separation and synthesis method using the filter has at least one zero at z = −1, and H ₀ (z ) | _{z = 1} = 1 is satisfied.

In the above-described method of designing a QMF filter and a channel separation and synthesis method using the filter, the first polynomial sets the high pass filter to a product of a symmetric polynomial having an order of 2p with the low pass filter, A high pass filter set as a product of the low pass filter and the symmetric polynomial is input to an inverse product filter set to z polynomial, and the result of the operation is the opposite of the result of the calculation. An inverse product filter is calculated and calculated by inputting the predetermined integer filter to the calculated inverse product filter.

Furthermore, in the above-described method of designing a QMF filter and a channel separation and synthesis method using the filter, the second inverse polynomial is that the set inverse product filter F (z) is z = j (e ^jw | _{w = π / 2} ). When the filter coefficient satisfying F (j) = 1 is calculated, the inverse product filter F (z) is set to a polynomial using the calculated filter coefficient, and the inverse product filter set to the polynomial ( 1 + z ^-1 ) ² is calculated by converting it to have a factor.

According to the present invention, a low pass filter presented as an integer filter and a corresponding high pass filter for reconstruction are set to polynomial and the filter coefficients of both are determined, so that there is no filter distortion in the QMF bank system and complete reproduction of an image is possible. 'Error-free' can be achieved by improving the filtering efficiency of the pixel values existing in the boundary region of the image.

1 is a flowchart illustrating a method of designing a QMF filter for band division coding according to an embodiment of the present invention.
FIG. 2 is a diagram illustrating, according to each order, a low pass filter presented as an integer filter employed in a design method of a QMF filter for band division coding according to an embodiment of the present invention.
3 is a flowchart illustrating a process of calculating a first polynomial in the QMF filter design method of FIG. 1 according to an embodiment of the present invention in more detail.
4 is a flowchart illustrating a process of calculating a second polynomial in the QMF filter design method of FIG. 1 according to an embodiment of the present invention in more detail.
5 is a view for explaining a channel separation method and a channel synthesis method using a QMF filter according to another embodiment of the present invention.

Before describing the embodiments of the present invention, the environment in which the embodiments are implemented will be briefly introduced, and related problem situations will be presented.

The QMF bank used for band division coding has been developed since Croiser et al. As described above, the QMF bank is a fully reproducible filter having 'alias-free' for aliasing bands generated between adjacent bands when the input signal is divided into several consecutive frequency bands. In the two-channel separation / synthesis QMF bank, 'alias-free' is proved in Equation 1 below in the frequency domain.

In Equation 1, X (z) represents the z transform of the input signal x (n), X _L (z) represents the z transform of the low pass signal X _L (n), and X _U (z) represents the high pass. Z z transform of signal X _U (n), H _L (z) and H ₀ (z) represent the low pass filter, and H ₁ (-z) represents the high pass filter.

Although the QMF bank has a structure capable of 'alias-free' full reproduction, there are many problems in the Sub Band Coding (SBC) system. QMF filters cause QMF filter distortion and QMF quantization distortion in the QMF bank system. QMF filter distortion always occurs regardless of coding because a non-ideal filter is used in the QMF bank, and QMF quantization distortion is a distortion generated in the QMF bank system itself due to the actual coding. These two distortions depend on the frequency response characteristics of the QMF filters used. In addition, the implementation of the two-dimensional QMF filter for band division of the two-dimensional image can be implemented simply by extension of the one-dimensional QMF by Vetteli, but since the image is a finite duration sequence, When filtering the pixel values, the use of uncorrelated neighborhood pixels due to circulation causes a problem that the filtering efficiency of the boundary area pixels is lowered.

Accordingly, embodiments of the present invention to be described below are devised to solve the above-mentioned problems, and have a property of full reproduction without phase and amplitude distortion, which are QMF filter distortions generated in QMF of band division coding. To provide a design method and filter coefficients for a QMF filter that is not sensitive to QMF quantization distortion. To this end, embodiments of the present invention have a frequency response characteristic of a 'sharp and symmetric' transition band while satisfying a perfect reproduction condition for an image, and have a first transfer function H ₀ (z) (hereinafter, referred to as a low pass filter). And first and second decomposition filters using a second transfer function H ₁ (z) (hereinafter referred to as a high pass filter). Hereinafter, embodiments of the present invention will be described in more detail with reference to the accompanying drawings. Like reference numerals in the drawings refer to like elements.

1 is a flowchart illustrating a method of designing a QMF filter for band division coding according to an embodiment of the present invention, and includes the following steps.

Linear phase lowpass filter with order of filter p + 1 (p is a positive integer) and linear phase highpass with order 3p + 1 at step 110 Set a highpass filter. This 110 step setting is performed by assuming that each of the low pass filter and the high pass filter is a FIR filter having a linear phase by using the conditions of a 2-channel QMF bank capable of perfect reconstruction shown in Equation 2 below. do.

Equation (2) is a signal decomposed by the low pass filter in the encoding stage (signal decomposition stage) can be restored to the original signal by the high pass filter in the decoding stage (meaning signal synthesis stage). Indicates.

In step 120, a half-band product filter corresponding to the product of the low pass filter and the high pass filter is set to a z polynomial having an order of 4p + 2 based on the setting of step 110. The set z polynomial is expressed as Equation 3 below.

와 같이 표현되므로, 이상의 수학식 3으로부터 반대역 곱 필터 F(z)는 다음의 수학식 4와 같이 표현된다.At this time, when F (z) is z = j (e ^jw | _{w = π / 2} ), the filter coefficient satisfying F (j) = 1 is

Since it is expressed as follows, the inverse product filter F (z) from Equation 3 is expressed as Equation 4 below.

In operation 130, the inverse product filter set in operation 120 is converted into the product of the square of the low pass filter and the symmetric polynomial, and the first polynomial is calculated using the low pass filter determined as the integer filter. Referring to FIG. 3, which shows step 130 in more detail with respect to each process, the following is described. In FIG. 3, 'A' corresponds to step 120 previously described.

In step 131, the high pass filter is set to the product of the low pass filter and the symmetric polynomial having the order of 2p. In other words, from the low pass filter H ₀ (z) that decomposes the input signal, the relationship between them is obtained by obtaining the high pass filter H ₁ (-z) that synthesizes the decomposition signal in order to restore the original input signal correspondingly. Let's define it as shown in Equation 5.

In step 132, the high pass filter set as the product of the low pass filter and the symmetric polynomial is input to the inverse product filter set as the z polynomial. In Equation 5, W (z) is a symmetric polynomial having an order of 2p and is a means for mediating the relationship between the low pass filter and the high pass filter. Therefore, if the above equation 5 is applied to the high pass filter H ₁ (−z) of Equation 3 described above, the inverse product filter F (z) is arranged as in Equation 6 below.

In operation 133, the operation result of operation 132 calculates the inverse product filter converted into the product of the square of the low pass filter and the symmetric polynomial. The converted inverse product filter is represented by Equation 6 above. At this time, the known filter used as the low pass filter is presented by the rule of thumb in the process of devising the embodiments of the present invention, illustrated through FIG.

FIG. 2 is a diagram illustrating, according to each order, a low pass filter presented as an integer filter employed in a design method of a QMF filter for band division coding according to an embodiment of the present invention. FIG. 2 shows that low pass filters are defined by different types of polynomials according to positive integer p values and variable α values according to respective orders. The low pass filter is designed to be completely regenerated and insensitive to QMF quantization distortion, and a person of ordinary skill in the art may implement a QMF filter bank in addition to the low pass filter shown in FIG. 2. It will be possible to present various filters accordingly.

와 W(z)는 다음의 수학식 7과 같이 각각 정의된다.In operation 134, the first polynomial is calculated by inputting and operating an integer filter to the inverse product filter calculated in operation 133. Low pass filter H ₀ (z) has at least one zero at z = -1 and H ₀ (z) | Assuming that the integer filter of FIG. 2 satisfies _{z = 1} = 1, the factor of Equation 6 above

And W (z) are defined as in Equation 7 below.

의 k_i (i=0,1,2,...,2p) (known)는 계수들로서, 도 2를 통해 제시된 p와 α에 의해 쉽게 산출된다.here,

K _i (i = 0,1,2, ..., 2p) (known) are coefficients, and are easily calculated by p and α shown through FIG.

Now, Equation (7) is substituted into Equation (6) to calculate a first polynomial such as Equation (8).

Now, since the calculation of the first polynomial has been completed, return to FIG. 1 and proceed to step 140 (corresponding to C (step 140) of FIG. 3).

In operation 140, the inverse product filter set in operation 120 is converted to calculate a second polynomial having (1 + z ⁻¹ ) ² as an argument. A description will now be given with reference to FIG. 4, which illustrates 140 steps with respect to each performance process. 'B' in FIG. 4 corresponds to step 130 previously described.

와 같이 표현됨을 설명하였다.In operation 141, when the inverse product filter F (z) set in operation 120 is z = j (e ^jw | _{w = π / 2} ), a filter coefficient satisfying F (j) = 1 is calculated. Earlier, the filter coefficients satisfying these conditions

It is described as follows.

In step 142, the inverse product filter F (z) is set as a polynomial using the filter coefficient calculated in step 141, which is also derived from the above-described equation (3) using equation (141). It has already been explained.

In operation 143, the second polynomial is calculated by converting the inverse product filter set to the polynomial in operation 142 to have (1 + z ⁻¹ ) ² as an argument. That is, the inverse product filter F (z) expressed as a polynomial as in Equation 4 has two zeros at z = -1, so that (1 + z ^-1 ) ² is expressed as in Equation 9 below. It can be expressed as a second polynomial having as an argument.

Now, since the calculation of the second polynomial has been completed, return to FIG. 1 again and proceed to step 150 (corresponding to D (step 150 in FIG. 4)).

Step 150 calculates a symmetric polynomial by comparing the coefficients of the first polynomial calculated in step 130 and the second polynomial calculated in step 140 and determines a high pass filter from the product of the low pass filter and the calculated symmetric polynomial. .

에 대하여 known 계수들인 k_{i (}i=0,1,2,...,2p)와 p+1개의 미지수(unknown) 계수들인 w_{i (}i=0,1,2,...,p)를 이용하여 다음의 수학식 10과 같이 표현될 수 있다.First, the coefficients of the first polynomial of Equation 8 and the second polynomial of Equation 9 are compared to calculate a symmetric polynomial. Coefficient G _{m in} Equation 8 for QMF Bank Filter Design Find (m = 0,1,2, ..., p). Where G _m is given

The known coefficients k _{i (} i = 0,1,2, ..., 2p) and p + 1 unknown coefficients w _{i (} i = 0,1,2, ..., p) It can be expressed as shown in Equation 10 below.

Here, [·] means the operation which rounds off the decimal point of the value in a square.

As shown in Equation 10, the coefficients of the first polynomial are summarized. Next, the coefficients of the second polynomial are derived. In Equation 9, the coefficient C _m (m = 0,1,2, ..., p) is given by using the known coefficients r _i (i = 0,1,2, ..., p) It can be expressed as in Equation (11).

As shown in Equation 11, the coefficients of the second polynomial are summarized.

Now, using the condition that Equation 8, which is the first polynomial, and Equation 9, which is the second polynomial, are equal, G _{m in} Equation 10 and C _{m in} Equation 11 are equal (but m = 0,1,2, ..., 2p). 2p + 1 equations are generated to obtain 2p + 1 unknown w _i (i = 0,1,2, ..., p) by comparing their coefficients. W (z) is determined from the obtained coefficients w _i (i = 0,1,2, ..., p). Finally, the high pass filter H ₁ (−z) is determined from the product of the low pass filter H ₀ (z) and the calculated symmetric polynomial W (z) from equation (5).

According to the embodiment of the present invention described above, the filter distortion in the QMF bank system by setting the low pass filter presented as an integer filter and the corresponding high pass filter for reconstruction to polynomial and determining both filter coefficients through a series of operations It is possible to design a QMF filter without a full picture and without any reproduction.

On the other hand, the embodiments of the present invention described above can be implemented in a computer-readable code on a computer-readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored.

Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disks, optical data storage devices, and the like, which may also be implemented in the form of carrier waves (for example, transmission over the Internet). Include. The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion. In addition, functional programs, codes, and code segments for implementing the present invention can be easily deduced by programmers skilled in the art to which the present invention belongs.

Now, a method implemented in the encoder and the decoder using a filter implemented according to the above-described QMF filter design method will be described with reference to FIG. 5.

5 is a diagram illustrating a channel separation method and a channel synthesis method using a QMF filter according to another embodiment of the present invention, and includes an encoder 500 (including a channel separation unit) 500 and a QMF filter using a QMF filter. And a decoder (including a channel synthesizer) 700. In addition, each of the encoder 500 and the decoder 700 may be designed according to two methodologies of [A] and [B] in the implementation method thereof. The overall configuration of FIG. 5 is based on a block diagram of a conventional two band sub band coding (SBC), wherein each filter is implemented according to the design method of the QMF filter according to the embodiment of the present invention. For convenience of explanation, the following description will focus on the embodiment of [A], but the synthesis filters 711 and 712 corresponding to the separation filters 511 and 512 and the down sampler for decay, respectively. A design method will be described based on a pair of up samplers 711 and 712 for interpolation corresponding to 531 and 532, respectively.

First, let's look at the channel separation method using the QMF filter.

First, the first band signal is separated from the input signal x (n) through the first pass filter 511, and the second band signal is separated from the input signal x (n) through the second pass filter 512.

Next, the down samplers 531 and 532 decrement each of the separated first band signal and second band signal in half. Through this reduction process, the two separated signals have the same size as the original input signal x (n). The shortened signal is transmitted to the decoder through appropriate communication means.

로 복원된다.Meanwhile, in the channel separation process, the first pass filter 511 is a low pass filter determined as a predetermined integer filter, and the reduced signals are passed through the first pass filter 511 and the second pass in the channel synthesis stage (representing a decoder). A signal corresponding to the original input signal through reconstruction filters 731 and 732 respectively corresponding to filter 512

Is restored.

At this time, the reconstruction filter 731 corresponding to the first pass filter 511 is a low-pass filter of the linear phase of which the order of the filter is p + 1 (p is a positive integer) and the order of the filter is 3p + 1. Set the high pass filter of the linear phase, set the inverse product filter corresponding to the product of the low pass filter and the high pass filter to the z polynomial with the order of 4p + 2, and set the set inverse product filter of the low pass filter A second polynomial having a (1 + z ^-1 ) ² as a factor by converting to a product of square and symmetric polynomials, calculating a first polynomial using a lowpass filter determined as an integer filter, and converting the set inverse product filter And calculate the symmetric polynomial by comparing the coefficients of the calculated first and second polynomials, and can be obtained from the product of the low pass filter and the calculated symmetric polynomial. Each process is already described through the design method of the QMF filter, so a detailed description thereof will be omitted.

Second, let's look at the channel synthesis method using the QMF filter.

First, the up samplers 711 and 712 receive the first band signal and the second band signal and interpolate twice. This is to recover the size of the signal portion previously lost by the reduction in the channel separation stage.

를 복원한다. Next, a signal corresponding to the original input signal at the channel separation stage is restored through reconstruction filters 731 and 732 corresponding to each of the interpolated signals, and the two reconstructed signals are transmitted through the signal synthesizer 750. By synthesizing as a signal

Restore it.

In this case, the first band signal is a signal separated from the original input signal through the low pass filter 511 determined as an integer filter at the channel separation stage, and the reconstruction filter 731 corresponding to the first band signal is the QMF described above. Naturally, the filter is obtained through the filter design method.

According to the embodiments of the present invention presented above, there is no filter distortion in the QMF bank system by setting the low pass filter presented as an integer filter and the corresponding high pass filter for reconstruction to polynomial and determining both filter coefficients, Full reproduction of the image is possible, and 'error-free' can be achieved by improving the filtering efficiency of the pixel values existing in the boundary region of the image. In particular, those skilled in the art may implement the above embodiments using the QMF 5-7 tap filter used in band division coding.

The present invention has been described above with reference to various embodiments thereof. Those skilled in the art will understand that the present invention can be implemented in a modified form without departing from the essential features of the present invention. Therefore, the disclosed embodiments should be considered in an illustrative rather than a restrictive sense. The scope of the present invention is shown in the claims rather than the foregoing description, and all differences within the scope will be construed as being included in the present invention.

500: encoder using a QMF filter (channel separator)
511, 512: filter for channel separation
531, 532: down sampler for decay
700: decoder using channel filter (channel synthesizer)
711, 712: filter for channel synthesis
731, 732: up sampler for interpolation
750: signal synthesizer

Claims (16)

In the design method of a quadrature mirror filter (QMF) filter for band division coding,
Setting a lowpass filter of linear phase with an order of filter p + 1 (p is a positive integer) and a highpass filter of linear phase with an order of filter of 3p + 1;
Setting a half-band product filter corresponding to the product of the low pass filter and the high pass filter to the z polynomial of the z transformed transfer function having an order of 4p + 2;
Converting the set inverse product filter to a product of a square of the low pass filter and a symmetric polynomial, and calculating a first polynomial using the low pass filter determined as a predetermined integer filter;
Converting the set inverse product filter to produce a second polynomial having (1 + z ⁻¹ ) ² as a factor; And
Comparing the calculated coefficients of the first polynomial and the calculated second polynomial to yield the symmetric polynomial, and determining a high pass filter from the product of the low pass filter and the calculated symmetric polynomial. The method of claim 1,
When the order p = 2 of the low pass filter H ₀ (z), the predetermined integer filter is

or

At least one of. The method of claim 1,
When the order p = 3 of the low pass filter H ₀ (z), the predetermined integer filter is

Method characterized in that. The method of claim 1,
When the order p = 4 of the low pass filter H ₀ (z), the predetermined integer filter is

Method characterized in that. The method of claim 1,
The low pass filter H ₀ (z) determined as the predetermined integer filter has at least one zero at z = −1, and H ₀ (z) | _{z = 1} = 1. The method of claim 1,
Computing the first polynomial,
Setting the high pass filter to the product of the low pass filter and a symmetric polynomial having an order of 2p;
Inputting and calculating a high pass filter set as a product of the low pass filter and the symmetric polynomial to the inverse product filter set to the z polynomial;
Calculating an inverse product filter converted into a product of the square of the low pass filter and the symmetric polynomial; And
Calculating the first polynomial by inputting and operating the predetermined integer filter to the calculated inverse product filter. The method of claim 1,
Computing the second polynomial,
Calculating a filter coefficient satisfying F (j) = 1 when the set inverse product filter F (z) is z = j (e ^jw | _{w = π / 2} );
Setting the inverse product filter F (z) to a polynomial using the calculated filter coefficients; And
Calculating a second polynomial by converting the inverse product filter set to the polynomial to have (1 + z ⁻¹ ) ² as an argument. A computer-readable recording medium storing a program for causing a computer to execute the method according to any one of claims 1 to 7. In the channel separation method using a QMF filter,
Separating the first band signal from the input signal through a first pass filter and separating the second band signal from the input signal through a second pass filter; And
Decimating the separated first band signal and the separated second band signal in half, respectively,
The first pass filter is a low pass filter determined as a predetermined integer filter,
The reduced signals reconstruct a signal corresponding to the input signal through a reconstruction filter corresponding to the first pass filter and the second pass filter, respectively, at a channel synthesis stage.
The reconstruction filter corresponding to the first pass filter sets a low pass filter of a linear phase in which the order of the filter is p + 1 (p is a positive integer) and a high pass filter of a linear phase in which the order of the filter is 3p + 1. And a counterpass product filter corresponding to a product of the lowpass filter and the highpass filter to a z polynomial of the z transformed transfer function having an order of 4p + 2, and setting the set counterpass product filter to the lowpass. Converts to the product of the square of the filter and the symmetric polynomial, calculates a first polynomial using the lowpass filter determined as a predetermined integer filter, and converts the set inverse product filter to factor (1 + z ^-1 ) ² Compute a second polynomial having, and compare the coefficient of the calculated first polynomial and the calculated second polynomial to calculate the symmetric polynomial, and multiply the low pass filter with the calculated symmetric polynomial Characterized in that is obtained from. The method of claim 9,
The low pass filter H ₀ (z) determined as the predetermined integer filter has at least one zero at z = −1, and H ₀ (z) | _{z = 1} = 1. The method of claim 9,
The first polynomial is
Set the high pass filter to the product of the low pass filter and a symmetric polynomial having an order of 2p,
A high pass filter set as a product of the low pass filter and the symmetric polynomial is input to an inverse product filter set to the z polynomial, and
Calculating an inverse product filter converted into a product of the square of the low pass filter and the symmetric polynomial;
And calculating the predetermined integer filter by inputting the calculated inverse product filter. The method of claim 9,
The second polynomial is
Calculating the filter coefficients satisfying F (j) = 1 when the set inverse product filter F (z) is z = j (e ^jw | _{w = π / 2} ),
The inverse product filter F (z) is set as a polynomial using the calculated filter coefficients.
Calculated by converting the inverse product filter set to the polynomial to have (1 + z ⁻¹ ) ² as an argument. In the channel synthesis method using a QMF filter,
Interpolating a first band signal and a second band signal by double;
Reconstructing a signal corresponding to the original input signal at the channel separation stage through a reconstruction filter corresponding to each of the interpolated signals; And
Synthesizing the two restored signals to generate one signal;
The first band signal is a signal separated from the original input signal through a low pass filter determined as a predetermined integer filter at the channel separation stage,
The reconstruction filter corresponding to the first band signal sets a low pass filter of a linear phase of which the order of the filter is p + 1 (p is a positive integer) and a high pass filter of the linear phase of which the order of the filter is 3p + 1. And a counterpass product filter corresponding to a product of the lowpass filter and the highpass filter to a z polynomial of the z transformed transfer function having an order of 4p + 2, and setting the set counterpass product filter to the lowpass. Converts to the product of the square of the filter and the symmetric polynomial, calculates a first polynomial using the lowpass filter determined as a predetermined integer filter, and converts the set inverse product filter to factor (1 + z ^-1 ) ² Compute a second polynomial having, and compare the coefficient of the calculated first polynomial and the calculated second polynomial to calculate the symmetric polynomial, and multiply the low pass filter with the calculated symmetric polynomial Characterized in that is obtained from. The method of claim 13,
The low pass filter H ₀ (z) determined as the predetermined integer filter has at least one zero at z = −1, and H ₀ (z) | _{z = 1} = 1. The method of claim 13,
The first polynomial is
Set the high pass filter to the product of the low pass filter and a symmetric polynomial having an order of 2p,
A high pass filter set as a product of the low pass filter and the symmetric polynomial is input to an inverse product filter set to the z polynomial, and
Calculating an inverse product filter converted into a product of the square of the low pass filter and the symmetric polynomial;
And calculating the predetermined integer filter by inputting the calculated inverse product filter. The method of claim 13,
The second polynomial is
Calculating the filter coefficients satisfying F (j) = 1 when the set inverse product filter F (z) is z = j (e ^jw | _{w = π / 2} ),
The inverse product filter F (z) is set as a polynomial using the calculated filter coefficients.
Calculated by converting the inverse product filter set to the polynomial to have (1 + z ⁻¹ ) ² as an argument.

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