TW382693B - Unified framework implementing cosine modulated filter banks (CMFBs) - Google Patents

Abstract

A unified framework for implementing modulated cosine transforms (MCTs) of various cosine modulated filters in audio compression standards. Said unified framework comprises a switch module and a transform calculation module. The calculation of a modulated cosine transform is done by first calculating through the switch module, and then the discrete cosine transform. The calculation of a reverse modulated cosine transform is done by first calculating a discrete cosine transform, and then calculating through the post switch module. In said unified structure, the computed discrete cosine transform is selected from the cosine transform groups of type-II, type-III, or type-IV. The calculation of the N-point discrete cosine transform is decomposed into three steps: the switch-addition step, the sub-transformation step, and the combination step. The sub-transformation step is selected from the calculation of two N/2-point discrete cosine transforms in the same group. The use of said unified structure generates a good regularity, has more popular applications, and a reduced complexity.

Description

Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs A7 B7 V. Description of the invention () Field of the invention The present invention relates to the posine modulated filter banks (CMFBs) in the current voice compression standard. In particular, it relates to the architecture of implementing CMFBs and the fast calculation of various modulated cosine transforms (MCTs) used in cMFBs. BACKGROUND OF THE INVENTION In the voice dust reduction standards, such as MPEG-1 level 1-3, MPEG-II level I-4, MPEG-IV and AC-3, CMFBs have been widely used to convert an audio sequence (audio sequence ) To convert from time domain to compression transform domain or subband domain. However, all CMFBs' formulas (fomormula) differ not only due to different standards, but also due to the standard order, block length (Mock length), and encoder or decoder. In the application of real time environments, these various forms need to be independently designed and tuned for accuracy, complexity, and memory movement. 'Turn 1 to indicate the structure of the CMFBs in the encoder or decoder. As shown in Figure 1, the program of CMFBs includes two steps, namely window-and-overlapping addition (WOA) and modulation cosine transformation. WO A performs multiplication and addition of windows of overlapping speech blocks. This paper size applies to China National Standards (M) specifications (210X297 centimeters)-installed-(Please read the notes on the back before filling out this page) I order. See k A7 B7 Staff Consumption of the Central Sample Bureau of the Ministry of Economic Affairs The cooperative prints 5. Description of the invention () ', the complexity of this step is 0 (κ) / each voice sample', where κ depends on the overlapping factors of the form. For example, κ is 16 for order 2 of MPEG_n, and 2 for AC-3 '. The second step is to modulate the cosine transform, the complexity of which is O (W) / each speech sample, where w is the length of the window, and it is different for different CMFBs. w ranges from 36 (for MpEGy level 3) to 4096 (for MPEG-IV). For WOA, it is usually implemented directly, and the design is straightforward. On the contrary, the complexity of the modulation cosine transformation is high, and, based on the concept of a similar fast Fourier transformation, has developed a rapid technology. It is well-known that the developed fast technology is similar to the fast Fourier transformation and the fast cosine transformation requires consideration and trade-off between computational complexity, regularity, modularity, and numerical accuracy. Therefore, designing the hardware or software of the modulation cosine transform is always an important issue. Many fast computer systems have been developed for modulating the cosine transform. These developed computer systems can provide different conversion lengths and different types of discrete cosine conversion. Regarding speech coding, the base-2 discrete cosine transform is the main consideration for length. The development of the base-2 fast discrete cosine transformation mechanism can be divided into two types of technologies, namely, indirect calculation of discrete cosine transformation via fast Fou.rier transformation or fast Hartley transformation, and by matrix factor Direct calculation of discrete cosine transformation of matrix factorization or recursive decomposition. This paper is again free to use Chinese National Standard (CNS) A4 specification (210X297%) (Please read the precautions on the back before filling out this page) Binding and binding. 0, printed by the Central Consumers Bureau of Ministry of Economic Affairs, Consumer Cooperatives A7 · B7 _ ^ _ 5. Description of the invention () Calculation. However, these two types of technologies have some disadvantages. The first type of technology requires additional complexity when the discrete .frame conversion corresponds to other transformations, while the second type of technology usually lacks modularity and data regularity. As written by Yun et al., "On the fixed-point-error analysis of several fast DCT algorithms, IEEE Trans. Circuits Syst. Video Technol., Vol. 3, Feb. 1991, pp. 27-41, Modularity and regularity are necessary for designing hardware and generalization of higher-order transformations. Recently, Kok has developed a fast rule for type-II discrete cosine transformation, which can recursively decompose a type N-II discrete cosine. Convert to two types of N / 2-type discrete cosine transforms (refer to "Fast algorithm for computing discrete cosine transform, s, IEEE Trans, on Signal Porcess., Vol. 45, No. 3, Mar. 1997, pp . 757-760). From a discrete cosine transformation, it is decomposed into two discrete cosine transformations, leading to the spirit of modularity and regularity. SUMMARY OF THE INVENTION The present invention overcomes the shortcomings and inefficiencies in the implementation and calculation of the various CMFBs in the pre-beta speech standard described above. The main purpose of the present invention is to provide a singular architecture that guides all modulation cosine transformations in the current voice compression standard into two modules including a front (or back) exchange and a discrete cosine transformation. . This paper size applies to China National (CNS) A4 specifications (210X297 is centimeter) '' ~~ (Please read the precautions on the back before filling out this page)-Binding, binding, and fees. L'y Ml-ULLi; ·- · '-A7' ------- B7_ 5. Description of the invention () According to the present invention, various time-domain aliasing cancellation (TDAC) filter layers, TDAC alternative-forms ( TDAC-variant) filter layer, and the modulation cosine conversion of the polyphase filter layer can be divided into two modules including a switching module and a discrete cosine conversion module. The forward transform is calculated by calculating the pre-exchange, followed by the discrete cosine transform. The inverse transform is calculated by calculating the discrete cosine transform followed by the post-commutation. The discrete cosine transform can be type-II, type-III, or type_IV. Another object of the present invention is to provide a fast calculation method applicable to three types of discrete cosine transforms, and a common calculation tool which can provide three types of discrete cosine transforms. Through this same calculation tool, all software modules or hardware modules for speech compression standards can be developed. Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs. To achieve a lower level of complexity, the present invention follows a direct calculation technique. In the development of sinusoidal transform, such as discrete Fourier transform and discrete cosine transform, recursive decomposition is a fast calculation method used. The present invention proposes a mechanism of recursive decomposition, which transforms a discrete cosine transformation type into a decomposition type-II, type_111, or type_IV. Accordingly, another object of the present invention is to provide a fast rule that recursively decomposes a discrete cosine transform of length N into other discrete cosine transforms of length N / 2. This paper uses + + Home Standard (CNS> 210x297 Volume Chu) Staff Consumption of Central Standards Bureau of the Ministry of Economic Affairs A7 _B7_ V. Description of the invention () Modulation cosine conversion in all speech compression standards, the architecture of the present invention has proven Good regularity, complexity, and characteristics of popular applications. Complexity analysis also shows that the present invention has the same complexity as the well-known discrete cosine transform technique. Brief description of the circle type./Figure 1 shows the general procedure of CMFB & in a speech encoder and decoder. Fig. 2 shows the modulation cosine conversion table according to the present invention as a commutative and discrete cosine conversion module. Figure 3 shows the formulas of the three types of CMFB, and the corresponding speech coding standards. γ / Figure 4 illustrates an 8-point version-II discrete cosine transform according to the present invention, which is decomposed into a 4-point version-II discrete cosine transform and a 4-point version-IV discrete cosine transform . Fig. 5 illustrates an 8-point type-III discrete cosine transformation according to the present invention, which is decomposed into a 4-point type-III discrete cosine transformation and a 4-point type-IV discrete cosine transformation. China National Standard (CNS) A4 specification (210X297j cents) (please read the precautions on the back before filling out this page). Packing. Printed by the Consumers 'Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs, printed A7' ___ —_B7__ V. Description of the invention (6) FIG. 6 illustrates an 8-point type-IV discrete cosine transform according to the present invention, which is decomposed into a 4-point type-III discrete cosine transform and a 4-point type-IV discrete cosine transform. . Figure 7 illustrates the computational complexity of the basis-2 discrete cosine transform of the present invention and the conventional art. Detailed description of the invention As mentioned above, the present invention guides the modulation cosine conversion of various CMFBs into two modules: front-back _) exchange module and discrete cosine conversion module I. FIG. 2 shows a modulation cosine conversion table as a commutative and discrete cosine conversion module according to the present invention. In addition, the discrete cosine transform derived from the modulated cosine transform can be one of three types of discrete cosine transform. These three types are commonly referred to as type_H, type_m, and type_jy. The switching module only needs direct calculation. However, the calculation of various discrete cosine conversion types greatly affects the efficiency and implementation results of the audio encoder or decoder. In order to achieve lower complexity, the present invention follows the technique of direct calculation 'which uses a recursive decomposition of discrete cosine transform. • The present invention uses a recursive decomposition method to calculate the discrete cosine transform. The method of the present invention derives two important characteristics. The first feature is that the technique has regularity. This regularity is the property of fast Fourier transformation, rather than the general nature of fast cosine transformation. For the data path design in large-scale integrated circuit chip design, and the memory in software programming (please read the precautions on the back before filling this page), and install. Order this paper rule against the Chinese National Standard (CNS) According to inspection (21GX297 Form A, printed by the Consumer Standards Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs, printed A7 B7 V. Description of the invention) This rule is very important. The first characteristic is that this fast method can be implemented in the language All modulation cosine transformations of phonetic symbols are optimized, because the method uses Wu covariant discrete cosine transformation to recursively and regularly decompose long-length transformations into short-length transformations, from length N to length N In the expansion of the recursive decomposition of / 2, the three types of discrete cosine transformations will be inserted. In other words, this fast method can be applied to all three types of discrete cosine transformations, and the three types of discrete cosine transformations The s-ten count tool is the same. Therefore, the invention of the invention confirms that all the different CMFas in the audio standard are led to different _swap or post_swap, but still The same calculation tool for discrete cosine transformation. As a result, through this same calculation tool, all software modules or hardware modules for speech compression standards can be developed. Moreover, for regularity and modularity The grouping, the decomposition developed by the present invention, replaces the same type of discrete cosine transformation by inserting the three types of discrete cosine transformations. Because this decomposition inserts the three types of discrete cosine transformations, this fast method can be applied to all This third-floor version of the discrete cosine transform is not just the type _n as proposed by Kok. The popularity of applicability is the key factor for the development of fast algorithms for the CMFBs in the current voice dust reduction standard. The following description Part is to detail how to guide all CMFBs from this paper to the applicable national standard (CNS) Α4 · _ (210 ^ 297 ^ 57 (Please read the precautions on the back before filling this page)

Printed A7 by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs ^ -____ B7 —__ V. Description of the invention () ~ '' ~~-To the exchange module and discrete cosine transformation, and confirm that the three types of discrete cosine transformation are decomposed For other types of discrete cosine transformation. In addition, the preferred embodiments of the decomposition of the discrete cosine transform of Type-Π and Type-K-IV are proposed respectively. Furthermore, the analysis of the computational complexity, regularity, modularity and numerical accuracy of the present invention is proposed. _Example 1 · The simplification type of CMFBs is based on two filter layers: the TDAC filter layer, another TDAC filter layer, and the polyphase filter layer, which are used for the modulation cosine conversion in the current speech standard. Can be divided into three categories. Figure 3 shows the formulas of these three types of CMFBs, and the corresponding speech coding standards. The following description shows that all CMFBs can be expressed as two modules of forward or backward exchange and discrete cosine conversion, as shown in Figure 2. And, the type of the discrete cosine transformation may be one of the following three types: DCT of type-II ^-1 = Σχ / cos (— (2i +1) (^)), k = 0, l, ... . DCT Ni k-cos (-z ~ r: ()) (2k + 1)) of Nj type-III, k = 0,1, ..., N-2 / = 0 2N (2) paper size Applicable to China National Standard (CNS) A4 specification (2ΐ〇 × 297βcenti) (Please read the precautions on the back before filling this page)

Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs

V. Description of the invention () DCT A7 B7 of type-IV

Xk = Ϋ x, .cos (— (2i + l) (2A: + l)), k = 0, 1, ..., Nl 4iV (3) The above equations (1)-(3), each equation There have been constant terms before, for example, the DCT of type-IV is

Xk cos (-^: (2i + l) (2 / c + l)), k = 0, 1, ..., Nl Because the constant term does not affect the result of the export, for simplicity, the constant term is'丨 1 Omit a. The single form of MCT in the TDAC filter layer. First, the method of converting the MCT in the TDAC filter layer into a switching module and a type-IV DCT will be described. As shown in Figure 3, the MCT and inverse MCT of the TDAC filter layer are defined as follows: = ^^ 008 (-(2 / + 1 +-) (2 ^: + 1)), k = 0,1, .. ., N / 2-1 2N 2 (4) (Read the notes on the back first, then fill out this page)

This paper size applies to China National Standard (CNS) A4 (210X297 Bismuth) Printed by the Consumer Cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs A7 ____B7___ V. Description of Invention ()

Λ72-1 XT ^ = Σ ^ c〇s (— (2 / + 1 + —) (2it + l)) fori = 0,1, ..., Nl k = ^ 〇2N 2 (5) each sum The previous constant term is omitted for the sake of simplicity. It should be noted that unlike ordinary conversions, given the same A, these feet are usually not equal. The TDAC filter layer's process of converting MCTs into switching modules and type-IV DCTs includes the following three steps: A1) Along the subscripts i and A :, extend the conversion pairs (3) and (4) to A form of length N. A2) This extension conversion of length N is shown as the conversion of length N and very similar to the DCT of type-IV. A3) The conversion of DCT of length N which is very similar to Type-IV is reduced to DCT of Type-iy of length N / 2. To accomplish this simplification, the following transformation pairs are defined:

^ -1 — \ T Α = ΣC0S (^ 77 (2Z · + 1 + 7) (2 is +1)), moxibustion = 〇, person ..., /:〇2.N λ Ν_: '⑹ x / =; 文 A cos (^: (2, · +1 +-^ ·) (2Α: +1)), / = 0, Λ ·., J

Z 々 = 〇2.NL ⑺ The relationship between the extension conversion and the TDAC conversion is as follows: -------- This paper size applies the Chinese National Standard (CNS) M specification (210 X 297 mm) --- a -, ml rn 1 ^ 1 111 m III (please read the notes on the back and fill in this page) Order • ⑩ ·

R1) in the sequence Z of (8) (is anti-symmetric, that is, if N is a multiple of 4, will be expressed as:% Xi cos ^ (2i + 1 + f) (2 (^- 1-fe) +1))

Sx / cos (^ (2 / + 1 + yX_1 ~ 2A:) + ^ (2i + i + Y)), k = o, ..., N-i

Ri's relationship was thus reached. f read the notes on the back of the poem before filling in this page) »imm printed by the Consumers Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs R2) for N is a multiple of 4, assuming a sequence of length N; ^ is extended length N / 2 If the sequence is completed, (5) and ⑺ are given, and the sequence of (5) is the same as the sequence of 毛. For N being a multiple of 4, the relationship between moxibustion from M2 to # -1 instead of R2 is thus reached. Through the relationship between R1 and R2, the MCT conversions of (4) and (5) are calculated by ⑹ and ⑺, respectively. In order to calculate the TDAC, first, a conversion similar to the DCT of Type-IV is defined as follows: The paper scale is applicable to the Chinese National Standard (CNS) A4 specification (210X297 centimeters) A7 B7 V. Description of the invention ()

Xk = y ^ jui c〇s (^: (2i + V) (2k + 1)), k = 0

u (= cos (— (2i + \) {2k +1)), i ^ O, 1, ..., Nl * Ξ〇2N (9) Establish some calculations of TDAC via (8) and (9) basis. That is, N- \ π Wu = ^ ^ cos (-τ (3 / · + 1) (2 ^ + 1) Η Σ-^ / C〇s (-(2/27 + 1) (21 + 1) )

J ^ N / 4 with V; 77 = 〇 々V ΛΜ Σ c〇s (— (2y + 1) (2 ^ +1)) =

/ = 〇ZiV This is from the following formula (10) ui = -X 3v, i = 0, 1, ... / + · 4 4 4 Nl Printed by the Central Sample Procurement Cooperative of the Ministry of Economic Affairs (10 ) For N being a multiple of 4, the sequence calculated from (7) can be obtained through the following exchange module (11) and sequence 5 calculated from (9). Bu 0'1 bucket 1 household * I · / Xi = Τ «7ΛΤ L —:--3N 3N D, ~ 4 +1, ..., Ν-1 because the calculation from ⑻ is anti-symmetric, that is [ The scale of this paper conforms to the national standard (CNS) A4 specification (210X29 ^^ 3-- V. Description of the invention (where k = 〇, i, 2, ···, as far as 1, the formula (12) 7V- 1 '= J% C〇S (will (2, + 1) (2々 + 1), ㈣ 人. ·, /

2 «, cos (^-(2 / + 1) (2 ^: + 1)), k ^ O, 1, ..., E.! 5 * 0 ΔΙΜ 2 χλΓ-1-k, none = it ... # · / A According to (3), form the DCT of type-IV of length (iW2) to get #

Yk = S ^ cos (— (2 / +1) (2A: +1)), k = 0, 1, ..., ϋ.! / = 〇ZJ \ 2 / @) sentence, r ί v .; 'Cao: Via the DCT of type (IV) of (13), in order to calculate the DCT conversion of (8) and (9) similar to type -IV, the following basic formula is established. That is, for == 0,1,2, ... (Λ // 2) -1, if —. • n I rn n It n Γ I 11 (#Please read the precautions on the back before filling this page) Order, where ί = 0, Λ…, printed by the Consumer Standards Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs (8) is the same as (13). # For / = iW, ..., 'Since ~ =, (9) The sequence is the same as (15 > The type-IV DCT has the same sequence. 'Wherein, the formula (丨 5) is as follows: This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 shirts). 5. Description of the invention (A7 B7 ^ = Xstcos (~; (2 / c + lX2i + l », 1 = 0,1,…, yi

k ^ O (15) .. In summary, it is calculated by obtaining the DCT of Type-IV of (1 3) and the MCT of (4) by inputting (10) and (14). And, through the DCT of type_IV of (15) and the output of (11), the inverse Mct of (5) can be calculated. The single form of the MCT in the other form of the wave filter layer In order to provide perfect resetting properties between different block sizes, the Dolby AC-3 encoder uses ^ types of filter layers. As shown in Figure 3, the first conversion pair is defined as

N-X

= Σcos ^ (2 / + +1 »= ftl ..., Ν / 2-1, / = 〇LN (16) (Please read the precautions on the reverse side before filling out this page)-equipment, τ = Σ ^ Ιcos (~ (2 / +1) (2 ^-+1 », i = 0,1, ..., Ν-1 ir» 0 The second conversion pair printed by the staff consumer cooperative of the Central Standards Bureau of the Ministry of Economic Affairs is defined as 07) Κ = Σ ^, 2 cos (^ (2 ^ + 1 + D), k = 0, l, ..., N / 2 ~ i ^ = ΣΧί 〇〇s (-^ (2i + l + NX2k + l)), i = 0, l, ..., Nl (18) This paper size applies to Chinese National Standard (CNS) A4 (210X297 ^ cent) (19) A7 B7 V. Description of the invention () (16) The procedure of converting MCT to switching module and type-IV DCT in another form of TDAC and filter layer of (17) includes the following steps: B1) Establish the conversion pair of (16)-(17) and The relationship between the conversion pairs of (9). _ B2) According to the equation, do = _ take w, where moxibustion = tear 2, tear 2 + 1, and Huang Bu passed through (8)-(9) similar to DCT. Conversion, establish the basis to derive another form of TDAC of (16) _ (17). B3) By establishing the aforementioned basis, calculate the conversion similar to DCT via the DCT of type _IV. The relationship of step B1 is, and the basis in step B2 is the relationship of the antisymmetric property of step and step B1. 1 »nn» 11 · " -1. Is--*-· I »I. m I {Please read the notes on the back before filling in this page) -—. INlL + ul- 一 Γι '· .!-The order is converted into the first form of the TDAC, so the exchange module and the type-IV DCT. The following formulas (20) and (21) illustrate another form of MCT of TDAC in (16)-(17 ^ 4, 0 and (18)-(19). Printed by the Consumer Cooperative of the Central Standardization Bureau of the Ministry of First-line Economy That is, if 1 = 0,1 ..., — ~ 1; χ ^ =-χι 2 /-Ν_Ν 2 'y + ^ :, N -1, the sequence in (U) is especially 2 and x 丨The same (20) '---- This paper size applies Chinese Standard (CNS) A4 size (210x297 this 褒 -------- This is because A7 B7 ΛΓ / 2-1 heart / 2 coffee (Report (2 ) + l) (2fc +1))-Σ #, + " / 2 cos (^ r (2w + 1) (2A: +1)) = ^ 1 · and if xf =-^ f〇ri = 0,, / = |, ^ + 1 ..., N-1, then the sequence 伫 in (19) is the same as 芣 (21) In summary, from the formulas (14) and (16), the first This type of TDAC is another form of MCT, which is calculated directly through the DCT of type (1 3) -IV and input exchange. 0 = Xi ~ xJf -1- / (22) Printed by two equals of the Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs One is the sequence tile of (9) and the sequence Yi of DCT of type-IV of (15). The other is sequence A of (9) and twice the sequence calculated from (9). (17) The first TDAC is another form of inverse MCT, via the form of (15) _IV DCT is calculated directly. From (14) and (20), (18) the second TDAC of another form of MCT, through the DCT of type _IV of (13), and the input exchange of (20) and (22), Straight Paper Standard Fitting Standard (CNS) 八 视 # " (210X297 @ y

From two equal relations, one is the sequence tile of (9) and the sequence brother of DCT of type -IV of (15), and the second TDAC in formulas (21) and (19), another form of inverse MCT , Calculated directly through the output exchange of (21) and the DCT of type-IV of (15). c .. D. Phase .. The single > π. report of the MCT in the filter layer is shown in Figure 3. The conversion pairs of mct and inverse MCT in the multi-phase wavelet layer are defined as follows: n ^ 'm ^ — Ttflu 3fn m ^ l Bm 1 nn n (Please read the notes on the back before filling this page) N-ι „Xk = ^ Zxi c〇s (~ 〇 ·-— \ 2k +1», k = 〇, 1, ..., N / 2-1 N / 2-l Σ ^^ (^ :( 1 + ^) (2 ^: + 1)), i = 〇, 7 ..., Nl The MCT of (23) and the inverse MCT of (24) provide the following two conversion formulas: (23) (24) Printed by N- \ K = |] m / C. s (— (0 (2A: +1)), k = 0, 1 ..., N / 2-1 (25) N / 2- \

= Σ Xkcos (. ^ (J) (^ k + \)), / = 0, 1 ..., Nl N λ = Γ〇 (26) With (23) and (25), if 19 papers Applicable to China National Standard (CNS) A4 specification (210X297 mm)

3N is the sequence calculated by (25); ^ equal column; ^. (27) Similar to the order calculated by (23), similarly, with (23) and (25) and F and A, the sequence brother calculated by (24) can be compared with the one calculated by (26) > < The sequence Qin exchange, the form of the parent exchange is the following formula (28) ^ = Ui + Nii, i ~ 〇… BN / 4-1 and χ (： = —2 ".. S 1 m * -3jv / 4, ι ^ 3N / 4, 3N / 4 + 1 ... Nl According to (1), the type of iW2 is _n and the DCT of it is (28) (29) (Please read the precautions on the back before filling this page) -Order l · Printing order A = A from the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs. From X /, the sequence of (26) can be obtained from formula (4):

Uj = 0, i = N / 2 ui = X {, i = 0, 1,:., N / 2-1 m N ur-X ^,-+ 2 ...., Nl This paper size applies to China檩 Standard (CNS) A4 size (210 X 297 cents) Φ line (30) Printed by the Consumer Cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs A7 B7 5. Description of the invention () According to (2) 'The length is iV / 2 type · The dct of ιιι is I; "", = 2 ^ .008 (^ (/) (2 ^ + 1)), k = 0, 1, ...... (31)-and if the sequence is linked via Equation (32) is calculated from sequence seven, then the sequence of (31); ^ is equal to the sequence meaning of (2S).

(32) In summary, it can be calculated by (3 1) DCT of type__type_m and MCT of (27) and (32) input exchange ”(23). And, through the DCT of Type-29 of Type-II, DCT of Type-IV, and the output exchange of (28) and (30), the inverse MCT of (24) can be calculated.

From the previous detailed description of the present invention, "TDAC filter layer, another form of TDAC filter layer, and all modulating cosine transformations of the polyphase filter layer" can be divided into two modules: exchange and discrete cosine. Conversion module. In particular, the pre-transform can be expressed as a pre-exchange module and a discrete cosine transform 'and the inverse transform can be expressed as a discrete cosine-transform module and a post-exchange module. The discrete cosine transform can be of the type-II, the type-III ', or the type-IV. 2. Decomposition of discrete cosine transformation is complete. Universal money family scales (CNS> Α4 · (2 丨 qx29 潘 病) —Vi n Γ— nm mi LII— I 1 ^ 1 J ^ nl · — T Λ.- e (Please read the notes on the back before filling this page) A7 B7 V. Description of the invention () The following is a method for decomposing a DCT of one type of length N into one of the above three types of length N / 2 Two types of DCT: a. The type-II of the DCT is calculated from (1) 'for an input sequence X, length N of type-II. The k-th coefficient of DCT printed by the Consumer Cooperatives of the Central Standard Bureau of the Ministry of Economic Affairs. Is NAcos (^ 7 (2, +), itUbu; = 〇2N First, the type-II DCT is decomposed into even-indexed and odd-indexed forms. Even below The standard output sequence is ^ 2 * = Z ^ C0S (i7 (2i + 1) (2 ^)), k = 0, ..., Ν / 2-1. / = 〇 丄 JS (33) The subscript output sequence and odd subscript output sequence can use the symmetry and antisymmetry properties of the cosine function to form a DCT of length N / 2 type-Π and a DCT of length N / 2 type-IV. Apply the following symmetry properties cos (-(2 (^-1-/) + 1) (ir) = cos ( ^ :( 2 / + 1) (^), NN obtained that this paper size applies Chinese National Standard (CNS) A4 specification (210X297 sap) (#First read the notes on the back before filling this page) • Stupid_ Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs A7 B7 V. Description of Invention () Ν! 1- \ π x2k = Σ (^ +%-i-/) c〇s (— (2 / + 1) (Α :)) / = 0 ^ (34) (34) is the DCT of type-II with input exchange. The output sequence of the odd subscript is the sense system = 1 ^, ^ (^ (2 / + 1) (2 ^ : + 1)), ζ · = υ / 2-7.

| = 〇 2JSI applies the following antisymmetric properties 008 (-^-(2 / + 1) (21 + 1) = -008 (^ (2 (^-1-/) + 1) (21 + 1) »

2N 2N gives N / 2-1 π ^ 2Α + 1 = Σ ^ χ < ~% -1-/) COS (t77 (2 / + 0 (2 ^ +])) »

i = o 27V (35) (35) is the DCT of type-IV with input exchange. It can be seen from (34) and (35) that a type-II DCT of length N can be decomposed into a type-II DCT of length N / 2 and a type-IV DCT of length N / 2. FIG. 4 illustrates an embodiment according to the present invention, decomposing an 8-point type-II DCT into a 4-point type-II DCT and a 4-point type-IV DCT. b. Decomposition of type-III DCT from (2), for an input sequence w, length N of type-II, the paper size of this paper applies the Chinese National Standard (CNS) A4 specification (210 parent 297 kick cent) (read first read Note on the back, fill in this page again)-Install. Order A7 B7 V. Description of the Invention () The k-th coefficient of DCT is not: = cos (^ r ⑺ 以 +1)), Α: = 0, /, ... (36) First, 'divide the input sequence of Type-III DCT; and turn out the sequence into *, * ·. The input is split into even and odd subscripts, and the rotation is split into the first and second half of the sequence; that is, ΛΤ / 2-1

Xk = N ^ X2icos (^^ 2k + iy) + & 2, + iC〇s (~ (2 / + 1) (2A: +1)), k ^ oj ^ ml (37) redundant N λ / 2 —1 _ «_ ^ = 2, ^ C0 ^ (〇 (2 ^ + Y > +1)) + Σ ^ + ι ^^ (2ι '+ ΐ) (2 (* +-) + ΐ)), j + k, 工 〇iV Zn / · = 〇IJS 2 k = 0, l, ..., N / 2-1 (38) Secondly 'substitute cos (^ (/) (2 (i + 令) +1 )) = (^ (^ (/) (2 (^^-1-4) +1)) and cos (specific (2 / + l) (2 (ir + y) + l)) = -cos (specific (2 / + 1) (2 (Quark-1-gram) +1)) (Please read the notes on the back of the first and then fill out this book) V Binding and Binding (38), we get the staff of the Central Standards Bureau of the Ministry of Economic Affairs Consumption cooperative prints N / 2— \ 4Γ ΛΓ ^ / 2-1, _ x ^ + i = Σ cos (^ -1-^) + ^)-Σ x2 / +. Cos (^ (2i + 1) ( 2 (γ -ι-λ) + ΐ)), k = 0… N / 2-1 (39) From the results of (37) and (39), a DCT of type N_in can be decomposed into one A DCT of the form N / 2-II and a DCT of the form N / 2-IV. Figure V5 shows the paper according to the present invention, which illustrates the implementation of this paper standard applicable to the Chinese National Standard (CNS) A4 specification (210X297®) printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs. A7 _B7_ The dot-type-III DCT is decomposed into a 4-point-type DCI and a 4-point-type DCV. c. Decomposition of DCT of Type-IV Before performing DCT of Type-IV, the present invention first provides the following properties: A (N + 1) xN type DCI of type III can be simplified to a DCT of type NxN type -III

Zx, cos (^; (') (2A: +1)) = Zhang, · cos (^ (〇 (2A: +1)).

/ = 〇 / = 〇 ZiV From (3), for an input sequence X /, the k-th coefficient of the form of the length N of the DCT of ΐν is JV-1

Xk = y \ xi cos (-(2 / + 1) (2Λ +1)), "hD-J

to 4N (40) because cosZ = ——--- (cos (^ 4 + ^) + cos (/ 4-5)) »(40 "« Γ 2 cos million xk = -it- ^ + l) (i )) + cos (; ^ (2A: + 1) (/ + 1))).

2〇〇 (^ (2 ^ + 1)) ^ 〇2N 2N (41) Secondly, the input is divided into odd and even terms, and it is concluded that this paper size applies the Chinese National Standard (CNS) A4 specification (210X297) I;-^ ------- (谙 Read the precautions on the back before filling this page)-Order A7 B7 V. Description of the invention () 1 Λ72-1

Xk

2cos (-(2k +1)) / = 〇AN {cos (-^: (2A: +1) (2 /) + ^ x2i + 1 cos {^-(2k +1) (2 / +1) • * V .- n fy N! 2- \ Σ a: 2 / cos (— (2A: +1) (2 / + 1) + x2i + iC〇s (— (2 ^: + 1) (2 / + 2)}

2N (42) In addition, the four items in (42) can be expressed as

Nil Λ72-1 2cos (— (2 ^ + l)) {Σ (λ2, + ^ 2 / -1) c〇s (— (2A: +1) (/) + (x2i + j: 2,. + I) cos (-(2 ^ + 1) (2 / + 1))}

2N • n ^ — m ^ — Hu 1 ^ 1 nn I n ^ d Hr. · 1 nn n (please read the precautions on the back before filling this page) Finally, use | >, one: ^ (〇 ( 2 moxibustion 4)) = ^^ (5 (0 (2 ^ 1))

, · = Η 2TV ί_η 27V Order N! 2- \

Xk 2cos (— (2A: + 1)) {^ (x2i + x2 (._,) cos (^ (2k +1) (/)) + (^ 2 ,. + ^ 2,. + 1) cos ( ^ (2k + 1) (2 / +1))} (43) From the result of (43), a DCT of type N-IV can be decomposed into a DCT of type N-IV and A type N / 2 type-III DCT. Figure 6 illustrates an embodiment according to the present invention, decomposing an 8-point type-such as DCT into a 4-point type-III DCT, and A 4-point type-IV DCT. 3. Complexity analysis This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 ^ centimeters) -® line · Ministry of Economic Affairs Central Standard Bureau Staff Consumer Cooperative Printed by the Ministry of Economic Affairs Central Printed by the Consumer Bureau of Standards Bureau A7 B7_ 5. Description of the invention () From Figure 4-6, the computational complexity of the three DCTs is DCT-II (iV) = A (iV) + DCT-IV (JV / 2) + DCT -II (M2) ♦ DCT-in (A〇 = A (A〇 + DCT-IV (iV / 2) + DCT-III (M2), and -DCT-IV (iV) = A (Ar-7) + M {A〇 + DCT-IV (A (/ 2) + DCT-ni (JV / 2) »where 'DCT-II (iV), DCT-III (A〇 and DCT-IV (A〇 are length N, respectively DCT of Type-II, Type-III, and Type-IV; and A (μ) and M (κ) indicate the addition and The number of multiplication operations are, and, ^ ^^ Figure 7 illustrates the complexity of the present invention and the conventional technique for the base-2 discrete cosine transform. As shown in Figure 7, this result shows the complexity of the present invention It is the same as the well-known discrete cosine transform technology. The decomposition method proposed by the present invention is to replace the same type of DCT by inserting three types of DCT ', which has regularity, modularity and low complexity. Even' because this decomposition is inserted These three types of DCT can be applied to all modulation cosine transformations in the current speech coding standard. 4. Conclusion Various modulation cosine conversion forms have been commonly used in different speech standards. The present invention has clarified all these modulations Variable cosine conversion, which can be guided into two modules: exchange and DCT modules. The adjustment paper in the encoder applies the Chinese national standard) 8 secrets (2ι〇χ297_)-{Read the first note on the back Please fill in this page again.) Assemble. Order _ V. Description of the invention (Variable cosine conversion, achieved by an input exchange and a DCT, and the modulation cosine conversion in the decoder, a DCT and reached a post exchange. DCT is used as a pattern _Π, type _ΠΙ, or type ·! V. The present invention provides a rapid architecture for the above three types of DCT. This new technology has been decomposed into one form of Dct, Form-II, Form-III 'or Form · IV. This decomposition technique has confirmed that all modulation cosine conversions in the current audio coding standards have good regularity, complexity, and universal applicability. However, the above are merely preferred embodiments of the present invention, and the scope of implementation of the present invention should not be limited in this way. That is, all equal changes and modifications made in accordance with the scope of the patent application of the present invention shall still fall within the scope of the patent of the present invention. (Read the notes on the back of the book first, and then fill out this page.) Packing--Order @ 线, Printed by the Central Labor Bureau of the Ministry of Economic Affairs, Printed by the Co-operative Consumer Cooperatives & Paper Waves New Zealand National Finance Standard (CNS) Α4 鄕(21GX297 side thin)

Claims (1)

Scope of patent application: The discrete V-string model of the printed points of the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economics: the river data with M input data points is used for a lifetime-the second data point is changed: the second group 'And -㈣M / 2 have already submitted a sub-conversion step, using the _ ° of the first group of points. One has M / 2 exchanged data. One exchanged data point: 2 points discrete cosine transform, and -One with M / 2 transformation to produce a second M / 2 point discrete cosine turn of a right group-one with a transformed / 2 :: transformed data point of the -group, and -combination steps, using The second group; and, the -group and the second group, the calculation module described in item 1 of the 2 plus St application domain with M / 2 converted data points, which makes the exchange_add step or This combination step is a transfer step, which is used to transfer the data without the processing of exchange or calculation. ^ ㈣M㈣ The calculation module described in item i, wherein the point: discrete cosine transform 'and the first and second Μ of the table. The discrete cosine transformation of a point is selected from the discrete cosine transformation group of type_11, type · ΠΙ ', and type-IV: The discrete cosine transformation table of this type-Π is as follows: Xk = NpiC〇S (^ (2i + l) Shuai N-bu The discrete cosine conversion table of this type-III is as follows: (Please read the precautions on the back before filling this page) Housekeeping (CNS) (210 ^ 7 ^ A8 B8 C8 D8 \ VI. Patent application scope N-1. Π Xk = 2 ^ cos (-^-(/) (2A: + 1)), k = 0, 1 , ..., Nl »/ = 0 on N. The discrete cosine conversion table of this type -IV is as follows: -X, = Xx, cos (^-(2 / + l) (2A: + l)), k = 0, 1, ..., Nl;; = 〇4iV where xz • Table 1 input data points are the converted data points in Table 1, and N is the number of input data points for each discrete cosine transform. Printed by the Consumer Cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs of the calculation module described in item 3 of the patent application scope, wherein the discrete cosine conversion of the centimeter is a type-II discrete cosine conversion, and the first M / The 2-point discrete cosine transform is a type-II discrete cosine transform. And the second discrete cosine conversion of the M / 2 point is a type-IV discrete cosine conversion. / The calculation module described in the third item of the patent application scope, wherein the discrete cosine of the M polynomial * is converted into one Form-III discrete cosine conversion, the first M / 2 point discrete cosine conversion is a type-III discrete cosine conversion, and the second M / 2 point discrete cosine conversion is a type-IV discrete Cosine transformation. 6. ◎: The calculation module described in item 3 of the scope of application for luxury application 'where' the M chi discrete cosine transformation is a type-IV discrete cosine transformation, the first ». V * · The discrete cosine conversion of M / 2 points is a type-III discrete cosine conversion, and the second discrete M / 2 point cosine conversion is a type-IV discrete cosine conversion. This paper uses China National Standard (CNS) A4 Specification (210X297 ^) —: ------- f Pack-(Please read the notes on the back before filling out this page) Printed by the Central Standards Bureau, Ministry of Economic Affairs, Consumer Cooperatives A8 B8 C8 " D8 VI. Patent application scope 7. —A kind of implementation of cosine modulation filter layer A unified structure, the filter layer is provided with a modulated cosine transform, and the unitary structure includes: a front-exchange module; and a conversion calculation module for calculating a discrete cosine transform; wherein the modulation The cosine transformation is decomposed into a pre-exchange, which is executed by the pre-exchange module, and a discrete cosine transformation, which is calculated by the transformation calculation module. The discrete cosine transformation is selected from type-II, type-III, The discrete cosine transformation group of sum type-IV, the discrete cosine transformation group of this type-II is expressed as the following type: A = ^ X C0S (^ 7 (2i + 1) W), moxibustion = 以 ·· ”尽 7, / = 〇 丄 · ^ The discrete cosine conversion table of this type-III is as follows: X, = Xx, .cos (^-(〇 (2A: + l)), k = 0, 1, ..., Nl »/ = 〇2iV The discrete cosine conversion table of this type-IV is as follows: = 2 ^ .008 (^-(2 / + 1) (2 ^ + 1)), k = 0, 1, ..., N- 1- / = 〇 Among them, • The input data points in Table 1 are converted data points in Table 1, and N is the number of input data for each discrete cosine transform. 8. The simplification architecture described in item 7 of the scope of patent applications, wherein the cosine modulation filter layer is a time-domain de-aliasing filter layer, and the modulation cosine transformation is decomposed into a pre-exchange and Type I-IV's paper size is in accordance with Chinese National Standard (CNS) Α4 specification (210X297 #) ί ---- ^ ------ / ί \ Install-(Please read the precautions on the back first (Fill in this page again), τ Economy? Printed by the Central Bureau of Standards M Cooperative, Sixth, apply for patent Fan Yuan scattered cosine transformation. A single cosine modulation filter layer as described in item 7 of the scope of patent application. Y,,, ~ of the other-Η * definition domain cancels the pseudonym filter layer type-with it = '^ modulation cosine transformation is Decomposed into ―front-commutation and-type discrete cosine transformations. 1Must • As described in the scope of patent application 帛 7, the cosine modulation filter layer is more than one, where the solution is regular-parent conversion and a type-m discrete cosine conversion. As the calculation module of the patent application scope item 7 further includes a poor solution, the transformation data point β, and is used to calculate a discrete cosine transformation with M rounds and crosses, the The calculation module contains the first group of _ exchanged data points, and the second group of data points with sum = two exchanged data points; each has a parent-a conversion step-used to calculate The first M / 2 points of this-group with μ / 2 points are discretely exchanged. The exchanged data are stored in a 〇 transform 'and the second group with M / 2 products: 4 points. The second M / 2 point discrete cosine — '^ yields a second group of M / 2 converted data points with a second group of M / 2 converted data points; and, σ combination steps for Combining M / 2 converted asset-groups and second groups. The installation page of the asset's point of view 1 \ 2 · Single structure as described in item η of the patent application scope, where Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs A8 B8 C8 Body D8 6. Scope of Patent Application The exchange-addition step or the combination step is a transfer step for transferring data without exchange or calculation. lj. A simplistic architecture implementing a cosine modulation filter layer, the filter layer is provided with an inverse modulation cosine transformation, the simplification architecture includes: a transformation calculation module for computing a discrete cosine transformation; and, A post-exchange module; .. where the inverse modulation cosine transform is decomposed into a discrete cosine transform, calculated by the conversion calculation module, λ-post-exchange, and by the post-intersection. Exchange module Implementation, the discrete cosine transformation is selected from the discrete cosine transformation groups of type-II, type-III, and type-IV. The discrete cosine transformation table of type-II is as follows: xk = X ^ / c〇s ( ^ 7 (2i + 1X ^)) > k = 0, l, ..., Nl > / = 〇2iv The discrete cosine conversion table of this type-III is as follows: χΑ = Σ ^ ε〇8 (^ -(〇 (2Λ + 1)), k = 0, 1, ..., Nl * / = 〇27V The discrete cosine conversion table of this type -IV is as follows: N- \ X, = ^^ cos (^ -(2 / + l) (2 ^ + l)), k = 0, 1, ..., Nl; / = 〇4A / where the input data point of Table 1 is the converted data point of Table 1, And N is the number of input data points for each discrete cosine transform. K4. The singular structure described in item 13 of the scope of patent application, in which the paper size applies to the Chinese National Standard (CNS) A4 specification (210 × 297M) i ml In In l (please read the precautions on the back before filling this page)- β scope of patent application The cosine modulation filter layer is a temporary q-line-domain definition pseudo-filter layer 'The modulation cosine conversion is divided into sub-characters, ^ ^. ^ The loose knife solution is a type-IV Discrete cosine conversion bang-post-swap. = Singularized architecture as described in item 13 of the patent application scope, where another opening of the layer 4, Xi, Nen time-unitary domain pseudo alias filter scattered cosine Spines: ί: The chord transformation is decomposed into -types, the double cosine transformation and the one-to-one drag 1 singularization as described in item 13 of the patent application scope, the cosine modulation filter layer is-multiple, medium The conversion is decomposed into a type · IV separator layer, the modulation cosine-to-discrete cosine conversion and a post-swap. 17. For example, the 13th calculation module of the scope of patent application includes-calculation center; ^ = the conversion information : Dot discrete discrete cosine transform of the r 2 exchange-add step The first group of M / 2 exchanged data points and the second group of solid data exchanges used to exchange the input data points; one has been submitted to the Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs for printing once -The conversion step is used to calculate a piece of data that has been exchanged: =: ΪΓ—M / 2 points of discrete residuals · The second group of M / 2 points of the second group has been discretely exchanged to generate the capital points to generate -A first group with a total of converted data points and a second group with M / 2 converted data points; a combination step for combining M / 2 converted data points The paper scale uses the Chinese National Standard (CNS) A4 specification (210X2974 ,! ) • i m (please read the notes on the back before filling this page). Order the printing and patent application for the first and second group of the Ministry of Economic Affairs and Standards Bureau. 1 8. As described in the patent application _ scope of the 17th cake, + early capture of the structure described in the early one, in which the "addition step" or the combination of steps, and "quotation" is the transfer step , Used to transfer funds without exchange or calculation. -A method for calculating the modulation cosine transformation, including the following steps: :: The modulation cosine transformation is-forward_exchange and a discrete cosine transformation, the: the scattered cosine transformation is selected from the type · π, the type welcome, " The cosine transform group of the formula π, this type · The discrete cosine conversion table of Π is expressed as the following type JV-1 ^ = § ^ C〇S (^ (2i + W) ^ k = 0 >], ..., N-Bukai The discrete cosine conversion of type-III is as follows: Ν ~ 1 π = E ^ c〇s (— (0 (2 ^: + 1)), k = 〇ih _ N_J, the discrete-cosine conversion of this type-IV The table has the following form: ΛΜ · A = Abstract (Report (2ί + 1) (2 无 十 1)), ㈣, i, τν >7; Among them, the input data point of the smart table is 'converted data point of the office' And N is the number of input data points for each discrete cosine transform; implement the pre-exchange; and, calculate the decomposed discrete cosine transform. 2.Q. —A method for calculating an inverse modulated cosine transform, including The following steps: page binding ^ paper size using Chinese National Standard (CNS) A4 specifications (210X297 ^% A8 B8 C8 D8 patent application Fanyuan decomposition the inverse modulation cosine conversion into a post-exchange and I for 'The discrete cosine transformation is selected from the discrete cosine transformation group of type IV, type 411, and IV under chord rotation, the discrete cosine of type -II 辕 = type column type: change the table into = 2x / C0S (^ 7 (2i + W) Λ ^ ο, ΐ, ..., Nl »/=»〇2.IS The discrete cosine conversion of this type-III is expressed as the following type is-ι π xk = YJxi cos (— (〇 (2Λ : + 1)), k = 0, 1, ..., Nl > / »0 The discrete cosine conversion table of this type -IV is as follows: / v-1 ^ = Σχί cos (— (2 / +1 ) (2A: + 1)), k = 0, 7, ..., Nl; the data points of i-〇4iV 'Among them, χζ · Table 1 input data points, Table 1 has been converted and N is each discrete The number of input data points of the cosine transform calculates the decomposed discrete cosine transform; and, the number; implements the post-exchange. Printed by the U.S. Central Government Bureau of the Ministry of Economic Affairs and the Zhengong Consumer Cooperative—a calculation of one with μ The method of transforming M points of input data points includes the following steps: discrete cosine exchanges the input data points and generates a first group with M / 2, and a first group of Wu Zizi, and a Μ / 2 submitted The second group point of the data point is calculated as a 'M / 2 point discrete cosine rod exchange of the first group with M / 2 exchanged data points, and a second one with μ / 2 exchanged data. The second M / 2 point discrete cosine transform of the second group to produce a ^ This paper size is applicable to China National Standards (CNS) A4 specifications (21〇 × 297 > ^^ The Ministry of Economic Affairs Central Standards Bureau employee consumer cooperative prints the patent application Range M / 2 of the converted data points-the second group of the changed data points; and, groups, and-there are M / 2 converted combinations with M / 2 converted data points # The first and second groups of data points changed. · Calculations as described in the M point ㈣ ^ of the patent data range of the patent application—a method with M inputs ^ * 1 Λ, the method of scattered cosine transformation, the M point transformation /: string transformation, and the first-and- Discrete cosine of the second listening point = is selected from the discrete cosine transformation group of type _Π, type · Π, and type W. The discrete cosine transformation group of this type -Π is expressed as the following type: 'Λ ^ -1 §X (C〇S (^ (2 / + W) Nl, the discrete cosine conversion table of this type-IΠ is as follows: N-1Xk = yLxicos (~ ^ (}) (2k + l)), k = 0 , 1, ..., Nl > The discrete cosine conversion table of this type-IV is as follows: N-1 ^ xk = Σχ, ¢ 08 (-(21 +1) (2 ^ +1)), 1 , ..., Nl; / = 〇. 4iv 3 Among them, "the input data point of Table 1 is used, the converted data point of Table 1 is used, and N is the input data point of each discrete cosine transformation. The M-scale scale is applicable to China. Standard (CNS) A4 Specification (210X297 #) (Please read the precautions on the back before filling this page)