Image and audio transform methods

Abstract

Inverse discrete cosine transform (type-III DCT), used in video/image and audio coding, is implemented in the form of FFT to lower computational complexity.

1 . A method of audio analysis filter bank operation, comprising the steps of:
 (a) receiving a block of N audio samples where N is a positive integer;   (b) including said block in an array of prior samples;   (c) windowing said array of samples;   (d) symmetric summing said array to form an N-vector S n  for n=0, 1, . . . , N−1;   (e) effecting a matrix multiplication V i Σ 0<MS,N M i,n  S n , for i=0, 1, . . . , N−1, where the matrix elements are M i,m =cos [πn(2i+1)/N]; and   (f) outputting said F 1 ;   (g) wherein said matrix multiplication of step (e) includes:
 (i) computing z, R [n] for 0≦n≦N−1 by: z R [n]=c(n)S n  cos [πn/2N] where c(n)−1 for all n except c(0)=1/√2; 
 (ii) computing z i [n] for 0≦n≦N−1 by: z i [n]=S n sin |πn/2N|; 
 (iii) computing u/[n] for 0≦n≦N−1 by u[n]=(z R [n]+z R [N−n])/2 for 1≦n≦N−1 together with u[0]=z R [0]; 
 (iv) computing v[n] for 0≦n≦N−1 by v[n]=(z i [n]−z i |M−n|)/2 for 1≦n≦N−1 together with v|0|=0; 
 (v) computing 
 (vi) computing G|k| as the N-point DFT of g|n|g|n| for 0≦n≦N−1 by g|n|=u|n|+v[n]; 
 (vii) computing V 2i =Re{G|k|}−Im {G|k|} for 0≦k≦N/2−1; and 
 (viii) computing V 2k,1 =Re {G|N−−k|}−Im{G|N−1−k|} for 0≦k≦N/2−1; and 
   
     
     
         2 . The method of  claim 1 , wherein:
 (a) N−32   
     
     
         3 . An audio spectral band reflection analysis filter bank, comprising:
 (a) a memory for audio samples;   (b) array circuitry coupled to said memory, said array circuitry operable to receive a block of N audio samples and to window plus symmetrically sum an array including said N audio samples plus audio samples stored in said memory to generate a length-N vector with components S 0 , S 1 , . . . , S A1 ; and   (c) transform circuitry coupled to said array circuitry and said memory, said transform circuitry operable to effect a matrix multiplication V i Σ 0≦n≦N  M i,n S n , for i=0, 1, . . . , N−1 matrix elements are M i,n =cos [πn(2i+1)/N];   (d) wherein said transform circuitry includes sub-circuitry operable to:
 (i) compute z R |n| for 0≦n≦N−1 by: z R [n]=c(n)S n  cos [πn/2N] where c(n)=1 for all n except c(0)=1/√2; 
 (ii) compute z i |n| for 0≦n≦N−1 by: z i [n]=S n  sin|πn/2N|; 
 (iii) compute u|n| for 0≦n≦N−1 by: u|n|=(z R |n|+z R |N−n|)/2 for 1≦n≦N−1 together with u|0|=z R |0|; 
 (iv) compute v|n| for 0≦n≦N−1 by v|n|=(z 1  [n]−z 1 |M−n|)/2 for 1≦n≦N−1 together with v|0|=0; 
 (v) compute g|n| for 0≦n≦N−1 by g|n|=u|n|+v|n|; 
 (vi) compute G|k| as the N-point DFT of g|n|; 
 (vii) compute V 2k =Re{G|k|}−Im{G|k|} for 0≦k≦N/2−1; and 
 (viii) compute V 2k,1 =Re{G[N−1−k]}−Im {G|N−1−k|} for 0≦k≦N/2−1. 
   
     
     
         4 . The filter bank of  claim 3 , wherein:
 (a) said transform circuitry and said output circuitry are implemented as a program on a programmable processor.   
     
     
         5 . The filter bank of  claim 3 , wherein:
 (a) N=32.   
     
     
         6 . A method of image data inverse DCT operation, comprising the steps of:
 (a) receiving a block of N2 image transform data S n,m  where n,m=0, 1, 2 . . . , N−1 where N is a positive integer;   (b) effecting a matrix multiplication V i,m =Σ 0<n≦N-1  M i,n S a,m  for i=0, 1, . . . , N−1, where the matrix elements are M i,n =cos [πn (2i+1)/N]; and   (c) effecting a matrix multiplication of said Vi,m with respect to the m index;   (d) wherein said matrix multiplication of step (b) includes:
 (i) computing z R |n,m| for 0≦n≦N−1 by: z R |n,m|=c(n)S n,m  cos |πn/2N| where c(n)=1 for all n except c(0)=1/√2: 
 (ii) computing z i |n,m| for 0≦n≦N−1 by: z i |n,m|=S n,m  sin |πn/2N|; 
 (iii) computing u[n,m] for 0≦n≦N−1 by u[n,m]=(z R [n,m]+z R N−n,m)/2 for 1≦n≦N−1 together with u[0,m]=z,[0,m]; 
 (iv) computing v|n, m| for 0≦n≦N−1 by v|n,m|=(z i [M−n,m])/2 for 1≦n≦N−1 together with v[0,m]=0; 
 (v) computing g|n| for 0≦n≦N−1 by g[n]=u[n]+v[n]; 
 (vi) computing G[k,m] as the N-point DFT of g[n,m]; 
 (vii) computing V 2k,m Re{G|k,m|}−Im{G|k,m|} for 0≦k≦N/2−1; and 
 (viii) computing V 2k-1,m  Re{G|N−1−k,m|}−Im{G|N−1−k,m|} for 0≦k≦N/2−1. 
   
     
     
         7 . The method of  claim 6 , wherein:
 (a) N=8.