An Efficient Algorithm for Computing 4M X 24-Point DFT

An efficient algorithm for computing 4^M x24 point DFT, called radix-4-24p efficient FFT algorithm (EFFT), is developed. To convert the computation of DFT of length N=4^M x 24 in M steps to the computation of 4 DFTs of length 24 by radix-4 decimation in time algorithm and from Mth to first , each step converts four DFTs of length L x 24 into one DFT of length (4 x L)x24 are the basic mentality, and an efficient algorithm for computing the 24 -point DFT, which requires only 24 real multiplications, is the core module of radix-4-24p EFFT algorithm. The total number of computational requirements for implementing N=4^M x 24- point DFT in the algorithm is (1+3 M)N-16(4^M -1) real multiplications, 4^M x 20 -4 real right- shiftings 1 bit and 4^M x 376+3 MN/2-124 real additions. The equation and block diagram of performing the radix-4-24p EFFT algorithm and a highly effective algorithm for computing directly 24- point DFT are represented in the text. The computing efficiency and computation amount of the radix-4-24p EFFT algorithm are improved than those of radix-4 FFT algorithm as a result of using effectivly cos(pi/3)=sin(pi/6)=1/2 andcos(pi/4)=sin(pi/4)= 0.707.