combine_2n.m

用dsp解压mp3程序的算法

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% combine_2N.m - Perform 2N-point FFT using a single 
%                N-point complex FFT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all; close all;

g = [1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1];
    
% Conventional 2N-point FFT approach

G = fft(g,16);

% N-point FFT approach

x1 = g(1:2:length(g));
x2 = g(2:2:length(g));
x = x1+(i*x2);
X = fft(x,8);
X_conj = [conj(X(1)) conj(X(8-(0:6)))];
X1_N = (X+X_conj)*0.5; 
X2_N = (X-X_conj)*(-i*0.5);

W_2N = exp(-j*2*pi*(0:1:15)/16);
G_N = [X1_N+W_2N(1:8).*X2_N X1_N+W_2N(9:16).*X2_N];


figure;
subplot(211), stem(abs(G)), title('FFT plot of 2N-point g(n)');
subplot(212), stem(abs(G_N)), title('FFT plot of N-point x -> DIT method');