《DSP using MATLAB》Problem 5.32

Posted 2020-12-30 ky027wh-sx

代码：

function [y] = ovrlpadd_v3(x, h, N)
%% Overlap-Add method of block convolution
%% ------------------------------------------------------
%% [y] = ovrlpadd(x, h, N)
%% y = output sequence
%% x = input sequence
%% h = impulse response
%% N = block length >= 2*length(h)-1

N = 2^(ceil(log10(N)/log10(2)))  

Lx = length(x);                        % ML    
L = length(h);                         % length of impulse response

Hk_FFT = fft(h, N);

M = floor((Lx)/(L))                   % number of bolck
Y = zeros(1, Lx+N-L)

% convolution with successive blocks
for m = 0:M-1
	xm = x(m*L+1 : m*L+L);                                     % length is L
	XMk_FFT = fft(xm, N);
	YMk_FFT = XMk_FFT .* Hk_FFT;
	ym = real(ifft(YMk_FFT))                                   % length is 2L-1
	%Y(m*L+1 : m*L+(2*L-1)) = Y(m*L+1 : m*L+(2*L-1)) + ym
	Y(m*L+1 : m*L+N) = Y(m*L+1 : m*L+N) + ym
end

y = Y;

　　

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf(‘
***********************************************************
‘);
fprintf(‘        <DSP using MATLAB> Problem 5.32 

‘);

banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

% -------------------------------------------------------------
%           Overlap-Add                 
% -------------------------------------------------------------

n1 = [0:8-1];
x1 = cos(pi*n1/500);
N1 = length(x1);

nh = [0:3];
 h = [1, -1, 1, -1];
 L = length(h);

M = N1/L;

N = 2*L-1; 

y = ovrlpadd_v3(x1, h, N);            % FFT

　　运行结果：

       原题中x(n)长4000，不好看图说明，这里假设长度只有8，便于上图说明道理。