代码：
function y = circonvt(x1,x2,N)
%% N-point Circular convolution between x1 and x2: (time domain)
%% ------------------------------------------------------------------
%% [y] = circonvt(x1,x2,N)
%% y = output sequence containning the circular convolution
%% x1 = input sequence of length N1 <= N
%% x2 = input sequence of length N2 <= N
%%
%% N = size of circular buffer
%% Method: y(n) = sum( x1(m)*x2((n-m) mod N) )
%% Check for length of x1if length(x1) > N
error('N must be >= the length of x1 !')
end
%% Check for length of x2if length(x2) > N
error('N must be >= the length of x2 !')
endx1 = [x1 zeros(1,N-length(x1))];
x2 = [x2 zeros(1,N-length(x2))];m = [0:1:N-1]; x2 = x2(mod_1(-m, N)+1); H = zeros(N,N);
for n = 1:1:N
H(n,:) = cirshftt(x2,n-1,N);
end
y = x1*conj(H'); % x1---row vector
% H
% y = H*x1'; % x1---column vector
主程序：
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.24 \n\n');banner();
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++% -------------------------------------------------------------------
%
% -------------------------------------------------------------------
N = 4;
n1 = [0:3];
x1 = [1, 2, 2];x2 = [1, 2, 3, 4];y1 = circonvt(x1, x2, N)
运行结果：
代码：
function [C] = circulnt(x, N)
%% Circulant Matrix from an N-point sequence
%% ------------------------------------------------------------------
%% [C] = circulnt(x, N)
%% C = Circulant Matrix of size NxN
%% x = sequence of length <= N
%%
%% N = size of circulant matrix
if length(x) > N
error('N must be >= the length of x !')
endx = [x zeros(1, N-length(x))]; for i = 1 : N
c(i) = x(i);
end m = [0:1:N-1]; x_fold = x(mod_1(-m, N)+1);
r = x_fold; C = toeplitz(c,r);
function y = circonvt_v3(x1,x2,N)
%% N-point Circular convolution between x1 and x2: (time domain)
%% ------------------------------------------------------------------
%% [y] = circonvt(x1,x2,N)
%% y = output sequence containning the circular convolution
%% x1 = input sequence of length N1 <= N
%% x2 = input sequence of length N2 <= N
%%
%% N = size of circular buffer
%% Method: y(n) = sum( x1(m)*x2((n-m) mod N) )
%% Check for length of x1if length(x1) > N
error('N must be >= the length of x1 !')
end
%% Check for length of x2
if length(x2) > N
error('N must be >= the length of x2 !')
endx1 = [x1 zeros(1,N-length(x1))];
x2 = [x2 zeros(1,N-length(x2))];C = circulnt(x2, N);%m = [0:1:N-1]; x2 = x2(mod_1(-m, N)+1); H = zeros(N,N);
%for n = 1:1:N
%H(n,:) = cirshftt(x2,n-1,N);
%end
%y = x1*conj(H'); % x1---row vector y = C*x1'; % x1---column vector
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.25 \n\n');banner();
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++% -------------------------------------------------------------------
%
% -------------------------------------------------------------------
N = 4;
n1 = [0:3];
x1 = [1, 2, 2];x2 = [1, 2, 3, 4];%C = circulnt(x2, 4);y1 = circonvt_v3(x1, x2, N)
运行结果：
代码：
function x3 = circonvf(x1, x2, N)
%% N-point Circular convolution between x1 and x2: (frequency domain)
%% ------------------------------------------------------------------
%% [x3] = circonvf(x1,x2,N)
%% x3 = output sequence containning the circular convolution
%% x1 = input sequence of length N1 <= N
%% x2 = input sequence of length N2 <= N
%%
%% N = size of circular buffer
%% Method: x3(n) = IDFT[X1(k)X2(k)] %% Check for length of x1
if length(x1) > N
error('N must be >= the length of x1 !')
end
%% Check for length of x2
if length(x2) > N
error('N must be >= the length of x2 !')
endx1 = [x1 zeros(1,N-length(x1))];
x2 = [x2 zeros(1,N-length(x2))]; X1k_DFT = dft(x1, N);
X2k_DFT = dft(x2, N); x3 = real(idft( X1k_DFT.* X2k_DFT, N));
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.26 \n\n');banner();
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++% -------------------------------------------------------------------
%
% -------------------------------------------------------------------
N = 4;
n1 = [0:3];
x1 = [4,3,2,1];
%x1 = [1,2,2];n2 = [0:3];
x2 = [1, 2, 3, 4];%C = circulnt(x2, 4);y1 = circonvf(x1, x2, N)
运行结果：
