《DSP using MATLAB》Problem 5.20

窗外的知了叽叽喳喳叫个不停，屋里温度应该有30°，伏天的日子难过啊！

频率域的方法来计算圆周移位

代码：

子函数的

function y = cirshftf(x, m, N)
%% -----------------------------------------------------------------------
%    Circular shift of m samples wrt size N in sequence x: (freq domain)
% ---------------------------------------------------------------------
%  y = cirshftf(x, m, N)
%     y : output sequence containing the circular shift
%     x : input sequence of length <= N
%     m : sample shift
%     N : size of circular buffer
%  Method : y(n) = idft( dft(x(n)) * WN ^ (mk)) 
 
%  if m is a scalar then y is a sequence (row vector)
%  if m is a vector then y is a matrix, each row is a circular shift
%        in x corresponding to entries in vector m
%   M and x should not be matrices
 
if length(x)>N
   error('N must >= length(x)' )
end
 
x = [x zeros(1, N-length(x))];
k = [0:1:N-1];
 
WN = exp(-j*2*pi/N);
mk = m*k;
 
y = real(idft( dft(x, N) .* ( WN .^ (mk) ), N ));

　　主函数的

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 5.20 \n\n');
 
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
% ---------------------------------------------------------------------------------
%        circular shift
%          method 1 :  cirshftt function, time domain
%          method 2 :  cirshftf function, freq domain
%
% ---------------------------------------------------------------------------------
 n = [0:10];
 x = [5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4];             % N=11 sequence
 
m1 = -5; N1 = 12;
n1 = [0:N1-1];
 
m2 = 8; N2 = 15;
n2 = [0:N2-1];
 
% -----------------------------------------------------
%     1st way to get circular shift---time domain
% -----------------------------------------------------
y1_1 = cirshftt(x, m1, N1);
y2_1 = cirshftt(x, m2, N2);
 
% --------------------------------------------------------
%     2rd way to get circular shift --- freq domain
% --------------------------------------------------------
y1_2 = cirshftf(x, m1, N1);
y2_2 = cirshftf(x, m2, N2);
 
figure('NumberTitle', 'off', 'Name', 'P5.20.a x(n) and its cir shift')
set(gcf,'Color','white');
subplot(3,1,1); stem(n, x);
xlabel('n'); ylabel('x(n)');
title('x(n), N=11');  grid on;
subplot(3,1,2); stem(n1, y1_1);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('n'); ylabel('y(n)');
title('TIME domain circular shift x(n), m=-5, N=12');  grid on;
subplot(3,1,3); stem(n1, y1_2);
xlabel('n'); ylabel('y(n)');
title('FREQ domain circular shift x(n), m=-5, N=12');  grid on;
axis([0, N1, 0, 6]);
 
figure('NumberTitle', 'off', 'Name', 'P5.20.b x(n) and its cir shift')
set(gcf,'Color','white');
subplot(3,1,1); stem(n, x);
xlabel('n'); ylabel('x(n)');
title('x(n), N=11');  grid on;
subplot(3,1,2); stem(n2, y2_1);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('n'); ylabel('y(n)');
title('TIME domain circular shift x(n), m=8, N=15');  grid on;
subplot(3,1,3); stem(n2, y2_2);
xlabel('n'); ylabel('y(n)');
title('FREQ domain circular shift x(n), m=8, N=15');  grid on;
axis([0, N2, 0, 6]);

　　运行结果：