《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：