代码：
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.16 \n\n');
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
% -------------------------------------------------------------------------------
% X(k) and Y(k) both 10-point DFTs of x(n) and y(n) respectively
% X(k) = exp(j0.2pi*k) k=[0:9]
% 1 y(n) = x((n-5))10
% -------------------------------------------------------------------------------
k1 = [0:9];
Xk_DFT = exp(j*0.2*pi*k1);
N1 = length(Xk_DFT); % length is 10
magXk_DFT = abs( [ Xk_DFT ] ); % DFT magnitude
angXk_DFT = angle( [Xk_DFT] )/pi; % DFT angle
realXk_DFT = real(Xk_DFT); imagXk_DFT = imag(Xk_DFT);
figure('NumberTitle', 'off', 'Name', 'P5.16.1 DFT(k) of x(n)')
set(gcf,'Color','white');
subplot(2,1,1); stem(k1, magXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFT magnitude of x(n), N=10'); grid on;
subplot(2,1,2); stem(k1, angXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFT angle of x(n), N=10'); grid on;
[xn] = idft(Xk_DFT, N1);
n = [0 : N1-1];
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 1st way to get y(n)-----circular shifft
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
m = 5; % shift
yn1 = cirshftt(xn, m, length(xn));
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 2ed way to get y(n)-----IDFT of Y(k)
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
k1 = [0:9];
Yk_DFT = exp(-j*0.8*pi*k1);
N1 = length(Yk_DFT); % length is 10
magYk_DFT = abs( [ Yk_DFT ] ); % DFT magnitude
angYk_DFT = angle( [Yk_DFT] )/pi; % DFT angle
realYk_DFT = real(Yk_DFT); imagYk_DFT = imag(Yk_DFT);
figure('NumberTitle', 'off', 'Name', 'P5.16.1 DFT(k) of y(n)')
set(gcf,'Color','white');
subplot(2,1,1); stem(k1, magYk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFT magnitude of y(n), N=10'); grid on;
subplot(2,1,2); stem(k1, angYk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFT angle of y(n), N=10'); grid on;
[yn2] = idft(Yk_DFT, N1);
n = [0 : N1-1];
figure('NumberTitle', 'off', 'Name', 'P5.16.1 x(n) & y(n)')
set(gcf,'Color','white');
subplot(3,1,1); stem(n, xn);
xlabel('n'); ylabel('x(n)');
title('x(n), IDFT of X(k)'); grid on;
subplot(3,1,2); stem(n, yn1);
xlabel('n'); ylabel('y(n)');
title('y(n) by circular shift x((n-5))_N N=10'); grid on;
subplot(3,1,3); stem(n, yn2);
xlabel('n'); ylabel('y(n)');
title('y(n) by IDFT of Y(k)'); grid on;
运行结果：
代码：
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.16 \n\n');
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
% -------------------------------------------------------------------------------
% X(k) and Y(k) both 10-point DFTs of x(n) and y(n) respectively
% X(k) = exp(j0.2pi*k) k=[0:9]
% 3 y(n) = x((3-n))10
% -------------------------------------------------------------------------------
k1 = [0:9];
Xk_DFT = exp(j*0.2*pi*k1);
N1 = length(Xk_DFT); % length is 10
magXk_DFT = abs( [ Xk_DFT ] ); % DFT magnitude
angXk_DFT = angle( [Xk_DFT] )/pi; % DFT angle
realXk_DFT = real(Xk_DFT); imagXk_DFT = imag(Xk_DFT);
figure('NumberTitle', 'off', 'Name', 'P5.16.3 DFT(k) of x(n)')
set(gcf,'Color','white');
subplot(2,1,1); stem(k1, magXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFT magnitude of x(n), N=10'); grid on;
subplot(2,1,2); stem(k1, angXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFT angle of x(n), N=10'); grid on;
[xn] = real(idft(Xk_DFT, N1));
n = [0 : N1-1];
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 1st way to get y(n)-----circular shifft
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
xn_cirfold = xn(mod(-n,N1)+1);
m = 3; % shift
yn1 = cirshftt(xn_cirfold, m, length(xn));
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 2ed way to get y(n)-----IDFT of Y(k)
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
k1 = [0:9];
Yk_DFT = exp(j*2*pi*(10-4*k1)/10);
N1 = length(Yk_DFT); % length is 10
magYk_DFT = abs( [ Yk_DFT ] ); % DFT magnitude
angYk_DFT = angle( [Yk_DFT] )/pi; % DFT angle
realYk_DFT = real(Yk_DFT); imagYk_DFT = imag(Yk_DFT);
figure('NumberTitle', 'off', 'Name', 'P5.16.3 DFT(k) of y(n)')
set(gcf,'Color','white');
subplot(2,1,1); stem(k1, magYk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('DFT magnitude of y(n), N=10'); grid on;
subplot(2,1,2); stem(k1, angYk_DFT);
xlabel('k'); ylabel('angle(k)');
title('DFT angle of y(n), N=10'); grid on;
[yn2] = real(idft(Yk_DFT, N1));
n = [0 : N1-1];
figure('NumberTitle', 'off', 'Name', 'P5.16.3 x(n) & y(n)')
set(gcf,'Color','white');
subplot(3,1,1); stem(n, xn);
xlabel('n'); ylabel('x(n)');
title('x(n), IDFT of X(k)'); grid on;
subplot(3,1,2); stem(n, yn1);
xlabel('n'); ylabel('y(n)');
title('y(n) by circular shift x((3-n))_N N=10'); grid on;
subplot(3,1,3); stem(n, yn2);
xlabel('n'); ylabel('y(n)');
title('y(n) by IDFT of Y(k)'); grid on;
运行结果：
X(k)的图见第1小题，这里不附了。
