《DSP using MATLAB》Problem 5.17
1、代码
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.17 \n\n'); banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ % -------------------------------------------------------------------------------------
% X(k) is 10-point DFTs of real-valued sequence x(n)
% X(k) = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j]
% N = 10 k=[0:9]
% 1 y(n) = x((2-n))10
% ------------------------------------------------------------------------------------- k1 = [0:9];
Xk_DFT = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j];
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', 'P5.17.1 X(k), DFT of x(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magXk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of x(n), N=10'); grid on;
subplot(2,2,3); stem(k1, angXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of x(n), N=10'); grid on;
subplot(2,2,2); stem(k1, realXk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of x(n), N=10'); grid on;
subplot(2,2,4); stem(k1, imagXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of x(n), N=10'); grid on; [xn] = real(idft(Xk_DFT, N1)); % real-valued sequence
n = [0 : N1-1]; % +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 1st way to get y(n)-----circular shifft
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
xn_cirfold = xn(mod(-n,N1)+1);
m = 2; % shift
yn1 = cirshftt(xn_cirfold, m, length(xn)); Xfk_DFT = dft(xn_cirfold, N1);
magXfk_DFT = abs( [ Xfk_DFT ] ); % DFT magnitude
angXfk_DFT = angle( [Xfk_DFT] )/pi; % DFT angle
realXfk_DFT = real(Xfk_DFT); imagXfk_DFT = imag(Xfk_DFT); figure('NumberTitle', 'off', 'Name', 'P5.17.1 X((-k)), DFT of x((-n))')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magXfk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of x((-n)), N=10'); grid on;
subplot(2,2,3); stem(k1, angXfk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of x((-n)), N=10'); grid on;
subplot(2,2,2); stem(k1, realXfk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of x((-n)), N=10'); grid on;
subplot(2,2,4); stem(k1, imagXfk_DFT);
axis([0, 10, -5, 5.05]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of x((-n)), N=10'); grid on; % +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 2ed way to get y(n)-----IDFT of Y(k)
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
k1 = [0:9];
Yk_DFT = exp(-j*2*pi*(2*k1)/10) .* Xk_DFT(mod(-k1, N1)+1);
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', 'P5.17.1 DFT(k) of y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magYk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of y(n), N=10'); grid on;
subplot(2,2,3); stem(k1, angYk_DFT);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of y(n), N=10'); grid on;
subplot(2,2,2); stem(k1, realYk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of y(n), N=10'); grid on;
subplot(2,2,4); stem(k1, imagYk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of y(n), N=10'); grid on; [yn2] = real(idft(Yk_DFT, N1));
n = [0 : N1-1]; figure('NumberTitle', 'off', 'Name', 'P5.17.1 x(n) & y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(n, xn);
xlabel('n'); ylabel('x(n)');
title('x(n), IDFT of X(k)'); grid on;
subplot(2,2,2); stem(n, yn1);
xlabel('n'); ylabel('y(n)');
title('y(n) by circular shift x((2-n))_N N=10'); grid on;
subplot(2,2,3); stem(n, xn_cirfold);
xlabel('n'); ylabel('x((-n))');
title('x((-n)) N=10'); grid on;
subplot(2,2,4); stem(n, yn2);
xlabel('n'); ylabel('y(n)');
title('y(n) by IDFT of Y(k)'); grid on;
运行结果：
4、代码：
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.17 \n\n'); banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ % -------------------------------------------------------------------------------------
% X(k) is 10-point DFTs of real-valued sequence x(n)
% X(k) = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j]
% N = 10 k=[0:9]
% 4 y(n) = x(n) Circular-Conv x((-n))10
% ------------------------------------------------------------------------------------- k1 = [0:9];
Xk_DFT = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j];
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', 'P5.17.4 X(k), DFT of x(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magXk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of x(n), N=10'); grid on;
subplot(2,2,3); stem(k1, angXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of x(n), N=10'); grid on;
subplot(2,2,2); stem(k1, realXk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of x(n), N=10'); grid on;
subplot(2,2,4); stem(k1, imagXk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of x(n), N=10'); grid on; [xn] = real(idft(Xk_DFT, N1)); % real-valued sequence
n = [0 : N1-1]; % +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 1st way to get y(n)-----circular
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
xn_cirfold = xn(mod(-n,N1)+1);
yn1 = circonvt(xn, xn_cirfold, N1); % +++++++++++++++++++++++++++++++++++++++++++++++++++++++
% 2ed way to get y(n)-----IDFT of Y(k)
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
k1 = [0:9];
Xfk_DFT = dft(xn_cirfold, N1); Yk_DFT = Xk_DFT .* Xfk_DFT;
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', 'P5.17.4 DFT(k) of y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magYk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of y(n), N=10'); grid on;
subplot(2,2,3); stem(k1, angYk_DFT);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of y(n), N=10'); grid on;
subplot(2,2,2); stem(k1, realYk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of y(n), N=10'); grid on;
subplot(2,2,4); stem(k1, imagYk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of y(n), N=10'); grid on; [yn2] = real(idft(Yk_DFT, N1));
n = [0 : N1-1]; figure('NumberTitle', 'off', 'Name', 'P5.17.4 x(n) & y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(n, xn);
xlabel('n'); ylabel('x(n)');
title('x(n), IDFT of X(k)'); grid on;
subplot(2,2,2); stem(n, yn1);
xlabel('n'); ylabel('y(n)');
title('y(n) by x(n) Circular-Conv x((-n))_N N=10'); grid on;
%subplot(2,2,3); stem(n, xn_cirfold);
%xlabel('n'); ylabel('x((-n))');
%title('x((-n)) N=10'); grid on;
subplot(2,2,4); stem(n, yn2);
xlabel('n'); ylabel('y(n)');
title('y(n) by IDFT of Y(k)'); grid on;
运行结果：
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