Magnitude Plot Incorrect Frequency

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Matt
Matt 2025-3-30
评论： Matt 2025-3-30
Hi there, I'm having a problem plotting the magnitude spectrum of simple cos wave.
dt = .001;
t = -.5:dt:.5;
x1 = 2*cos(2*pi*20*t);
Wmax = 2*pi*100;
K = 2000;
w = (0:K-1) * Wmax / K;
X1 = x1 * exp(-j * t' * w) * dt;
mag_X1 = 2 * abs(X1);
display (X1);
subplot(2,1,1);
plot(t, x1);
xlabel('time');
ylabel('x(t)');
title('time domain');
subplot(2,1,2);
plot(w/2*pi, mag_X1);
axis([0 1000 0 7]);
xlabel('frequency Hz');
ylabel('|x(w)|');
title('magnitude spectrum');
The problem I'm having is that the plot shows a spike at 200 Hz rather than 20 Hz, if somebody could help me understand where I'm going wrong it would be greatly appreciated.

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采纳的回答

Paul
Paul 2025-3-30
Recheck the conversion from rad/sec to Hz in the plot command for the magnitude of the spectrum
  3 个评论
显示 1更早的评论
Paul
Paul 2025-3-30
Ran in:
Yes, the relationship is. Is that what the code implements?
Suppose omega = 6.28 so that f is approximately equal to 1. The code in the question would compute f as
w = 6.28;
f = w/2*pi
f = 9.8646
which is incorrect. Recall that Matlab follows PEMDAS for the basic math operators (Operator Precedence), so that computation for f is effectively being evaluated as
f = (w/2)*pi
f = 9.8646
Matt
Matt 2025-3-30
Thanks so much, can't believe how silly I am.

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更多回答（1 个）

Hassaan
Hassaan 2025-3-30
编辑：Hassaan 2025-3-30
Ran in:
% Time step
dt = 0.001;
% Time vector
t = -0.5 : dt : 0.5;
% Define the signal: x1 = 2 cos(2π·20t)
x1 = 2 * cos(2*pi*20*t);
% Maximum angular frequency (rad/s)
Wmax = 2*pi*100;
% Number of frequency samples
K = 2000;
% Frequency vector in rad/s
w = (0 : K-1) * (Wmax / K);
% Compute Fourier transform via integration (numerical)
X1 = x1 * exp(-1j * t' * w) * dt;
% Magnitude (scaled by 2 for plotting)
mag_X1 = 2 * abs(X1);
% --- Plot time-domain signal ---
figure;
subplot(2,1,1);
plot(t, x1);
xlabel('Time (s)');
ylabel('x(t)');
title('Time Domain');
% --- Plot magnitude spectrum ---
subplot(2,1,2);
% Use w/(2*pi) to convert rad/s to Hz
plot(w/(2*pi), mag_X1);
xlabel('Frequency (Hz)');
ylabel('|X(\omega)|');
title('Magnitude Spectrum');
% Optional axis limits for clarity
axis([0 100 0 7]);
-----------------------------------------------------------------------------------------------------------------------------------------------------
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It's important to note that the advice and code are based on limited information and meant for educational purposes. Users should verify and adapt the code to their specific needs, ensuring compatibility and adherence to ethical standards.
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