I have a task to simulate a sequence of rectangular pulses. As a result, I wrote Python code, but the end results are not encouraging. A = np.random.randint(1, 6) # random amplitude (from 1 to 5) tilda = 0.5 # pulse duration SR = 1000 # sampling rate t = np.linspace(0, 3, SR) # time range from 0 to 2 seconds n_pulses = 3 # number of pulses t_i = 0.5 # interval between pulses pulse1_start = 0.25 # the beginning of the first pulse rect_pulses = np.zeros_like(t) for i in range(n_pulses): pulse_start = pulse1_start + i * (tilda + t_i) pulse_end = pulse_start + tilda rect_pulses = np.where((t >= pulse_start) & (t <= pulse_end), A, rect_pulses) FFT = fft(rect_pulses) # magnitude of FFT FFT_n = FFT / len(FFT) # normalization f_ax = np.linspace(0, (SR), len(FFT)) # frequency axis half_fft = len(FFT) // 2 # half the length of the FFT f_half = f_ax[:half_fft] # frequencies up to f_ax / 2 FFT_half = np.abs(FFT_n[:half_fft]) # FFT module up to f_ax/2 FFT_half *= 2 # doubling the magnitude plt.figure(figsize=(10, 10)) plt.subplot(2, 1, 1) plt.plot(t, rect_pulses, linewidth=1.7) plt.title('Rect. Pulse', fontsize=21) plt.xlabel('t', fontsize=21, fontweight='bold') plt.ylabel('x(t)', fontsize=21, fontweight='bold') plt.grid() plt.subplot(2, 1, 2) plt.plot(f_half, FFT_half, 'r-', linewidth=1.7) plt.title('FFT of Rect. Pulse', fontsize=21) plt.xlabel('$f$', fontsize=21, fontweight='bold') plt.ylabel('S($f$)', fontsize=21, fontweight='bold') plt.xlim([0,40]) plt.grid() plt.tight_layout() plt.show() As you can see in the picture, the sequence turned out to be acceptable. But the spectrum didn't work out. Increasing the sampling rate doesn't help me at all. What is wrong with my code that causes such an incorrect FFT to be built? Continue reading...
