# Inconsistency in DFT in Python

import numpy as np
import matplotlib.pyplot as plt

Fs = 200                        # sampling rate
Ts = 1.0/Fs                      # sampling interval
t = np.arange(0, 1, Ts)            # time vector

f_f = np.arange(30, 80, 0.001)
a = np.arange(0, len(f_f), 1)

for i in range(len(f_f)):
y2 = y2 +  np.sin(2 * np.pi * (f_f[i]) * t)

n = len(y2)
k = np.arange(n)
T = n/Fs
frq = k/T               # two sides frequency range
freq = frq[range(int(n/2))]     # one side frequency range

Y = np.fft.fft(y2)/n                # fft computing and normalization
#Y = np.fft.fft(y2)
Y = Y[range(int(n/2))]
plt.plot(freq, abs(Y), 'r-')    # Fourier data
plt.show()


Here, as you may have noticed I have chosen df = 0.001 and the corresponding DFT is shown in the attached pic. However, while I am considering df = 1 instead, DFT comes out as sort of continuous square wave over the frequency domain of the signal (expected since amplitude of all the waves are equal). Why is it then getting distorted for df = 0.1 or smaller ? I mean why two peaks are appearing at f = 30 Hz & f = 80 Hz and not the entire band ?

Even, sampling rate has been so chosen so that nyquist rate exceeds maximum frequency component of the pulse

• Sorry, I don't know what your code is doing, but it does NOT look like a DFT. Sep 22 at 12:22
• @Hilmar I have edited the complete code now, kindly have a glimpse and let me know. Sep 23 at 5:09