Frequency domain of a sine wave with frequency 100

Question

I'm starting DSP on Python and I'm having some difficulties: I'm trying to define a sine wave with frequency 1000Hz

I try to do the FFT and find its frequency with the following piece of code:

import numpy as np

import matplotlib.pyplot as plt

sampling_rate = int(10e3)
n = int(10e3)

sine_wave = [100*np.sin(2 * np.pi * 1000 * x/sampling_rate) for x in range(0, n)]

s = np.array(sine_wave)

print(s)

plt.plot(s[:200])
plt.show()

s_fft = np.fft.fft(s)
frequencies = np.abs(s_fft)
plt.plot(frequencies)
plt.show()

So first plot makes sense to me. Second plot (FFT) shows two frequencies: i) 1000Hz, which is the one I set at the beggining ii) 9000Hz, unexpectedly freqeuncy domain

Answer 1

Your data do not respect Shannon criterion. you do not set a correct frequencies axis.

It's easier also to use rfft rather than fft when the signal is real.

Your code can be adapted like :

import numpy as np
import matplotlib.pyplot as plt

sampling_rate = 10000
n = 10000
signal_freq = 4000 # must be < sampling_rate/2 
amplitude = 100

t=np.arange(0,n/sampling_rate,1/sampling_rate)
sine_wave = amplitude*np.sin(2 * np.pi *signal_freq*t) 
plt.subplot(211)
plt.plot(t[:30],sine_wave[:30],'ro')

spectrum = 2/n*np.abs(np.fft.rfft(sine_wave))
frequencies = np.fft.rfftfreq(n,1/sampling_rate)
plt.subplot(212)
plt.plot(frequencies,spectrum)
plt.show()

Output :

There is no information loss, even if a human eye can be troubled by the temporal representation.