如何使用 np.fft.fft function 进行傅里叶变换？

Question

I want to generate two sinusoidal signals where =5 Hz and f2=3 Hz, the time duration of the signal is =1. x1(t)=sin(2) X2(t)=sin(2(1+f2)) X()=1()+2() So, I will try to analyze the frequency domain respresentation of this signal. How can I take the Fourier Transform using np.fft.fft function by using DFT size =64, sampling frequency =64 and =1 that is the time duration that you will have samples. In the end, I want to plot () and () which is the Fourier Transform of x(t). Thanks, If you help me, I will be grateful to you.

In the end, it will be seen how to distinguish two signals. Thanks for everything for everyone.

Answer 1

It is not entirely clear what the final signal is you want to do a Fourier Transform on, but I made the following assumptions:

• your time domain signal x(t)=sin(21)+sin(22) . From what your wrote it wasn't entirely clear
• you want to have the FFT of above x(t)
• your total time T=1s (you wrote T=1 , units are important)
• your sampling frequency fs=64 sample/s (you wrote fs=64 , units are important)

With these givens, you can do something like the following:

import numpy as np
import math
import matplotlib.pyplot as plt

# Entering your input variables
fs = 64
T = 1
f1 = 3
f2 = 5

# Creating the time and frequency axis
time = np.arange(0, T, 1/fs)
freq = np.arange(0, fs/2, 1/T)

# Creating the time domain x signal
x1 = np.sin(2*math.pi*f1*time)
x2 = np.sin(2*math.pi*f2*time)
x = x1 + x2

# Making the FFT, while normalizing to make sure the amplitude is correct
X = np.fft.fft(x)/len(time)*2

# Plotting the time domain + frequency domain signals on a subplot. For the
# frequency domain plot, we only take the first half of the frequency axis
# (going up to fs/2) because we're dealing with a real signal.
fig, axs = plt.subplots(2,1)
axs[0].plot(time, x)
axs[0].set_xlabel('Time [s]')
axs[0].set_ylabel('Amplitude')
axs[1].plot(freq, abs(np.split(X,2)[0]), "x")
axs[1].set_xlabel('Frequency [Hz]')
axs[1].set_ylabel('Amplitude')
plt.show()

Out of this, you get the following plot:

As you can see, you clearly see peaks with amplitude 1 on 3 and 5 Hz: :)

Now, it's possible I didn't perfectly understand what your x(t) signal needed to be, but you can easily change the definitions of x1 , x2 and x and get the output you want.

Hope this helps!