Plotting the Fourier Transform in Python (DFT/FFT)

#Electrical Engineering #Engineering #Signal Processing #python #fourierseries #fouriertransform #fourier
In this video, I'l explain how we can use python to plot the (Discrete) Fourier Transform of signals. I'll explain how we can use FFTShift in Numpy to rearrange the Fourier Transform so negative frequencies are on the left and positive frequencies are on the right.
Here is a link to the Python Notebook to follow along: www.dropbox.com/scl/fo/0uw6r1...

[@acelaox6836]

Thank you so much now I didn't know about fftshift in numpy till today!

[@starx8771]

This was so helpful, thank you so much!

[@idreeskhan-zp5ey]

Thnak You!

[@angeloc700]

Nice video. As a suggestion, if you turned the VS autocomplete dialogues off, I’m sure the viewer’s experience would be much better; it’s very difficult to focus on what you’re saying and typing when modal boxes are popping up and changing all over the place.

[@SignalProcessingWithPaul]

This is good suggestion, thanks

[@anonymousguy438]

How to know what are the different frequencies which constructs your main signal? I am asking about the frequency values not its amplitude.

[@SignalProcessingWithPaul]

I may make a video on this. To answer your question, it will be divisions of the sampling frequency of your signal (which is 1/T, where T is the time interval between samples). Given a sampling frequency Fs and N samples in the time domain, each index of the FFT will be at k*Fs/N. However at Fs/2, (meaning for all indices larger than N/2), the frequency "wraps around" and becomes negative due to aliasing. So I believe the frequency can be written concisely as (k*Fs/N) - ((N - k)*Fs / N * I(k > N/2)), where I is the indicator function.

[@adityanagarkar4326]

Here you have sampled the signal at intervals of 1. what if I want to sample it at a higher frequency?

[@code2compass]

What is your question?

[@imk820]

Hi can I ask you a question?

[@SignalProcessingWithPaul]

Yeah sure, go for it

[@thiagodavidmoreiramadeiros4458]

@@SignalProcessingWithPaul Hi, I am working with a sinusoidal signal made of two different frequencies that i have to find. How can i get the indexes that correspond to these frequencies when i apply the fft

[@yabool2001]

Hi Paul. Why do you call DFT in the title when you don't show DFT at all in this video? The DFT operates exclusively on discrete sets of data and produces a spectrum comprising discrete frequency components.

[@SignalProcessingWithPaul]

The only way you can compute a frequency domain representation in a computer is with the DFT (the FFT is a way of computing the DFT that uses some symmetries to reduce the number of computations explicitly needed from Log(n^2) to n log2(n)).
Since a computer cannot process an infinite number of datapoints or have infinite precision in amplitudes, you need a signal that is discrete in time and discrete in frequency to do any operation like this.
Hope this helps

[@yabool2001]

@@SignalProcessingWithPaul Thx for explanation.