YOU CAN RELAX. THIS IS NOT A MATH CLASS. THIS IS A DEMONSTRATION PROJECT. ALL THE INFORMATION YOU NEED CAN BE FOUND HERE.
This project is based on How to Compute FFT and Plot Frequency Spectrum in Python using Numpy and Matplotlib (YouTube)
The project goals are:
- compute Fast Fourier Transform (FFT) using Numpy "fft" function
- Plot the frequency spectrum using mathplotlib
Introduction
Transforms and FFT are a complex subject but, hopefully, there is enough information here for this project. No research Required.
Note: The following is from Wikipedia; Hopefully simplified.
What are Fast Fourier Transform (FFT) used for?
FFTs are mainly used to visualize signals. For example signal filtering, data compression, audio/video production, spectral analysis, computational physics, and other applications.
It is used in MRI scanners. It converts the human body into a spatial frequency spectrum that is then used to create meaningful images.
What is a Fast Fourier Transform (FFT)?
A Fast Fourier Transform (FFT) is a numerical algorithm that can be used to convert a signal from a time domain to a frequency domain.
What is a time domain?
A time domain refers to the analysis of mathematical functions or signals with respect to time.
You can think of it as a collection of time/value pairs. A pair is a time T and the signal's value/strength/magnitude at that time.
The pairs are usually generate by taking a sample of the signal at a series of times. (Monotonically increasing times.)
Time is the independent variable and the signal's value/strength/magnitude is the dependent variable.
What is a frequency domain?
A frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time.
Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies.
What is a transform?
A transform is a function or process that can convert a signal between a time domain and a frequency domain.
Who was Fourier?
French mathematician and physicist. (1768 - 1830)
How are sine waves related to circles?
Click HERE (YouTube)
Project #1
Create a program to replicate the
program described HERE
.
Project #2
Create an interactive program that allows the user to
- use sines and cosine to generate signals
- assign different signal frequencies
- change sampling frequency
- generate plots for the new configuration -
make them look pretty
(see Project #1 for the required plots)
Did you find the frequencies in the plots?
Links
How to Compute FFT and Plot Frequency Spectrum in Python using Numpy and Matplotlib