Name: Fourier Transform Explained
Rating: 4.43 (70 reviews)

What you learn in Fourier Transform Explained ?

Fourier Transform

Application of Fourier Transform

Example problems of Fourier Transform

About this Free Certificate Course

The Fourier transform is a function that is popularly used in applied mathematics on the lines of image analysis, frequency analysis, and a lot more. It is a functional concept that helps us understand the behaviour of single-valued functions when shifted across domains such as frequency and time. This course has been put together to provide you with a comprehensive understanding of what Fourier transforms are and how you would use them to solve multiple problems. The instructor also discusses multiple examples throughout the course as well.

Course Outline

Introduction to Fourier Transform

Fourier Transform Examples

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Fourier Transform Explained

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Frequently Asked Questions

What does the Fourier transform do?

Fourier Transform is a mathematical transform that is mostly applied to domains like image processing and frequency analysis which decomposes functions depending on their space or time into functions depending on spatial or temporal frequency. It breaks a waveform or a signal, into an alternative representation characterized by sine or cosines.

What is Fourier transform with a simple explanation?

Fourier transform decomposes functions depending upon their space or time functions. It is used to find the base frequencies of the wave it is composed of and represents it in an alternative form.

What is the Application of Fourier Transform?

Fourier transform can be applied to many fields. A few of them are:

Image analysis
Image restoration
Image filtering
Image compression
Image reconstruction
Distinguishing notes in a musical chord
Approximation theory
Signal processing
Control theory
Differential partial equation

What are the advantages of Fourier transform?

Advantages of Fourier Transform:

Very little information is lost during signal transformation.
It maintains information on amplitude, harmonics, and phase.
It uses all parts of the waveform to translate the signal into the frequency domain.
It converts the time domain into the frequency domain.

How do you calculate the Fourier transform of an image?

To calculate the Fourier Transform of an image,

Take 1D FFT of each row, then 1D FFT of each column.
Start by taking the FFT of N pixel values in row 0 of the real array.
The real part of the FFT output is put back in row 0 of the real array and the imaginary part is put in row 0 of the imaginary array.
Repeat this procedure on rows 1 through N-1, both the real and imaginary arrays contain intermediate images.
Repeat this procedure on each of the columns of intermediate data.
Take N pixel values from column 0 of the real array and N pixel values from column 0 of the imaginary array.
Calculate FFT.
The real part of the FFT output is put into column 0 of the real array and the imaginary part in column 0 of the imaginary array.
Repeat this on column 1 through N-1, both arrays have been overwritten with image frequency spectrum.