Fourier Transform Examples

Explore a comprehensive series of examples demonstrating the application of Fourier Transform, including two-dimensional cases for image processing. Delve into topics such as the Fourier Transform of cosine functions with and without phase shifts, duality principles, transform properties of rectangular and sinc functions, and the transformation of delta function sums. Examine system examples using cosine inputs, gain an introduction to image processing with 2D Fourier Transforms, and investigate the bandwidth of digital clock waveforms. Learn about the Fourier Transform of rectified sinusoids, tackle typical exam questions on transform properties, and understand the practical applications of Fourier Transforms in various fields.

Syllabus

Fourier Transform of Cos.
Fourier Transform of Cos with Phase Shift.
Duality Example of Fourier Transforms.
Fourier Transform Duality Rect and Sinc Functions.
Fourier Transform of a Sum of Delta Functions.
Why is the Fourier TF of a Sum of Deltas also a Sum of Deltas?.
System Example using Fourier Transforms with Cosine Input.
Introduction to Image Processing with 2D Fourier Transform.
What is the Bandwidth of a Digital Clock Waveform?.
Fourier Transform of a Rectified Sinusoid.
Typical Exam Question on Fourier Transform Properties.
What is the Fourier Transform used for?.