Explore the fundamentals and applications of the Fourier Transform in this comprehensive 2.5-hour video series. Delve into the definition, properties, and relationships with other transforms, including its extension to two-dimensional image processing. Learn about orthogonal basis functions, negative frequency, time and frequency scaling, and the importance of phase. Examine the differences between continuous and discrete time Fourier Transforms, and understand the connections between various transforms such as Fourier Series, DTFT, DFT, FFT, Laplace Transform, and Z-Transform. Investigate the Gibbs Phenomenon and clarify the distinctions between Fourier Transform and Inverse Fourier Transform. Gain practical insights through examples, with additional applications available in a separate playlist on the channel titled "Fourier transform Examples".
Overview
Syllabus
What is the Fourier Transform?.
What is the Fourier Transform used for?.
Fourier Transform Equation Explained.
Fourier Transform of Cos.
Orthogonal Basis Functions in the Fourier Transform.
What is Negative Frequency?.
Time and Frequency Scaling.
Is Phase important in the Fourier Transform?.
Duality Example of Fourier Transforms.
Continuous Time and Discrete Time Fourier Transforms.
Fourier Transform of Discrete Time Signals are not Discrete.
2D Fourier Transform Explained with Examples.
How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?.
What is the Gibbs Phenomenon?.
Fourier Trfm and Inv FT: What's the difference?.
Taught by
Iain Explains Signals, Systems, and Digital Comms
