Fourier Transform: Properties and Applications

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Related lectures (30)

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Fourier Transform: Derivatives and Formulas

Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.

Fourier Properties

Covers the properties of the continuous-time Fourier transform and provides examples to illustrate these concepts.

Image Processing: Smoothing and Filtering

Covers image smoothing, noise reduction, and segmentation techniques using filters and transforms.

Fourier Series: Extension and Periodicity

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

Fourier Transform: Basics and Examples

Explains the basics of Fourier transform and demonstrates its application through examples, including periodic functions and Fourier Transform Pairs.

Fourier Series and Transforms: Introduction and Properties

Covers Fourier series, Fourier transforms, and convolution properties, including linearity and commutativity.

Central Limit Theorem

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

Fourier Transform: Derivatives and Laplace Transform

Explores the Fourier transform properties with derivatives and introduces the Laplace transform for signal transformation and solving differential equations.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.