UsefulLinks
Mathematics
Transform Methods in Mathematics
1. Foundations of Transform Methods
2. The Laplace Transform
3. Fourier Analysis
4. Discrete Transform Methods
5. Specialized Integral Transforms
6. Advanced Applications
7. Computational Aspects and Numerical Methods
5.
Specialized Integral Transforms
5.1.
Mellin Transform
5.1.1.
Definition and Basic Properties
5.1.2.
Relationship to Other Transforms
5.1.2.1.
Connection to Laplace Transform
5.1.2.2.
Connection to Fourier Transform
5.1.3.
Applications
5.1.3.1.
Asymptotic Analysis
5.1.3.2.
Number Theory
5.1.3.3.
Probability Theory
5.2.
Hankel Transform
5.2.1.
Definition with Bessel Function Kernel
5.2.2.
Properties and Transform Pairs
5.2.3.
Relationship to Fourier Transform
5.2.3.1.
Cylindrical Coordinates
5.2.3.2.
Radial Symmetry
5.2.4.
Applications
5.2.4.1.
Problems with Cylindrical Symmetry
5.2.4.2.
Heat Conduction
5.2.4.3.
Wave Propagation
5.3.
Hilbert Transform
5.3.1.
Definition as Principal Value Integral
5.3.2.
Properties
5.3.2.1.
Phase Shifting
5.3.2.2.
Causality Relations
5.3.3.
Analytic Signals
5.3.3.1.
Complex Envelope
5.3.3.2.
Instantaneous Frequency
5.3.4.
Applications
5.3.4.1.
Signal Processing
5.3.4.2.
Communications
5.3.4.3.
Amplitude Modulation
5.4.
Wavelet Transforms
5.4.1.
Continuous Wavelet Transform
5.4.1.1.
Definition and Properties
5.4.1.2.
Time-Frequency Localization
5.4.1.3.
Wavelet Functions
5.4.2.
Discrete Wavelet Transform
5.4.2.1.
Multiresolution Analysis
5.4.2.2.
Scaling Functions
5.4.2.3.
Filter Bank Implementation
5.4.3.
Comparison with Fourier Methods
5.4.3.1.
Time-Frequency Resolution
5.4.3.2.
Non-stationary Signal Analysis
Previous
4. Discrete Transform Methods
Go to top
Next
6. Advanced Applications