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Session 6
Numerical Computation
Fast Fourier Transform and Signal Processing Applications
4 hours
Duration
8
Materials
6
Objectives
Session Overview
Comprehensive study of FFT algorithms, DFT properties, and applications in signal processing, image processing, and solving PDEs using spectral methods.
Learning Objectives
By the end of this session, you should be able to:
- Understand DFT theory and its relationship to continuous Fourier transform
- Implement Cooley-Tukey FFT algorithm with bit-reversal and twiddle factors
- Master radix-2, radix-4, and mixed-radix FFT implementations
- Apply FFT to convolution, correlation, and filtering operations
- Use FFT for solving PDEs with spectral methods
- Implement real-valued FFT and multi-dimensional FFT algorithms
Course Materials
Download materials for offline study and reference
Fourier Transform Theory and Applications (60 pages)
Available material
Complete FFT Algorithm Implementations
Available material
Signal Processing Applications and Examples
Available material
Spectral Methods for PDE Solution
Available material
Multi-dimensional FFT and Real-valued FFT
Available material
Performance Optimization and Memory Management
Available material
Image and Audio Processing Applications
Available material
FFT-based PDE Solver Development
Available material