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Fast Signal Processing Algorithms

Fast Signal Processing Algorithms. Summary and Requirements. Summary. Time continuous signals and their spectrum; Time discrete signals Relationship to analog signals (sampling) Spectrum: Discrete Time Fourier Transform (DTFT) Discrete Fourier Transform and its relationship to DTFT.

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Fast Signal Processing Algorithms

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  1. Fast Signal Processing Algorithms Summary and Requirements

  2. Summary • Time continuous signals and their spectrum; • Time discrete signals • Relationship to analog signals (sampling) • Spectrum: Discrete Time Fourier Transform (DTFT) • Discrete Fourier Transform and its relationship to DTFT

  3. Summary • Fast Fourier Transforms • Derivation of radix 2 Decimation-in-time FFT, radix 2 Decimation-in-frequency FFT, and Radix 4 FFT. Comparison of their efficiency in terms of multiplications required. • Fast Convolution • Relationship between linear and circular convolutions (details) • Overlap-save and overlap add algorithms (details)

  4. Summary • Multirate operations: • Upsampling • Downsampling followed by upsampling • Downsampling • Effects to spectrums • How and when will liaising occur? • Polyphase decomposition • Noble identities

  5. Summary • Polyphase operations • Polyphase decimation • Interpolation • Two-channel filter banks • PRC • QMF filter banks • General form (FIR filters) • Polyphase implementation of analysis and synthesis filter banks

  6. Summary • M-channel filter banks • Tree structure • Octave-band tree structure • Uniform M-channel filter banks • DFT modulated and Cosine modulated filter banks • Wavelet transforms • principles

  7. Thank you!

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