References & Further Reading

References

1. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice Hall, 2010

   The definitive textbook on discrete-time signal processing. Covers the DFT, FFT algorithms, filter design, and spectral analysis in depth. Chapters 5 and 8 are especially relevant.

2. J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications, Pearson, 2007

   Comprehensive DSP textbook with excellent coverage of filter design (FIR and IIR), the DFT, and spectral estimation methods.

3. S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press, 2009

   The standard reference on wavelets, multi-resolution analysis, and sparse signal representations. Covers denoising, compression, and the mathematical foundations of wavelet theory.

4. F. J. Harris, On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform, Proceedings of the IEEE, 1978

   The classic paper on window functions. Comprehensive comparison of window shapes, sidelobe levels, and equivalent noise bandwidths. Still the standard reference after 45+ years.

5. SciPy Community, scipy.signal — Signal Processing, 2024

   Official documentation for SciPy's signal processing module. Covers filter design, spectral analysis, wavelets, and resampling with examples.

6. J. W. Cooley and J. W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier Series, Mathematics of Computation, 1965

   The paper that launched the FFT revolution. Describes the radix-2 decimation-in-time algorithm that reduces the DFT from $O(N^2)$ to $O(N \\log N)$ operations.

Further Reading

• Adaptive filtering and the LMS algorithm

  S. Haykin, *Adaptive Filter Theory*, 5th ed., Pearson, 2014

  Adaptive filters adjust their coefficients in real time to minimize error. The LMS (Least Mean Squares) algorithm is the workhorse of echo cancellation, channel equalization, and noise cancellation — all implemented as filter operations.

• Compressed sensing and sparse recovery

  M. Elad, *Sparse and Redundant Representations*, Springer, 2010

  Wavelet sparsity is the foundation of compressed sensing, which enables signal recovery from far fewer measurements than the Nyquist rate requires.

• GPU-accelerated signal processing

  cuSignal documentation (https://github.com/rapidsai/cusignal)

  For processing large batches of signals (e.g., multi-antenna wireless receivers), GPU-accelerated FFTs and filters provide 10-100x speedups over CPU implementations.

• Time-frequency analysis beyond wavelets

  P. Flandrin, *Time-Frequency/Time-Scale Analysis*, Academic Press, 1998

  Covers the Wigner-Ville distribution, Cohen's class, and reassignment methods for high-resolution time-frequency analysis beyond the STFT and wavelet approaches.