Skip to content

References: Convolution and Correlation

  1. Convolution - Wikipedia - Covers continuous, discrete, and circular convolution, algebraic properties, graphical interpretation, and connections to transforms and LTI systems.

  2. Cross-correlation - Wikipedia - Explains cross-correlation, autocorrelation, normalization, lag estimation, and signal-matching applications central to this chapter.

  3. Matched filter - Wikipedia - Derives matched filtering as correlation with a known template and explains optimal signal-to-noise performance in additive noise.

  4. The Scientist and Engineer's Guide to Digital Signal Processing - Steven W. Smith - California Technical Publishing - Smith’s input-side and output-side graphical explanations make discrete convolution intuitive before introducing equations.

  5. Discrete-Time Signal Processing (3rd Edition) - Alan V. Oppenheim and Ronald W. Schafer - Pearson - Oppenheim and Schafer’s impulse-decomposition treatment established a widely adopted bridge between convolution, LTI systems, and transforms.

  6. Continuous-Time Convolution - Engineering LibreTexts - Derives convolution from shifted impulses and illustrates how an LTI impulse response determines system output.

  7. SciPy Convolution - SciPy - Documents direct and FFT convolution modes with executable examples, output sizing rules, and computational tradeoffs.

  8. FFT Convolution - DSP Guide - Explains overlap-add processing and why frequency-domain multiplication accelerates convolution for long filters and signals.

  9. Signals and Systems Lecture Notes - MIT OpenCourseWare - Includes dedicated lectures on convolution, impulse response, Fourier relationships, and applications, supported by problems and solutions.

  10. SciPy FFT Convolution - SciPy - Provides practical multidimensional FFT-convolution examples and explains speed, precision, padding, and boundary effects.