Deep Signal Processing

Accompanying notebooks for [TBA]

The Atlas of Convolutions

Part 1: Memory, Causality and Parameter Scaling

• basics: introduces the basic idea of a linear convolution and the different ways of implementing it
• fft_conv: discusses diagonalization of circulant matrices, motivating an efficient method to convolve signals
• causality: investigates how to enforce causality of a convolution
• ssm_kernel: provides a showcase of a simple diagonal state space and the resulting kernel
• transfer_function: primer on transfer functions, properties and how to parametrize a convolution as a ratio of polynomials over the complex numbers
• analysis: explains how to leverage amplitude and phase of a frequency response to inspect input-output pairs for pure sinusoidal signals
• parametrizations: provides a set of minimal nn.Module classes implementing the different convolution parametrizations introduced in the notes.

Other excellent resources

State spaces:

• state-spaces (repo).
• Simplifying S4 (blog).