Lecture: Smart Numerical Signal Processing Techniques

Enrico M. Staderini

This course is focused on the practical issues regarding numerical signal processing techniques which are often neglected in conventional university signal processing classes. For teaching purpose the students are indeed introduced to the use ofstandard processing software like MATLAB, R, SciLab, Octave, Mathematica, LabView to name a few, but they eventually are left without any competence to implement effective signal processing techniques into practical devices for the real world. Would you embed MATLAB into the firmware of a mobile phone?

After a preliminary, but tricky, recall of what really matters in numerical signal processing, the focus is given on the practical implementation (with C or pseudocode listing) of most useful signal processing techniques able to be implemented on biomedical devices, where the designer is often challenged with low memory or low processing power constraints.

Techniques are discussed for fast signal averaging and detrending, convolution, integer coefficients numerical filters (Lynn filters), digital wavelet filters based on decimation in the wavelet domain, real time frequency estimation through cumulative zero‐crossing counting and some “exotic” methods concerning the benefits of under‐sampling and the purposely use of noise for one‐bit correlation and analog‐digital conversion. Unconventional techniques for interpolation and fitting are also presented.

The course requires a good preliminary knowledge of mathematics at bachelor level.

This is a short list of topics:

Preliminary recall of trivial and basic concepts

  • Sampling, Aliasing, Analog‐Digital Conversion, Conversion noise
  • The time domain vs the transform domains (Laplace, Fourier, Z, Wavelet)
  • Understanding the transform domains in the continuous and the sampled form
  • Digital frequency filters basics (FIR, IIR, bandwidth)

Smart signal processing when you have low memory and/or low processing power

  • Averaging and De‐trending
  • Lynn filters
  • Digital Wavelet “filters” through decimation in the Wavelet domain
  • Real time frequency estimation through cumulative zero‐crossing counting
  • When noise is a tool and not an issue
    • One‐bit correlation
    • Analog‐Digital conversion through noise and Montecarlo methods
  • Interpolation of data and Fitting to data