A guided journey · 20 lessons

Signal processing

From waves and sampling to spectra, filters and a denoising investigation.

Prerequisites are included automatically. Suggested lesson time: 9 hours, plus extra time for experimentation and projects. This is an estimate, not a measured completion time.

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  1. What is a signal?What does a waveform actually tell you?15 min · Progress unavailable without JavaScript
  2. Frequency, amplitude and phaseHow can three numbers describe an oscillation?20 min · Progress unavailable without JavaScript
  3. Vectors and similarityHow does a list of numbers become a geometric object?20 min · Progress unavailable without JavaScript
  4. Complex numbers and rotationWhy do transforms use an imaginary coordinate?20 min · Progress unavailable without JavaScript
  5. Slopes and gradientsHow do you decide which way to change a parameter?25 min · Progress unavailable without JavaScript
  6. Probability and uncertaintyHow should several plausible outcomes share one unit of probability?20 min · Progress unavailable without JavaScript
  7. Noise and signal-to-noise ratioHow much unwanted variation is in a measurement?25 min · Progress unavailable without JavaScript
  8. Sampling and timeHow do equally spaced measurements encode motion?20 min · Progress unavailable without JavaScript
  9. Aliasing and NyquistCan different waves produce exactly the same samples?25 min · Progress unavailable without JavaScript
  10. Quantisation and clippingWhat changes when sample values have a finite alphabet?20 min · Progress unavailable without JavaScript
  11. Resampling safelyWhy is keeping every other sample sometimes wrong?25 min · Progress unavailable without JavaScript
  12. Projection onto wavesHow can a dot product detect a frequency?25 min · Progress unavailable without JavaScript
  13. The discrete Fourier transformWhat exactly is in an FFT output array?30 min · Progress unavailable without JavaScript
  14. Windows and leakageWhy does one tone make many spectral bars?30 min · Progress unavailable without JavaScript
  15. Time-frequency analysisWhat if the signal’s frequency changes over time?30 min · Progress unavailable without JavaScript
  16. Linearity and time invarianceWhen can one impulse response describe a whole system?25 min · Progress unavailable without JavaScript
  17. Convolution step by stepWhich input samples contribute to one output?30 min · Progress unavailable without JavaScript
  18. Frequency response and filter trade-offsWhy does averaging suppress some frequencies more than others?30 min · Progress unavailable without JavaScript
  19. Recurrence and stabilityWhen does yesterday’s state fade, persist or explode?30 min · Progress unavailable without JavaScript
  20. Project: a denoising pipelineCan you reduce interference without hiding signal distortion?75 min · Progress unavailable without JavaScript

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