Signal Processing by Hand: Sampling & Aliasing, Quantisation, the Discrete Fourier Transform, Spectra, Windows, Moving-Average & Exponential Filters and Convolution
Take signals apart into frequencies. You will sample sine waves, predict aliasing, quantise samples and measure the error, compute an 8- and 16-point discrete Fourier transform with SIN and COS, read magnitude and phase spectra, apply a window, smooth with moving-average and exponential filters, convolve short signals and check a filter's frequency response, all with toy signals and every cell checked as you go.
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About this course
This course takes signals apart with formulas you can see. You sample a sine wave from a given index column, predict where fast tones alias with MOD and prove it with samples, and quantise values to 4 bits to measure the signal-to-noise ratio in dB. You compute an 8- and a 16-point discrete Fourier transform with SUMPRODUCT, SIN and COS, turn the result into magnitude, phase with a hand-made quadrant correction and decibels, and tame spectral leakage with a Hann window. Finally you smooth noisy data with moving-average and exponential filters, compute their frequency response and convolve short signals with echo and smoothing kernels.
Lessons
- Sampling a Sine Wave: Index n, Sample Times and a Sampled Signal Pro
- Aliasing: The Nyquist Frequency and Where Fast Tones Fold To Pro
- Quantisation: Rounding to N Bits, the Error and the Signal-to-Noise Ratio Pro
- The Discrete Fourier Transform by Hand: 8 and 16 Points with SIN, COS and SUMPRODUCT Pro
- Magnitude and Phase Spectra: Bin Frequencies, |X|, ATAN with Quadrant Correction and Decibels Pro
- Windows and Leakage: A Tone Between Two Bins and the Hann Window Pro
- Filters: Moving Average, Exponential Smoothing and the Frequency Response |H(f)| Pro
- Capstone – Convolution: Echo and Smoothing Kernels with SUMPRODUCT Pro