Signal Processing by Hand: Sampling & Aliasing, Quantisation, the Discrete Fourier Transform, Spectra, Windows, Moving-Average & Exponential Filters and Convolution

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn a 5 Hz test tone into 20 samples at 100 samples per second: the sample period, the time of every sample, the sampled values with amplitude and phase, and a chart of one full cycle.
• Find the Nyquist frequency of a 1000 Hz sampler, predict the apparent frequency of seven tones with MOD and prove with eight samples that a 620 Hz tone is indistinguishable from a 380 Hz tone.
• Quantise twelve samples to 4 bits, measure the signal-to-noise ratio of the rounding error in decibels and compare it with the 6.02·N + 1.76 dB rule of thumb.
• Compute the real and imaginary parts of an 8-point and a 16-point DFT with one SUMPRODUCT each and read off which bins hold the cosine and the sine of each toy signal.
• Turn a 16-point DFT result into a readable spectrum: the frequency of every bin, the magnitude, the phase in degrees with a hand-made quadrant correction and the level in dB against a reference.
• Take the spectrum of a tone with 2.5 cycles in a 16-sample window, see its energy leak into every bin, apply a Hann window and measure how much the leakage in the far bins drops.
• Smooth a noisy ramp with a 4-point moving average and a one-pole exponential filter, then compute from the coefficients how strongly each filter passes a 12.5 Hz test tone.
• Convolve a short toy signal with an echo kernel and a smoothing kernel using a sliding SUMPRODUCT, verify the result with the sum rule and chart input and both outputs together.