Ada Audits the Alias Calculations

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Ada Audits the Alias Calculations

Sampling a slow sensor at 80 Hz puts Nyquist at 40 Hz, so ambient 50 Hz mains hum cannot be represented honestly — it folds to a phantom 30 Hz wander that a digital filter can never separate from a real signal. The reflex is to clean that wander up in software afterwards. This audit re-derives the fold arithmetic and asks whether a 30 Hz alias is a software problem at all, or a sample-rate and analog-filter decision that must happen before the ADC.

Companion to the chapter Aliasing and Anti-Alias Filter Contracts — every number here comes from that chapter.

Ada: Aliasing checks are useful only when the numbers expose both the frequency ceiling and the false frequency that software will see. Carry the sample-rate arithmetic through before deciding whether filtering or faster sampling is the real fix.

fs = 80 Hz, so Nyquist = fs / 2 = 80 / 2 = 40 Hz

50 Hz mains hum is above 40 Hz, so it cannot be represented honestly

f_alias = |fin - fs x round(fin / fs)| = |50 - 80 x round(50 / 80)| = |50 - 80 x 1| = 30 Hz

For the 100 Hz table: Nyquist = 100 / 2 = 50 Hz; 80, 120, and 180 Hz all fold to 20 Hz

Oversampling rule of thumb from this page: a 20 Hz signal band at 5x to 10x means fs = 100 Hz to 200 Hz, leaving transition-band room for the analog filter

The decision follows the arithmetic: if a 30 Hz wander matters to the product, do not try to remove it later with digital cleanup. Move the analog cutoff below the dangerous interference, raise the sample rate enough to leave filter transition room, or prove by sweep testing that the out-of-band source is below the error budget.

Every number above is taken from the chapter’s own material and re-derived step by step.