Bandpass (undersampling) demo
Set a signal band [fL, fH] and a sampling rate Fs, then see where the spectral copies land and whether they overlap. Presets include the article’s 90–100 Hz band at 56 Hz (valid, spectrum inverted) and nearby invalid rates. Full write-up: bandpass sampling article.
Spectral replicas of a smooth bandpass spectrum, repeated every Fs.
How to use. Start with the 90–100 Hz @ 56 Hz preset. Read the alias map (edges fold with inversion). Drag Fs until the banner turns orange — that is an invalid zone where copies overlap. Switch to Noise folding and toggle the preselection filter; switch to Jitter to see SNR fall as carrier or σt rises.
Article: Bandpass / IF / undersampling · Baseband lab: Nyquist sampling demo
How to use this demo
Set the RF band edges and drag Fs. The banner reports whether the rate is valid, on a zone boundary, or overlapping. The alias map shows how fL, fc, and fH fold into (−Fs/2, Fs/2]. Use the view menu for time-domain samples, noise folding with/without preselection, and jitter-limited SNR.
Shareable presets: 90–100 Hz @ 56 Hz, invalid overlap, zone n = 1.
FAQ
Why isn’t Fs ≥ 2B enough? The information bandwidth must fit in a Nyquist zone, but the RF band’s absolute location also has to avoid collisions between positive- and negative-frequency replicas. That is what the zone inequalities enforce.
Why do 90, 95, and 100 Hz become 22, 17, and 12 Hz at Fs = 56 Hz? Folding with period Fs maps them to −22, −17, and −12 Hz (shown as 22/17/12 with inverted band order). The upper RF edge lands at the lower IF edge.
What does the preselection filter change? It limits which out-of-band noise and interferers can fold into the sampled band. It does not remove noise already inside [fL, fH].