Loading the page
Loading
Loading
Lesson 8
A sampler can't tell f from |f − k·fs|: the spectrum folds like a paper strip at every multiple of fs/2. Once a tone has folded, nothing after the sampler can take it out again. Commit to where a tone lands and to the filter that keeps it out, then fire up the scope and watch the spectrum fold.
Predict · 1 of 2 · the alias
An ADC samples at 10 kS/s with no filter in front of it. The input is a clean 7 kHz sine at full scale. Its codes go to a DAC and an ideal reconstruction filter. What frequency does the reconstructed output show?
Result
Waiting on your call.
Make your mark, then lock it in. The answer, your error and the reason behind it land here, and the scope and every view below fire up.
Engine: the anti-alias filter is an LC ladder solved by the in-browser MNA engine's AC analysis, every tone through its exact complex gain (steady state, no start-up). Sampling, the hold and an ideal, noiseless mid-rise quantizer are the lesson's own math; without dither, a tone under 1 LSB on its own comes out as a ±½ LSB square, as it would on a perfect converter. The spectrum is a real FFT of 4,096 samples under a 7-term Blackman–Harris window, never drawn from the alias formula. Checked by scripts/sampling-check.mjs (the FFT peak against the fold over seven zones, the ladder against the Butterworth closed form to 10⁻⁸, the SNR against 6.02N + 1.76 dB, the hold's sinc droop). SPICE: its numbers show once you're in the lab (they'd give the answers away).