Anti-Alias Filter Attenuation
Check how much a Butterworth anti-alias filter knocks down out-of-band energy at Nyquist and at the worst-case fold frequency before your ADC samples it.
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The engineering
Any energy above fs/2 doesn't disappear when you sample — it folds back into the passband as an alias you can never remove digitally. This card evaluates the Butterworth magnitude response of an N-pole anti-alias filter at two frequencies that matter: Nyquist (fs/2), and the worst-case fold frequency fs − fc, which is the lowest frequency that aliases directly on top of your cutoff. The attenuation at fs − fc is the honest spec: it tells you how far down interference must be before it lands in-band.
The gotcha is how fast filter requirements explode when fc crowds Nyquist. At 2× oversampling (fc = fs/4) the alias frequency is only 3·fc, and even an 8-pole filter buys you ~76 dB; push fc to 40% of fs and you'll need a brick wall. The cheap fix is oversampling — every doubling of fs pushes fs − fc another octave out and buys you 6N dB for free. Enter a target attenuation and the card tells you the minimum Butterworth order at your current rates.
Reality check: Butterworth is the optimistic case (maximally flat, monotonic rolloff). Real filters with component tolerance typically give a few dB less at the corner, and elliptic filters give more stopband but with response ripple. Treat the required-order output as a floor, not a design.
Where this math comes from
Harry Nyquist worked out in 1928 — studying telegraph channels at Bell Labs — that a signal must be sampled at least twice per cycle of its highest frequency, and Claude Shannon nailed the theorem down formally in 1949. What neither paper solved was the analog problem it created: real-world signals don't stop at your bandwidth of interest, so somebody has to filter them before the sampler, in the analog domain, forever.
Stephen Butterworth, a British physicist working on vacuum-tube amplifiers, published his maximally-flat filter response in 1931 — the closed-form attenuation this card evaluates. The pairing of Butterworth math with ADC front ends became standard practice as sampled-data systems spread in the 1970s–80s, and Analog Devices' application notes (AN-282, Fundamentals of Sampled Data Systems, and Walt Kester's seminar series) turned the fs − fc worst-case-fold analysis into the checklist every DAQ engineer runs today.
- 1928Harry NyquistShows telegraph channels need ≥2 samples per cycle of the highest frequency — the Nyquist rate.
- 1931Stephen ButterworthPublishes the maximally-flat filter response, A = 10·log₁₀(1 + (f/fc)^2N).
- 1949Claude ShannonFormal proof of the sampling theorem; aliasing gets its mathematical footing.
- 1980Analog Devices / Walt KesterAN-282 and the ADI seminar series codify anti-alias filter sizing (fs − fc fold analysis) for ADC front ends.
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