Signal Processing & DAQ Calculators
Nyquist, FFT bins, windowing, jitter, and the DAQ error budget.
- Nyquist Rate & AliasingCheck whether your sample rate clears Nyquist and find the alias frequency a tone folds down to.f_N = f_s / 2 , Nyquist rate = 2·f_sig , f_alias = |f_sig − f_s·round(f_sig/f_s)|
- FFT Bin Width & ResolutionGet frequency resolution, capture time, and bin count from sample rate and FFT size before you set up a spectrum capture.Δf = fs / N , T_capture = N / fs = 1 / Δf , f_Nyquist = fs / 2
- Window Amplitude & Scallop LossCoherent gain, scallop loss, ENBW, and processing loss for common FFT windows — read off the amplitude penalty before you trust an FFT peak.CG = (1/N)·Σ w[n] scallop = 20·log₁₀( CG / |W(½ bin)| ) ENBW = N·Σ w[n]² / (Σ w[n])² A_true = A_meas / CG
- Sinc Interpolation ErrorEstimate the aliasing/truncation error floor when reconstructing a band-limited signal from finite samples.ε ≈ 1 / [π·N·(f_s/2f_max − 1)] , floor(dB) = 20·log₁₀ ε
- Anti-Alias Filter AttenuationCheck 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.A(f) = 10 · log₁₀( 1 + (f/fc)^(2N) ) f_alias = fs − fc
- FIR Filter Group DelayGroup delay and time lag of a linear-phase FIR filter from its tap count and sample rate.τ_g = (N − 1) / 2 samples , τ_g(s) = (N − 1) / (2·f_s)
- Butterworth Filter OrderMinimum Butterworth order to hit a stopband spec given passband ripple, attenuation, and the two edge frequencies.n ≥ log₁₀[(10^(A_s/10)−1)/(10^(Aₚ/10)−1)] / (2·log₁₀(f_s/fₚ)) , ω_c = fₚ/(10^(Aₚ/10)−1)^(1/2n)
- LSB Dither RMSRMS amplitude and quantization-noise floor for uniform (flat-PDF) dither in an ADC or DAC LSB.RPDF: σ = V_pp / √12 , TPDF: σ = V_pp / √24 , σ_total = √(σ_dither² + σ_q²) , σ_q = LSB/√12
- Envelope Detector RC ConstantSize the diode-detector RC so an AM envelope tracks cleanly — big enough to smooth carrier ripple, small enough to dodge diagonal clipping.RC ≤ √(1 − m²) / (2π · f_m · m) RC ≥ 10 / f_c RC* = √(RC_min · RC_max)
- Cross-Correlation Peak LagFind the time delay between two sampled signals from the lag of their cross-correlation peak.τ = k* / fₛ , k* = argmaxₖ Rₓᵧ(k) Δd = c · τ