Signal Processing and FFT Simulator
Explore sampled signals, frequency content, and filtering through linked time-domain and frequency-domain visualizations.
Generate, sample, and filter a signal
Generate periodic waveforms, harmonics, or a chirp with reproducible Gaussian noise. Inspect sampled input and output in linked time-domain and calibrated FFT plots, examine the applied digital filter, or follow frequency content through a spectrogram.
- Time-domain comparison with record replay, a movable viewing window, and sample inspection.
- Single-sided FFT with selectable windows, V-peak or dBV scaling, and explicit Nyquist and bin-spacing readouts.
- Causal Butterworth low-pass and high-pass sections, cascaded band-pass filtering, and a tunable notch, with transfer and impulse responses.
- Input/output RMS and peaks, dominant output bin, phase inspection, and an output STFT spectrogram.
Equations used
The radix-2 FFT uses window coherent-gain correction and single-sided peak-amplitude scaling:
- X[k] = Σ x[n]·w[n]·e^(−j2πkn/N)
- Nyquist frequency: f_Nyquist = fs / 2
- Frequency resolution: Δf = fs / N
- Biquad response: H(z) = (b₀ + b₁z⁻¹ + b₂z⁻²)/(1 + a₁z⁻¹ + a₂z⁻²)
Frequently asked questions
- What is the Nyquist frequency?
- The Nyquist frequency is half the sample rate, and it is the highest frequency a sampled signal can represent unambiguously. Sampling at 200 Hz gives a Nyquist frequency of 100 Hz. Any content above it is not lost quietly — it folds back into the spectrum as a lower frequency, which is aliasing.
- What is aliasing and how do you avoid it?
- Aliasing is a frequency above the Nyquist limit appearing in the sampled data disguised as a lower frequency, and it cannot be undone after sampling. Avoid it by sampling at more than twice the highest frequency in the signal, and by applying an analogue anti-aliasing low-pass filter before the converter so out-of-band content never reaches it.
- What does an FFT actually show?
- It decomposes the signal into the sinusoids that make it up, and the magnitude spectrum shows how much of each frequency is present. A pure 5 Hz sine gives a single spike at 5 Hz; a square wave gives a spike at its fundamental plus a decaying series of odd harmonics; broadband noise spreads energy across the whole spectrum.
- What is the cut-off frequency of a filter?
- The cut-off, or corner, frequency is where the filter's output power has fallen to half its passband value — a drop of 3 dB, or a factor of about 0.707 in amplitude. It marks the transition between the passband and the stopband rather than a hard edge; a first-order filter rolls off at 20 dB per decade beyond it.