Signal Processing and FFT Simulator

Generate, sample, and filter a signal

Build a sine, cosine, square, sawtooth, triangle, or noise-corrupted waveform, choose the sample rate and record length, then look at the same signal in the time domain and as a single-sided DFT magnitude spectrum. Apply a filter and compare before and after.

• Time-domain plot with real axes and, when the sample rate is low enough to see them, individual sample markers.
• Frequency spectrum with the peak frequency called out, the Nyquist limit marked, and the filter corner frequency drawn on the plot.
• Low-pass, high-pass, and band-pass filtering with adjustable cut-off and order.
• RMS, peak amplitude, and dominant frequency reported for both the original and the filtered signal.

Equations used

The spectrum is a discrete Fourier transform with single-sided magnitude scaling:

• X[k] = Σ x[n]·e^(−j2πkn/N)
• Nyquist frequency: f_Nyquist = fs / 2
• Frequency resolution: Δf = fs / N
• First-order low-pass response: H(s) = 1 / (1 + s/ω_c)

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.