Signal Generator: Plot a Signal and Its Spectrum

Write x(t) as an equation, choose the sample rate and duration, and see the samples and their spectrum side by side. Nothing is sent anywhere.

Signal x(t)ExampleSample rate (Hz)Duration (s)

Use t, pi, + − × / ^ and sin, cos, tan, exp, log, abs, sqrt, square, sawtooth, u (unit step).

Time domain

Amplitude spectrum

200 samples, bins every 1 Hz up to 100 Hz (the Nyquist frequency). Largest peaks: 5 Hz (1), 20 Hz (0.5).

The formulas

x[n] = x(n / f_s), \quad n = 0, 1, \dots, N - 1

Sampling at f_s for T seconds gives N = f_s T samples.

X[k] = \sum_{n=0}^{N-1} x[n]\, e^{-j 2\pi k n / N}, \quad f_k = \dfrac{k f_s}{N}

The DFT, with bin k at frequency k f_s / N. The tool plots 2|X[k]|/N, the amplitude of each sinusoid, up to f_s / 2.

x(t) = sin(2π·5t) + 0.5 sin(2π·20t), sampled at f_s = 200 Hz for 1 s, gives N = 200 samples.
The bins are f_s / N = 1 Hz apart, so 5 Hz and 20 Hz fall exactly on bins 5 and 20.
The spectrum shows 1.0 at 5 Hz and 0.5 at 20 Hz and nothing else, matching the two amplitudes.
Change the duration to 1.05 s and the peaks spread into neighboring bins: 5 Hz no longer fits a whole number of cycles (spectral leakage).

Frequencies above f_s / 2 fold back (alias): a 150 Hz sine sampled at 200 Hz shows up at 50 Hz.
A square wave shows peaks at the odd harmonics, with amplitudes 4/π, 4/(3π), 4/(5π) and so on.