Fourier Transform Calculator
Find dominant frequencies inside a sampled signal
Fourier Transform Calculator
Table of Contents
How to Use
- Enter or paste your signal samples separated by commas or spaces
- Provide the sampling rate in hertz
- Choose how many dominant components to display
- Press Analyze signal to view the spectrum
How the Discrete Fourier Transform Works
The discrete Fourier transform (DFT) rewrites a finite sequence of samples as a weighted sum of sinusoids. Each frequency bin "k" describes how strongly that sinusoid contributes to the original signal.
Core relationship
X(k) = Σ x(n) · e^{-j2πkn/N} where N is the sample count. The amplitude is |X(k)|/N and the phase is arg(X(k)).
Interpreting the spectrum
Use the Nyquist frequency (sample rate ÷ 2) as the upper bound for meaningful frequencies. The spacing between bins equals the sample rate divided by the number of samples.
Practical tips
- Window or zero-pad the data to reduce leakage when needed.
- Look for the highest amplitude bins to identify the dominant tones.
- Phase values describe when in time each sinusoid peaks relative to the sample window.