Discrete Fourier Transform (DFT) Calculator
Compute the DFT of a real sample sequence: magnitude, phase and frequency of every bin, and the dominant frequency.
How to use the Discrete Fourier Transform
- Enter or select: Samples (comma or space separated), Sampling rate fₛ.
- The results (Samples N, Dominant frequency, Dominant amplitude, DC component (mean), Bins: k → frequency, |X[k]|, phase) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- X[k] = Σₙ x[n]·e^(−j2πkn/N)
- fₖ = k·fₛ/N
- amplitude of a sinusoid = 2|X[k]|/N
About this tool
Bins above N/2 mirror the lower half for real signals. This direct O(N²) implementation is exact and suitable for up to 4096 samples.