Fourier Transform Calculator — Advanced

What this page adds. The basic calculator runs the DFT in your browser, on up to four columns without a time axis. This page takes a time column, so the spectrum reads in real frequencies, and adds the FFT, two more windows, the phase and the mirrored half. To do that it sends your table to the server, computes there, and sends the numbers back. Nothing is stored, but the data does leave your machine. If that matters for your data, use the basic page. The Fourier transform article explains what a spectrum can and cannot show.

The t column must step evenly, within 0.1%. Uneven t is refused, and the status line names the first t that breaks the step - resample it evenly with the interpolation calculator first.

1. Paste your data into the Input grid — straight from a spreadsheet, or as CSV/TSV text. First column is t, time in seconds, every other column a signal y1, y2, … There is no column limit on this page. Rows may come in any order; they are sorted by t.
2. Or press import to load a CSV or TSV file. The file is read in your browser; only transform talks to the server.
3. Pick a method. DFT is the direct sum, up to 2,048 samples. FFT gives the same numbers fast, for any length, no padding.
4. Pick a window. Rectangular (none) when every tone completes a whole number of cycles; Hann, Hamming or Blackman to tame leakage for everything else.
5. Press transform. The Output grid lists the frequency f in Hz, then an amplitude and a phase per signal. A sine of amplitude A reads A. The select beside export switches to real/imag - the same numbers as re + i·im. Phase is in radians, measured from the first sample.
6. Sample rate shows the data's own rate, read from the t column: 1/Δt Hz, Δt the time step. Half of it, the Nyquist frequency, is the highest frequency the output can show.
7. Show mirrored half lists all N bins in the order np.fft.fft returns them, negative frequencies included. Each half then carries half the amplitude.
8. Press export to save the Output grid as a CSV/TSV file.

Blank cells and text are skipped. Every signal needs its numbers on the same x rows - the output has one frequency column for all of them.