What this page adds. The
basic calculator runs the IDFT in your
browser, on one one-sided spectrum with an even N. This page takes a frequency
column and any number of spectra, as amplitude/phase or real/imaginary parts,
one-sided or full, and adds the IFFT. 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
inverse Fourier transform article explains
what decides the signal that comes out.
The f column must step evenly, within 0.1%. A one-sided spectrum starts at f = 0;
a full one holds f = 0 once. Uneven f is refused, naming the first f that breaks
the step.
- Paste your spectrum into the Input grid — straight from a
spreadsheet, or as CSV/TSV text — or import a file. First column
is f in Hz, then one pair per signal: y1 amp + y1 phase, or y1 re + y1 im. The
Fourier transform calculator's output pastes
in as it is.
- Pick a method. IDFT is the direct sum, up to N = 2,048. IFFT
gives the same numbers fast, for any N.
- Pick the input format: amp/phase (phase in radians) or
real/imag.
- Pick the spectrum type. N is the number of samples the signal
will have. A real signal's spectrum is mirrored, so it is often stored as one half
only - the one-sided spectrum, bins 0 up to the middle. From that half alone, two
different N fit, so the type says which:
- even: one-sided, N even. Bins 0 to N/2; the last one is the
Nyquist bin, which has no mirror partner. 9 bins give N = 16.
- odd: one-sided, N odd. Bins 0 to (N−1)/2; there is no
Nyquist bin. 9 bins give N = 17.
- full: all N bins, both halves, in the order
np.fft uses - 0, the positive frequencies, then the negative
ones. Nothing is mirrored; 16 bins give N = 16.
- Window: rectangular only. A window tapers a record before a
forward transform to tame leakage - see
windows on the Fourier transform
page. An inverse has no record to taper, so the only window here is none.
If the spectrum came from a windowed FFT, the signal comes back windowed.
- Press transform. The Output grid lists t in seconds - the step
is 1 / (N × f step) - and one column per signal. A full spectrum that is not
mirror-symmetric gives a complex signal: its imaginary parts get their own
columns, and the status line names the largest.
- Press export to save the Output grid as a CSV/TSV file.