fft

Compute the discrete fourier transform of a real signal using the fft or the dft algorithm.

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Usage 1

fft(n)

n

desired signal window length (scalar)

Result 1

The next (nearest) possible signal window length.

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Usage 2

fft(x)

x

signal vector or matrix; if x is a matrix a spectrum of each column is computed

Result 2

A matrix y with ncol(x) columns and L+2 rows, where each column y[*,j] contains the complex spectrum of the column (channel) x[*,j]. The transformation length L is set to npow2(nrow(x)).

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Usage 3

fft(x, n {, ytype, poffset, prange, aref})

x

signal vector or matrix; if x is a matrix a spectrum of each column is computed

n

desired length of analysis window;

• If n < nrow(x), the analysis window length L is set to nrow(x), otherwise L is set to n.
• If the analysis window length L is a power of 2 (L=2^M), the fft algorithm is used, otherwise the dft is used.
• If L is greater than nrow(x), zero padding is applied to the signal.

ytype

select the type and format of the computed spectrum (see Result 3)

poffset

offset in samples to the signal begin or the selected zero phase position (default=0)

poffset='0	-> phase[i] = atan2(im[i], re[i])
otherwise	-> phase[i] = (atan2(im[i], re[i]) - 2*pi*i/L * poffset) % (2 * pi)

prange

selects the range of phase values

prange='0	-> 0 <= phase[i] < 2*pi
otherwise	-> -pi <= phase[i] < pi

aref

reference amplitude if the log. spectrum (ytype=4) is requested (default=1)

Result

A matrix y with ncol(x) columns, where each column y[*,j] contains the spectrum of the column (channel) x[*,j]. The type and the length of the spectra is selected by the argument ytype.

ytype	description	content of y[*,j]	nrow(y)
0	complex spectrum in cartesian format	{ re0, im0, re1, im1, ... }	L+2
1	complex spectrum in polar format	{ amp0, phase0, amp1, phase1, ... }	L+2
2	amplitude spectrum	{ amp0, amp1, ... }	L+1
3	power spectrum	{ amp02, amp12, ... }	L+1
4	logarithmic amplitude spectrum	{ lev0, lev1, ... } with: levi=20*log10(levi/aref)	L+1

See also

ifft, dft, dct, cepstrum, lpc, , complex arithmetic

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