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 (default=0) → 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 (default=0)

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 3

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, ... } with: ampi=sqrt(rei2 + imi2), phasei see poffset	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(ampi/aref)	L+1

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See also

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

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