cepstrum

Compute the real cepstrum or the cepstrum smoothed/liftered spectrum of the logarithmic spectrum x.

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Usage 1

cepstrum(x)

x

a vector containing a log. amplitude spectrum

• note: because the fft/ifft is used for the computation, the spectrum stored in x must be computed from a signal with L=2^M</samples> (-> nrow(x)=2^M/2+1).

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

<function list>

cepstrum

Cepstrum.

Usage:

cepstrum(x)

Function:

Computes the real cepstrum of x.

Result:

A vector containing the cepstrum coefficients.

Usage:

cepstrum(x, n)

Function:

Computes the cepstrum smoothed spectrum of x using the first n coefficients.

Result:

The cepstrum smoothed spectrum. This is the same type as x.

Usage:

cepstrum(x, o, n)

Function:

Computes the cepstrum smoothed spectrum of x using the coefficients o to o+n-1.

Result:

The cepstrum smoothed spectrum. This is the same type as x.

Notes:

x must be a log. amplitude spectrum computed with a radix-2 fft.