``Specmurt'' Domain

The Fourier transform of linear-scaled power spectrum with linear-scaled frequency is autocorrelation function according to the Wiener-Khinchine theorem; thus the Fourier transform of log-scaled power spectrum gives a similar but different domain called cepstrum[1] by Tukey et al in their quefrency alanysis instead of frequency analysis.

In the present approach, $V(y)$ is defined as the inverse Fourier transform of linear power spectrum $v(x)$ with logarithmic frequency $x$. We call it specmurt to clarify the relationship and difference between well-known cepstrum and the present method. The present analysis is contrasted with cepstrum by log frequency and linear spectrum.

, imitating the anagramic naming of cepstrum[1], that is the inverse Fourier transform of logarithmic spectrum with linear frequency and called ``quefrency alanysis''. In the same way, as cepstrum, a special terminology for this new domain can be defined as shown in Table 1.

figure=Fig/cepstrumandspecmurt.eps,width=

表: Comparison betrween cepstrum and specmurt.
表 1: Variables in spectrum, cepstrum[1] and specmurt domains; lefthandside anagrams were defined in [1]

height 0.8pt original	Fourier Transform of / with
domain	log spec / lin freq	lin spec / log freq
height 0.8pt spectrum	cepstrum	specmurt
analysis	alanysis	anasylis
frequency	quefrency	frencyque
magnitude	gamnitude	magniedut
convolution	novcolution	convolunoit
phase	saphe	phesa
filter	lifter	filret
height 0.8pt

表 2: Experimental conditions for specmurt anasylis.

analysis	sample rate	16(kHz)
	frame length	64(msec)
	frame shift	32(msec)
filter	type	Gabor function
	variance	6.03% [$\approx$100(cent)]
	Q-value	8.35% [$\approx$140(cent)]
	resolution	12.5(cent)
$h(x)$	type	line spectrum pattern
	envelope	$1/f$
	# of harmonics	14