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, is defined as the inverse Fourier transform of linear power spectrum with logarithmic frequency . 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.
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Fourier Transform of / with | |
domain | log spec / lin freq | lin spec / log freq |
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cepstrum | specmurt |
analysis | alanysis | anasylis |
frequency | quefrency | frencyque |
magnitude | gamnitude | magniedut |
convolution | novcolution | convolunoit |
phase | saphe | phesa |
filter | lifter | filret |
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