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Topic: Cepstrum

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	United States Patent: 5,732,188
		According to the second and third aspects of the invention, the relationship between the input signal and the corresponding masking function chosen in view of human psycho-acoustic characteristics is calculated in the n-order LPC cepstrum domain and this relationship is utilized for the modification of the LPC cepstrum coefficients.
		In a fifth aspect, the present invention is directed to a method which modifies LPC coefficients for use as filter coefficients of an all-pole or moving average digital filter that synthesizes a signal by using p-order LPC coefficients in the input indexes and perceptually or psycho-acoustically suppresses quantization noise for the synthesized signal.
		According to the fourth and fifth aspects of the invention, the relationship between the input-index decoded synthesized signal and the corresponding enhancement characteristic function chosen in view of human psycho-acoustic characteristics is calculated in the n-order LPC cepstrum domain and this relationship is utilized for the modification of the LPC cepstrum coefficients.
	www.brl.ntt.co.jp /people/moriya/patent/US_patent/USP5732188.htm (6687 words)

	Cepstrum: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-11-02)
		verbally: the cepstrum is the FT of the log of the FT mathematically: cepstrum of signal = FT(log(FT(the signal)))
		that the cepstrum is the "inverse Fourier transform of the log of the spectrum".
		This is a result of the cepstrum separating the energy resulting from vocal cord vibration from the "distorted" signal formed by the rest of the vocal tract.
	www.absoluteastronomy.com /encyclopedia/c/ce/cepstrum.htm (917 words)

	Cepstrum - Wikipedia, the free encyclopedia
		A cepstrum (pronounced /ˈkɛpstrəm/) is the result of taking the Fourier transform (FT) of the decibel spectrum as if it were a signal.
		verbally: the cepstrum is the FT of the log (with unwrapped phase) of the FT mathematically: cepstrum of signal = FT(log(FT(the signal))+j2πm) (where m is the integer required to properly unwrap the angle or imaginary part of the complex log function)
		This peak occurs in the cepstrum because the harmonics in the spectrum are periodic, and the period corresponds to the pitch.
	en.wikipedia.org /wiki/Cepstrum (552 words)

	Special Topics (Signal Processing Toolbox) (Site not responding. Last check: 2007-11-02)
		Cepstrum analysis is a nonlinear signal processing technique with a variety of applications in areas such as speech and image processing.
		The complex cepstrum for a sequence x is calculated by finding the complex natural logarithm of the Fourier transform of x, then the inverse Fourier transform of the resulting sequence.
		The real cepstrum of a signal x, sometimes called simply the cepstrum, is calculated by determining the natural logarithm of magnitude of the Fourier transform of x, then obtaining the inverse Fourier transform of the resulting sequence.
	www.rdg.ac.uk /ITS/Topic/Graphics/GrGMatl601/Matlab6/toolbox/signal/specto11.html (311 words)

	Cepstrum Analysis :: Special Topics (Signal Processing Toolbox)
		Cepstrum analysis is a nonlinear signal processing technique with a variety of applications in areas such as speech and image processing.
		The complex cepstrum transformation is central to the theory and application of homomorphic systems, that is, systems that obey certain general rules of superposition.
		The real cepstrum of a signal x, sometimes called simply the cepstrum, is calculated by determining the natural logarithm of magnitude of the Fourier transform of x, then obtaining the inverse Fourier transform of the resulting sequence.
	www.mathworks.com /access/helpdesk/help/toolbox/signal/f11-7373.html (520 words)

	Cepstrum (Site not responding. Last check: 2007-11-02)
		The Cepstrum is the forward Fourier Transform of a spectrum.
		But in the cepstrum, they will be separated similar to the way the spectrum separates repetitive time patterns in the waveform.
		The cepstrum is closely related to the auto correlation function.
	www.dliengineering.com /vibman/gloss_cepstrum1.htm (182 words)

	3.4.2 Noise cepstral smoothing
		The cepstrum is a spectral technique that represents the frequency distribution of the spectrum curve fluctuations.
		The cepstrum order must be chosen to yield a smooth spectral envelope that approximates the magnitude spectrum somewhat faithfully while leaving out sharp peaks in the magnitude spectrum.
		An example of the computation of the spectral envelope using a cepstrum of order 30 is showed on top of the magnitude spectrum for a single frame in figure 3.10.
	www.music.mcgill.ca /~thibault/Thesis/node43.html (428 words)

	Capgo - Vibration Monitoring
		The cepstrum is the forward fourier transform of the log of a power spectrum.
		The unit of the cepstrum was named quefrency, derived by inverting the syllables of frequency and is a measure of time but not the time we normally consider.
		The cepstrum is closely related to the auto correlation function.
	www.users.on.net /~capgo/Resources/ConditionMonitoring/Vibration.html (1321 words)

	Cepstral Analysis
		To work with the cepstrum via the discrete Fourier transform, it is useful for us to manipulate the signal as a sequence of data.
		While not as useful for deconvolution applications, the real cepstrum (usually simply referred to as the cepstrum) is applied where the energy in various parts of the signal needs to be computed.
		Computation of the inverse cepstrum is somewhat simpler than the cepstrum, since special care is not required with respect to the phase.
	documents.wolfram.com /applications/signals/CepstralAnalysis.html (1186 words)

	[No title]
		Therefore, the cepstrum can separate out the periodicity characteristic of a perfectly periodic voiced speech waveform (and hence is useful for pitch determinition), but cannot separate out the glottal flow spectral characteristic which remains combined within the low quefrency signal.
		In obtaining the cepstrum, the height of the rahmonic peaks (logEp(f)) are dependent on the depth of the valleys between adjacent harmonic locations (consider taking the Fourier transform of the spectrum in Fig.
		In the cepstrum approach two Fourier transforms are still required as opposed to one but the resultant rahmonic peaks are generally fewer in number and more easily located.
	icassp2000.sdsu.edu /authors/sample97.doc (5546 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		A cepstrum of the digitized signal is then performed to determine the cepstrum coefficients.
		The unvoiced sounds are discarded before the cepstrum coefficients are calculated in both the training phase and the verification phase.
		The cepstrum coefficients of each of the utterances are determined to form the training utterances.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=98/54694.981203&ELEMENT_SET=DECL (3798 words)

	Cepstrum (Site not responding. Last check: 2007-11-02)
		The word "Cepstrum" is an anagram of the word "Spectrum".
		The cepstrum is a measure of the periodicity of a frequency response plot.
		The shape of the resulting log signal is represented by the low frequencies and the fine detail by the high frequency components.
	www.mor.itesm.mx /~omayora/Tutorial/node18.html (201 words)

	7.5. Source Filter Analysis
		The important property of the cepstrum is that since the dB spectrum is the sum of two spectra, so the cepstrum is the sum of two components corresponding to the source and the filter.
		A further operation on the cepstrum is to remove the central part of the reflected cepstrum, the part that corresponds to the source, and perform a fourier transform to again generate a frequency domain version of the signal.
		The cepstrum can also be used as a means of determining the fundamental frequency of voiced speech since the part of the cepstrum corresponding to the source is often manifested as a single spike.
	www.ics.mq.edu.au /~cassidy/comp449/html/ch07s05.html (739 words)

	Definitions of CEPSTRUM (Site not responding. Last check: 2007-11-02)
		But in the cepstrum, they will be separated in a way similar to the way the spectrum separates repetitive time patterns in the waveform.
		The transformation of a signal into its cepstrum is a homomorphic transformation, and the concept of the cepstrum is a fundamental part of the theory of homomorphic systems for processing signals that have been combined by convolution.
		Cepstrum Co., Ltd. is a developer of digital signal processing system/software in Japan.
	www.zayra.de /soulcom/cepstrum (583 words)

	[No title]
		The cepstrum is widely used in speech processing and has found use in pitch estimation.
		In spite of this, the cepstrum and MEL cepstrum are fundamentally different features because the key dimension reduction occurs before the log operation in the MEL cepstrum, but after the log operation in the cepstrum.
		Cepstrum estimates are computed by taking the log of each element of y, then taking the inverse DFT, preserving just a few of the cepstrum samples as features.
	www.npt.nuwc.navy.mil /csf/ceps.html (349 words)

	Poles and Zeros of the Cepstrum
		In §12.4, we use the cepstrum to compute minimum-phase spectra corresponding to a given spectral magnitude--an important tool in digital filter design.
		Poles and zeros outside the unit circle contribute anticausal exponentials to the complex cepstrum, negative for the poles and positive for the zeros.
		As discussed in §12.4, any spectrum can be converted to minimum-phase form (without affecting the spectral magnitude) by computing its cepstrum and replacing any anticausal components with corresponding causal components.
	ccrma-www.stanford.edu /~jos/filters/Poles_Zeros_Cepstrum.html (652 words)

	Engine Balance–The Thinking Has Changed (Site not responding. Last check: 2007-11-02)
		A signal fault is caused by a tooth crack/fracture and breakage, a spall in a gearing or in an inner or outer race of a bearing, a spall on a rolling element of a bearing; distributed faults are caused by uneven wear (pitting, scuffing, abrasion, erosion).
		The cepstrum is a function of time [s] is given in Fig.13 for three different gearing conditions defined by a local fault and the reference error function.
		For explicit detection of a tooth crack/fracture or breakage cepstrum and time-frequency spectrogram signal analysis in an advanced method is used and given in Fig.14 and 17.
	www.maintenanceresources.com /ReferenceLibrary/ezine/gearboxdiagfaultdet.htm (3301 words)

	Cepstrum (Site not responding. Last check: 2007-11-02)
		The cepstrum is a common transform used to gain information from a person’s speech signal.
		It is similar to a channel vocoder or LPC in its applications, but using the cepstrum as a spectral analyzer is a completely different process.
		(It is also worth pointing out that cepstrum is “spectrum” with the first syllable flipped… we will encounter several words with this naming convention.) Before describing the details of the cepstrum, a little background in speech models is needed.
	cnx.org /content/m12469/latest (536 words)

	Reflecting on Echoes and the Cepstrum
		The terminology surrounding the computation of the cepstrum came from the original article by Bogert et al [2], in which various terms from signal processing (spectrum, frequency, phase, analysis) were rearranged into anagrams (cepstrum, quefrency, saphe, alanysis).
		Compare the cepstrum of figure 4 to that in figure 5, which is the equivalent cepstrum for the no-reflector data of figure 2.
		For all cepstrums, the responses were first gain adjusted so that the main flat-response region of the spectrums were near the 0 dB line (the Liberty Audiosuite cepstrum analysis process applies the dB display gain before calculating).
	www.libinst.com /cepst.htm (3603 words)

	A DISTANCE MEASURE FOR OBJECTIVE QUALITY EVALUATION OF SPEECH COMMUNICATION CHANNELS USING ALSO DYNAMIC SPECTRAL ...
		These coefficients are transformed into 16 cepstrum coefficients plus the log-energy, and a regression analysis was applied to each time function of the cepstrum coefficients over seven frames every 8 ms.
		The regression coefficients extracted from the cepstrum are used as an objective measure together with the cepstrum sequences and energy contours.
		The correlation coefficients between MOS and the various distance measures were 0.926 using cepstrum coefficients alone, 0.937 using a combination of cepstrum and their regression coefficients, and 0.954 using a combination of cepstrum and regression coefficients and log-energy.
	fonsg3.let.uva.nl /Proceedings/Proceedings20/ShuzhenWu/ShuzhenWu.html (4535 words)

	DeltasFeatureExtractor (Sphinx-4)
		Suppose that the original cepstrum has a length of N, the first N elements of the feature are just the original cepstrum, the second N elements are the delta of the cepstrum, and the last N elements are the double delta of the cepstrum.
		Refering to Figure 2, the delta is computed by subtracting the cepstrum that is two frames behind of the current cepstrum from the cepstrum that is two frames ahead of the current cepstrum.
		It is computed by subtracting the delta cepstrum one time frame behind from the delta cepstrum one time frame ahead.
	cmusphinx.sourceforge.net /sphinx4/javadoc/edu/cmu/sphinx/frontend/feature/DeltasFeatureExtractor.html (436 words)

	Papers by Furui (Site not responding. Last check: 2007-11-02)
		In this papaer cepstrum coefficients are extracted by LPC analysis to form the time functions (spectral analysis).
		The cepstrum coefficients are averaged over the duration of the entire utterance and average values subtracted from the cepstrum coefficients of every frame to compensate for frequency responses of the distortions introduced by the transmission system.
		The use of cepstrum coefficients alone and used with the polynomial coefficients are examined, showing that the error rates increase when the polynomial coefficients are omitted.
	www.ee.columbia.edu /~patricia/papers/furui.html (642 words)

	LIDS Student Conference 2006
		Bogert et al suggested that the cepstrum might be useful for detection of echos.
		Schafer (Ph.D. thesis, 1968) and Oppenheim generalized the cepstrum by defining the complex cepstrum as the inverse Fourier transform of the complex logarithm of the Fourier transform of the signal, and showed that the complex cepstrum could be used for separating (or filtering) the components of a convolution of two or more signals.
		Cepstrum ideas have been particularly important in speech processing, having been applied in areas such as pitch detection, formant estimation, speaker verification, and speech recognition.
	lids.mit.edu /LIDSCONF/invspeak.html (2200 words)

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