Questions tagged [cepstral-analysis]

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Let a LTI system be causal and stable with the transfer function being… show that

if the system is an IIR LTI causal and stable one, and the transfer function is \[H(z)=\sum_{n=0}^{\infty}h[n]z{^{n}}= \frac{G}{1 -\sum_{k=1}^{p}a_kz{^{-k}}}\] show that the cepstrum of this system ...
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1answer
36 views

Minimum phase conversion with Cepstrum method, how to scale the result?

I am trying to convert a zero phase spectrum (magnidue response curve with zero phases) to a minimum phase spectrum, because I need a totally causal impulse response for FFT spectral filtering, and ...
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25 views

Help in understanding MFCC (Mel-Frequency Cepstral Coefficients)

I've been trying to wrap my head around MFCC for a while now, and I have some questions. My understanding is that MFCC is basically windowing, framing, and Fourier Transforming (STFT) the sound signal,...
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42 views

How to apply cepstrum coefficient gains (BFCC, MFCC) to an input signal?

I'm trying to understand RNNoise (https://arxiv.org/pdf/1709.08243.pdf, https://github.com/xiph/rnnoise). One aspect in particular, the input signal BFCC coefficients and output signal BFCC ...
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39 views

discrete Cepstrum: can you help me understand it?

Since months I am working on a spectral envelope estimation algorithm. I even devised an innovative one (90% done) but I first wanted to have a complete panorama of the present art. I pretty ...
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1answer
118 views

How does modulation frequency appear in the modulation spectra?

I'm trying to familiarise myself with the concept of modulation spectra that I met in this work. My main question appears in the title: how does the modulation frequency appear in the modulation ...
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39 views

Right discrete cepstrum implementation in python

I know that the cepstrum is mainly computed as follow: $ C_{r}={\mathcal {F}}^{-1}\left\{\log({\mathcal {|{\mathcal {F}}\{f(t)\}|}})\right\} $ What I am wondering is if I should take the whole fourier ...
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1answer
75 views

What do different Cepstral or MFCC coefficients represent intuitively?

I understand the explanation for separating slow and rapid changing log spectral components but i need to understand: Why lower coefficients have higher and mostly positive magnitudes? Why Higher ...
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1answer
70 views

Cepstrum of white gaussian noise

What are the statistics of the cepstrum of gaussian white noise? \begin{align}\newcommand{\Nfft}{ {N_{\mathrm{FFT}} }}\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT} x_i &\sim \...
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417 views

Understanding liftering as the final step in MFCCs features extraction

In the book here, they apply liftering, as a final step of MFCCs features extraction, to isolate the system component by multiplying the whole cepstrum by a rectangular window centred on lower ...
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42 views

Why do we use the term “cepstral” in MFCCs, and how does it related to the cepstral domain?

As I know, we can get the cepstrum by taking the Inverse Discrete Fourier Transform (IDFT) of the log of the power spectrum. And we can get the Mel-frequency cepstral coefficients (MFCCs) by taking ...
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116 views

Cepstrum calculation with 5-smoothing zero padding

I am trying to compute cepstrum of a signal x An implementation of this in python is: ...
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1answer
46 views

Synchronising audio in realtime without knowledge of original signal

Was doubting whether this is the right SE forum to ask my (elaborate) question, so don’t hesitate to let me know if it’s not. Also, if anyone knows of a better way to title the question, feel free to ...
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1answer
280 views

What is an intuitive explanation of cepstrum for a 12-year-old?

In Feynman's spirit of "If you truly understand a concept, you should be able to explain it clearly" and the explanation should make solid sense. There are two main challenges: The axis of "...
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1answer
185 views

Cepstrum Calculation of Rational Function H(z)

I am trying to solve my first problems at cepstrum calculation. I want to calculate the complex cepstrum $\hat{h}[n]$ of a signal $h[n]$ with Z-Transform: $$H(z)=\frac{(1-0.5z^{-1})(1+4z^{-2})}{(1-0....
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1answer
228 views

Intuition behind cepstrum analysis terminology

In multiple books I found a parallel between spectrum-analysis terminology and cepstrum-analysis terminology that says low pass filter $\rightarrow$ short pass lifter I didn't read explicitly what ...
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1answer
3k views

Formula to calculate Cepstral coefficients (not MFCC)

I am currently working with non-audio signals of which I would like to calculate the Cepstrum coefficients with Python so that I can use them with machine learning algorithms. That's probably a quite ...
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1answer
696 views

Cepstrum: IFFT or FFT to enter the cepstral domain?

I'm trying to implement source-filter separation of some pre-recorded speech in Max/MSP. I'm unsure of whether one uses an FFT to enter the cepstral domain, or an IFFT. Some of the textbooks and ...
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350 views

Why the Room Impulse Response (RIR) obtained form cepstrum is not correct?

I generate a synthetic room Room Impulse Response(RIR) function to filter a speech signal, and want to reveal the RIR from the filtered signal by using complex cepstrum. Generating the convolved ...
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1answer
197 views

Cepstrum calculus disambiguation

Learning the cepstrum analysis for speech recognition, I have met two different definitions of cepstrum (for discrete signals): $F^{-1}(ln|F(x[n])|)$ . That is, the cepstrum is the inverse Fourier ...
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1answer
389 views

Dynamic Time Warp through SPTK tool

I'm an IT student and got an assignment to do about Dynamic Time Warping(DTW) using the Speech Signal Processing Toolkit (SPTK) and comparing some words spoken by 2 speakers and finding the ...
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686 views

Linear Frequency Cepstral Coefficients, is Filter bank needed?

I am working on my master thesis on acoustic pattern recognition and have a question to the calculation of cepstral coefficients. I understand the step with a filter bank in MFCC calculation, it is ...
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2answers
600 views

Difference between rceps and cceps in MATLAB

I'm trying to construct a cepstrum using MATLAB built in function but I don't get the difference between MATLAB's functions rceps and cceps. Can anyone explain to me the difference between rceps and ...
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466 views

Implement Cepstral analysis in Matlab

I have a bit complex time signal. When trying to plot its spectrum, I get some weird result. Denoting the time signal as x and time vector as ...
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137 views

Closed form solution for the minimum phase of a continuous magnitude response

Let's say I have a continuous real function $F(\omega)$ defined in the region $\omega = [-\pi, \pi]$. Let's also say that I have a minimum phase $z$-domain transfer function $H(z)$ defined as: $$\...
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153 views

Cepstrum of finite impulse train

In Acero's Spoken language processing (p. 309) it says that the cepstrum of a finite length impulse train $$x[n] = \sum^{M-1}_{k=0} \delta[n-kN]$$ is given by $$\hat{x}[n] = \sum^{ \infty}_{r=1} \frac{...
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1answer
235 views

Is there a way to do a DFT with low latency and fine frequency resolution at low frequencies?

I am learning about the DFT in order to design a fundamental pitch detector for the human singing voice. Using the cepstrum technique. I am concerned about the latency for low frequency detection at &...
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1answer
101 views

Normalizing Cepstrum by Energy

I have separately computed the cepstrum and the energy of a finite discrete-time signal. If the energy of the signal is high, we would expect (on average) larger cepstral values than if the energy of ...
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1answer
316 views

Calculating phase response of maximum phase filter using Hilbert Transform

Given only a magnitude response $A(\omega)$ of a minimum phase filter, one can calculate the phase response using the Hilbert Transform: $$θ(ω) = -\mathcal{H}\{\ln(A(\omega)\}$$ This paper suggests ...
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1answer
811 views

Preserving formants using Cepstrum

I've implemented an harmonizer, using Stefan Bernsee's code, which works great. I figured out the logic of finding the root note, and the right harmony in the scale. The only problem is that, my ...
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1answer
270 views

How to interpret the sign of a cepstral coefficient?

I feel like I've got a decent intuition for what the magnitude of a cepstral coefficient represents (i.e. how much of the signal's energy is contained in harmonics of a given wavelength), but I don't ...
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1answer
1k views

What's the difference between using DFT, IDFT or DCT to calculate cepstrum of a power spectrum?

I've seen different equations that calculate cepstrum from power spectrum, but the equations are not consistent. Some people use Fourier transform, some use the inverse Fourier transform, and some use ...
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2answers
1k views

Why is cepstrum used in MFCC instead of autocorrelation sequence?

I know that the inverse Fourier transform of the power spectral density $P(k)$ gives the autocorrelation sequence $A(n)$ (By Wiener-Khinchin theorem): $${\cal F}^{-1}\left\{P(k)\right\}=A(n)$$ And ...
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1answer
977 views

Verification of all steps needed to extract MFCCs from raw audio data

I need some verification on steps required to extract MFCCs from raw audio as I'm finding that some sources outline them slightly differently. Get raw audio frame Run window function (eg Blackman) on ...
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1answer
499 views

MFCC extraction last step DCT or IDCT

I'm confused with the last step of extraction MFCC where we have to take DCT or IDCT. Cepstrum is defined as IDFT of log(power spectrum). Since MFCC are cepstral coefficients so I think we have to ...
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1answer
191 views

Recursively obtaining all-pole coefficients from complex cepstral coefficients?

This is a problem from the book Discrete-Time Speech Signal Processing by Thomas Quatieri, Chapter 6 Problem 13: Suppose $h[n]$ is all-pole (minimum-phase) of order $p$. Show that the all-pole (...
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154 views

Cepstrum: subtracting the mean vs. dividing by the variance

In cepstral speech analysis, it is relatively easy to understand why subtracting the mean removes any "channel" effects (including that of recording equipment and the vocal tract). There is a good ...
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1answer
965 views

Image 2D Real Cepstrum with DFT, Is `ifftshift` Needed?

This is my testing image,it is taken from this paper: I tried to transform it into its real cepstrum domain with this simple MATLAB code: ...
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2answers
389 views

Interpreting Cepstrum of plucked string

in my attempts to synthesize a plucked electric guitar string (using supercollider's digital waveguide, which is based on the Karplus-Strong algorithm) I came to a dead end and decided to look that ...
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1answer
575 views

How can I use time-series transforms for detecting malware? [closed]

I am student of network security, and very unfamiliar with the domain of signal processing. Do pardon my naivety at asking very basic stuff. My work deals with detecting malicious activity in network ...
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0answers
882 views

bearing frequency detection

I am working on bearing faults detection. I am doing the following steps: signal->mean zero->high pass->hilbert->y->fft->cepstrum of y. my code is: ...
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1answer
151 views

Suggestions for FFT based tools to analyze music - Preferably MATLAB/free software packages [closed]

I am interested in analyzing full length songs for general features of the track which are not otherwise apparent. For e.g., I want to look at various parts of the song with time-frequency plots/...
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1answer
7k views

MFCC Deltas, Delta-Deltas

I have just a quick question about how to calculate Deltas from MFCC. I have found the formula for calculating deltas here: $$d_t=\frac{\sum_{n=1}^{N}n\left(c_{t+n}-c_{t-n}\right)}{2\sum_{n=1}^{N}n^2}...
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1answer
717 views

Can't compute real cepstrum of real signal

I'm trying to compute the real cepstral coefficients of recorded telephone audio in Matlab using the rceps function. On some audio frames (480 samples per frame -- 60ms of audio at 8kHz), I get a ...
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1answer
756 views

cceps (complex cepstrum) function in Matlab

My doubt is in regards to the usage of the function cceps in Matlab. The function is giving me the cepstrum for the entire speech signal of 3 or 4sec. This works ...
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0answers
563 views

Questions about Bark scale filter bank implementation for bfcc's

I have a few questions regarding the implementation of Bark scale filter banks for the calculation of bark frequency cepstral coefficients. 1) Which filter shape is most commonly used and why? ...
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0answers
142 views

How to measure the short-time change in an audio signal?

The choice of frame length for calculating the Mel Frequency Cepstral Coefficients of a signal, depend on the how much the signal change over a small time scale. I guess that human speech change ...
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0answers
81 views

Length of frames for calculating cepstral coefficients

For audio classification we are using the cepstral coefficients and their derivatives. Which I calculate using the Matlab libary voicebox. I am looking for some literature for how to choose the frame ...
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0answers
1k views

DFT, cepstrum, LPC for feature extraction

I am a newbie in speech processing and experimenting to get a feel. I have extracted some speech segments using a window function and I want to find distance between a pair of segments. First, I took ...
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1answer
3k views

How to decide the number of cepstral coefficients?

For audio classification we are using cepstral coefficients, but how should I decide the number of coefficients?