Questions tagged [cepstral-analysis]

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1 vote
3 answers
116 views

Why is my Cepstrum mirrored and how do I relate it back to the original signal to find an echo

I am not a signal processor but need to use Cepstrums in a bigger project I am writing to help identify echoes in seismic signals. I need to understand why the Real and Complex Cepstrums I create, in ...
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0 votes
0 answers
27 views

How to calculate Cepstral Peak Prominence (Smoothed) for speech signal - when to take logs

I understand the main steps of finding smoothed cepstral peak prominence, but am confused on some specifics: You first take the log of the Fourier transform of the signal, getting the spectrum. I'm ...
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1 vote
0 answers
33 views

Realtime classification of (one of 12) vowel phonemes

I'm attempting realtime classification of (one of 12) vowel phonemes, sung (steady-state-ish) into a microphone. MOTIVATION: Suppose my user sings a MIDI note using a steady-state vowel phoneme (no ...
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1 vote
1 answer
96 views

Interpreting the cepstrum of a signal

Let $\omega= e^{-2\pi i/N}$ and let $$\mathbf{W}= \left[\omega^{jk}\right]_{j,k=0,\cdots,N-1}$$ Then we can take a vector $\mathbf{x}\in \mathbb{R}^N$ and transform it via $$\mathbf{X} = \mathbf{W}\...
1 vote
2 answers
87 views

Understanding the two different forms of the Cepstrum

I'm learning about Cepstrum and I see that there are two different forms to calculate it: $$ C_p = \Big| \mathscr{F}^{-1} \big\{\log(|\mathscr{F}\{f(t)\}|^2) \big\} \Big|^2 $$ $$ C_p = \Big| \mathscr{...
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4 votes
1 answer
175 views

Why is taking the inverse Fourier transform the same as taking the Fourier transform when computing the cepstrum?

Usually, the cepstrum of a signal is introduced as the result of taking the logarithm of its power spectrum, then applying the inverse Fourier transform: $$C_p = |F^{-1}\{\log(|F\{f(t)\}|^2)\}|^2$$ It ...
2 votes
1 answer
178 views

inverse fourier transform coefficients

Context I want to implement (real) cepstrum on stock data (for example MSFT stock) and achieve cepstral coefficients of this time series. as noted in "Cepstral-based clustering of financial time ...
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0 votes
0 answers
75 views

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 ...
0 votes
1 answer
204 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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0 votes
0 answers
51 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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1 vote
1 answer
184 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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1 vote
1 answer
167 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 ...
0 votes
1 answer
119 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 \...
0 votes
0 answers
832 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 ...
0 votes
0 answers
89 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 ...
0 votes
0 answers
189 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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3 votes
1 answer
63 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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4 votes
1 answer
453 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 "...
1 vote
1 answer
223 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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1 vote
1 answer
300 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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1 vote
1 answer
4k 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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1 vote
1 answer
884 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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1 vote
0 answers
433 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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4 votes
1 answer
270 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 ...
0 votes
1 answer
440 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 ...
3 votes
0 answers
796 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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2 votes
2 answers
729 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 ...
1 vote
0 answers
534 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 ...
0 votes
0 answers
167 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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2 votes
0 answers
216 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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1 vote
1 answer
275 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 &...
0 votes
1 answer
127 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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4 votes
1 answer
344 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 ...
2 votes
1 answer
950 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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2 votes
1 answer
281 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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4 votes
1 answer
2k 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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1 vote
2 answers
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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-1 votes
1 answer
1k 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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2 votes
1 answer
598 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 ...
1 vote
1 answer
205 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 (...
1 vote
0 answers
168 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 ...
7 votes
1 answer
1k views

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

This is my testing image, it is taken from the paper Image Restoration for Linear Local Motion-Blur Based on Cepstrum: I tried to transform it into its real cepstrum domain with this simple MATLAB ...
0 votes
2 answers
419 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 ...
1 vote
1 answer
589 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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0 votes
0 answers
901 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: ...
0 votes
1 answer
160 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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1 vote
1 answer
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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1 vote
1 answer
799 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 ...
1 vote
1 answer
778 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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3 votes
0 answers
591 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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