Questions tagged [cepstral-analysis]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
1 answer
58 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}\...
user avatar
1 vote
2 answers
60 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{...
user avatar
  • 113
4 votes
1 answer
159 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 ...
user avatar
2 votes
1 answer
106 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 ...
user avatar
  • 121
0 votes
0 answers
68 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 ...
user avatar
0 votes
1 answer
185 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 ...
user avatar
  • 301
0 votes
0 answers
49 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 ...
user avatar
  • 301
1 vote
1 answer
158 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 ...
user avatar
  • 97
1 vote
1 answer
145 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 ...
user avatar
0 votes
1 answer
109 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 \...
user avatar
0 votes
0 answers
697 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 ...
user avatar
0 votes
0 answers
78 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 ...
user avatar
0 votes
0 answers
172 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: ...
user avatar
  • 133
3 votes
1 answer
55 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 ...
user avatar
  • 131
4 votes
1 answer
421 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 "...
user avatar
1 vote
1 answer
210 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....
user avatar
  • 285
1 vote
1 answer
284 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 ...
user avatar
  • 323
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 ...
user avatar
  • 11
1 vote
1 answer
832 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 ...
user avatar
  • 111
1 vote
0 answers
413 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 ...
user avatar
  • 111
4 votes
1 answer
256 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 ...
user avatar
0 votes
1 answer
436 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 ...
user avatar
3 votes
0 answers
782 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 ...
user avatar
  • 31
2 votes
2 answers
692 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 ...
user avatar
1 vote
0 answers
521 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 ...
user avatar
0 votes
0 answers
158 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: $$\...
user avatar
  • 827
2 votes
0 answers
203 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{...
user avatar
  • 268
1 vote
1 answer
266 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 &...
user avatar
0 votes
1 answer
117 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 ...
user avatar
  • 185
4 votes
1 answer
340 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 ...
user avatar
2 votes
1 answer
893 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 ...
user avatar
  • 373
2 votes
1 answer
279 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 ...
user avatar
  • 185
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 ...
user avatar
  • 161
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 ...
user avatar
  • 161
-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 ...
user avatar
  • 99
2 votes
1 answer
573 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 ...
user avatar
1 vote
1 answer
202 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 (...
user avatar
1 vote
0 answers
163 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 ...
user avatar
6 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 ...
user avatar
0 votes
2 answers
412 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 ...
user avatar
1 vote
1 answer
585 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 ...
user avatar
  • 111
0 votes
0 answers
896 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: ...
user avatar
0 votes
1 answer
159 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/...
user avatar
  • 175
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}...
user avatar
  • 432
2 votes
1 answer
779 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 ...
user avatar
1 vote
1 answer
774 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 ...
user avatar
  • 11
3 votes
0 answers
587 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? ...
user avatar
  • 155
0 votes
0 answers
144 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 ...
user avatar
  • 323
1 vote
0 answers
82 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 ...
user avatar
  • 323
1 vote
0 answers
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 ...
user avatar
  • 111