Questions tagged [cepstral-analysis]
The cepstral-analysis tag has no usage guidance.
60
questions
1
vote
1
answer
53
views
Questions on Cepstral Analysis
I have a few questions regarding cepstral analysis, that the numerous articles and papers I've read on the topic didn't answer.
What I understood: The cepstrum captures the periodicity of harmonics in ...
- 81
1
vote
0
answers
26
views
What is gained by transforming a convolution to an addition with the cepstrum?
In automatic speech recognition the spectrum $f$ is interpreted as the convolution of elicitation $e$ and impulse response $h$.
By applying the cepstrum $cep(f) = FT^{-1}(log(FT(f)))$ this convolution ...
- 111
0
votes
0
answers
47
views
How to detect "buzz" components in audio by frequency domain analysis
I am trying to detect the amplitude, frequency and phase of the dominant "buzz" in an audio signal. By "buzz" I mean a periodic signal with sharp edges. For example, an impulse ...
- 133
1
vote
3
answers
334
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 ...
- 11
1
vote
0
answers
41
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 ...
- 1,319
1
vote
1
answer
349
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
$$\mathbf{X} = \mathbf{W}\...
- 121
1
vote
2
answers
163
views
Understanding the two different forms of the Cepstrum
I'm learning about Cepstrum and I see that there are two different forms to calculate it:
$$ C_p = \Big| \mathscr{F}^{-1} \big\{\log(|\mathscr{F}\{f(t)\}|^2) \big\} \Big|^2 $$
$$ C_p = \Big| \mathscr{...
- 113
4
votes
1
answer
298
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 ...
- 185
2
votes
1
answer
399
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 ...
- 121
0
votes
0
answers
81
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 ...
- 69
0
votes
1
answer
332
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 ...
- 331
0
votes
0
answers
56
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 ...
- 331
1
vote
1
answer
397
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 ...
- 107
1
vote
1
answer
244
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
191
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
1k
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 ...
- 31
0
votes
0
answers
140
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 ...
- 31
0
votes
0
answers
231
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:
...
- 133
3
votes
1
answer
69
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 ...
- 131
4
votes
1
answer
542
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 "...
- 157
1
vote
1
answer
286
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....
- 285
1
vote
1
answer
360
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 ...
- 313
2
votes
1
answer
5k
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 ...
- 21
1
vote
1
answer
1k
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 ...
- 111
1
vote
0
answers
502
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 ...
- 111
4
votes
1
answer
299
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
458
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 ...
4
votes
0
answers
872
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 ...
- 41
2
votes
2
answers
824
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 ...
- 313
1
vote
0
answers
568
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 ...
- 313
0
votes
0
answers
179
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:
$$\...
- 846
2
votes
0
answers
241
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
$$\hat{x}[n] = \sum^{ \infty}_{r=1} \frac{...
- 268
1
vote
1
answer
308
views
Is there a way to do a DFT with low latency and fine frequency resolution at low frequencies?
I am learning about the DFT in order to design a fundamental pitch detector for the human singing voice. Using the cepstrum technique.
I am concerned about the latency for low frequency detection at &...
- 123
0
votes
1
answer
152
views
Normalizing Cepstrum by Energy
I have separately computed the cepstrum and the energy of a finite discrete-time signal. If the energy of the signal is high, we would expect (on average) larger cepstral values than if the energy of ...
- 185
4
votes
1
answer
358
views
Calculating phase response of maximum phase filter using Hilbert Transform
Given only a magnitude response $A(\omega)$ of a minimum phase filter, one can calculate the phase response using the Hilbert Transform:
$$θ(ω) = -\mathcal{H}\{\ln(A(\omega)\}$$
This paper suggests ...
- 41
2
votes
1
answer
1k
views
Preserving formants using Cepstrum
I've implemented an harmonizer, using Stefan Bernsee's code, which works great. I figured out the logic of finding the root note, and the right harmony in the scale.
The only problem is that, my ...
- 373
2
votes
1
answer
298
views
How to interpret the sign of a cepstral coefficient?
I feel like I've got a decent intuition for what the magnitude of a cepstral coefficient represents (i.e. how much of the signal's energy is contained in harmonics of a given wavelength), but I don't ...
- 185
4
votes
1
answer
2k
views
What's the difference between using DFT, IDFT or DCT to calculate cepstrum of a power spectrum?
I've seen different equations that calculate cepstrum from power spectrum, but the equations are not consistent. Some people use Fourier transform, some use the inverse Fourier transform, and some use ...
- 161
1
vote
2
answers
1k
views
Why is cepstrum used in MFCC instead of autocorrelation sequence?
I know that the inverse Fourier transform of the power spectral density $P(k)$ gives the autocorrelation sequence $A(n)$ (By Wiener-Khinchin theorem):
$${\cal F}^{-1}\left\{P(k)\right\}=A(n)$$
And ...
- 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 ...
- 99
2
votes
1
answer
676
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 ...
- 123
1
vote
1
answer
233
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
191
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 ...
- 154
5
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 ...
- 215
0
votes
2
answers
439
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
621
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 ...
- 111
0
votes
0
answers
910
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:
...
- 41
0
votes
1
answer
192
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/...
- 175
1
vote
1
answer
8k
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}...
- 432
1
vote
1
answer
886
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 ...
- 125