# Questions tagged [cepstral-analysis]

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### 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 ...
1 vote
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### 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 ...
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### 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 ...
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### 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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### 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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### 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 ...
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### 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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### 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 ...
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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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