https://github.com/liufeigit/cepstrum

https://github.com/liufeigit/cepstrum

Last synced: about 1 month ago
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• Host: GitHub
• URL: https://github.com/liufeigit/cepstrum
• Owner: liufeigit
• Created: 2016-06-12T07:36:49.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2015-03-22T19:48:45.000Z (almost 10 years ago)
• Last Synced: 2024-10-15T23:56:17.587Z (3 months ago)
• Language: Objective-C
• Size: 1.03 MB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
Welcome to the Cepstrum repository

This is a sample application which aim is to transform a signal by modifying its Cepstrum.

The Cepstrum is the iFFT of the natural Log of the FFT of the original signal. The Cepstrum is complex.

The original signal in this project is a decreasing sinus to which echos are applied. The aim of this project is to eliminate

the echos:

the original signal is to be considered as a decreasing sinus convoluted by some diracs. The FFT will transform the convolution to

a multiplication of the spectrums. The Cepstrum, being a Log, will tansform the multiplcation into an addition. The Cepstrum

domain is a kind of time domain called quefrency domain. A filter in the spectrum domain is called a lifter in the quefrency

domain. By lifting the echos (kind of high quefrency lifter), it should be possible to reconstruct the original decreasing

sinus which is what I am trying do achieve. 

I am looking for some help to achieve this.

The application have yet:

the original signal construction

some displays

a delay slider which helps to move the time when the echo(s) occur(s)

a lifter slider which apply the lifter filter base on the value

at the launch of the project, there is no echo (delay slider is set to 0) and the lifter is at its maximum value which mean the

that the Cepstrum is not modified. Therefore, by reconstruction (which does not work yet), the modified signal should be the

same as the input data.

Please help if you find this project interesting for you

Some thoughts:

no windowing yet. Might be necessary to add windowing + overlap for further realtime possibility

phase problem issue introduced by FFT and Log?

Other?

Patrick

here are some screenshots

Original signal

![Alt text](https://github.com/PatrickMuringer/Cepstrum/blob/master/Cepstrum/images/signal.png?raw=true "Original Signal")

Original signal cannot be reconstructed (see Modified signal) even if no echo or no lifter is used

![Alt text](https://github.com/PatrickMuringer/Cepstrum/blob/master/Cepstrum/images/app%20startup.png?raw=true "Startup of the project")

Result when adding echo

![Alt text](https://github.com/PatrickMuringer/Cepstrum/blob/master/Cepstrum/images/app%20startup%20with%20echo.png?raw=true "When adding echo")