homomorphic filtering and speech processing using cepstrum analysis
TRANSCRIPT
![Page 1: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/1.jpg)
Homomorphic filtering and speech processing using cepstrum analysis
![Page 2: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/2.jpg)
OutlineIntroduction of Homomorphic
filteringHomomorphic SystemsZ-transform in HomomorphicApplication in speech processingVoiced and unvoiced speechCepstral Analysis of windowsConclusion
![Page 3: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/3.jpg)
IntroductionFiltering is a non-linear transformation
Applied to the image and speech processing
Used to convert a signal from a convolution of two original signal into the sum of two signals
![Page 4: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/4.jpg)
Consider some linear transformation L
L is a linear system it will satisfy the principle of superposition
Define a class where addition is replaced by convolution
System having this property are known as Homomorphic systems for convolution
![Page 5: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/5.jpg)
Homomorphic system has a important property is that they can be viewed as a cascade of three Homomorphic systems
![Page 6: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/6.jpg)
Homomorphic Systems The first system takes inputs
combined by convolution and transforms them into an additive combination of the corresponding outputs
D* is a Homomorphic system in which convolution is converted in to the addition
![Page 7: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/7.jpg)
Contd………. The second system is a conventional linear
system that obeys the principle of superposition
Some linear System
The third system is the inverse of the first system: it transforms signals combined by addition into signals combined by convolution
Some inverse Homomorphic system in which addition is converted in to convolution
![Page 8: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/8.jpg)
This is important because design of such systems reduces to the design of linear system
![Page 9: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/9.jpg)
Z-transformZ-transform of two convolved signals
is the product of their z-transforms
Then take logs to obtain
so log of Z-transform is viewed as a Homomorphic systems
![Page 10: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/10.jpg)
The frequency domain representation of a Homomorphic system for deconvolution can be represented as
![Page 11: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/11.jpg)
Represent signals as sequence rather than in the frequency domain, then the systems ∗[ ]and 𝐷
∗𝐷 −1[ ] can be represented as
![Page 12: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/12.jpg)
speech processing Homomorphic systems are very
frequently used in speech processing applications
We have to separate the excitation from the vocal tract filter h(n) by using a Homomorphic transformation
![Page 13: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/13.jpg)
Do so easily as the filter parameters usually reside in the lower quefrencies
While the excitation parameters have higher quefrencies
We have to recover filter’s response from a periodic signal ( such as a voiced signal excitation)
![Page 14: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/14.jpg)
The filter response can be recovered if we can separate the output of the Homomorphic transformation using a simple filter
![Page 15: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/15.jpg)
Deconvolution of speech
![Page 16: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/16.jpg)
Cepstrum of a generic voiced signal
![Page 17: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/17.jpg)
Contributions to the cepstrum due to periodic excitation will occur at integer multiples of the fundamental period. NOTE that for children and high-pitch women we might have a problem
Contributions due to parameters usually modeled by the filter will concentrate in the low quefrequency region and will decay quickly with n
![Page 18: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/18.jpg)
Cepstral analysis of speech (voiced signals)
![Page 19: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/19.jpg)
Cepstral analysis of speech (unvoiced signal)
![Page 20: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/20.jpg)
Cepstral analysis of vowel (rectangular window)
![Page 21: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/21.jpg)
Cepstral analysis of vowel (tapering window)
![Page 22: Homomorphic Filtering and Speech Processing Using Cepstrum Analysis](https://reader033.vdocument.in/reader033/viewer/2022061105/54409045b1af9f5d0b8b4637/html5/thumbnails/22.jpg)
THANK YOUANY QUESTIONS??????