1 2.5.4.1 Basics of Neural Networks. 2 2.5.4.2 Neural Network Topologies.

transcript

2.5.4.1 Basics of Neural Networks2.5.4.1 Basics of Neural Networks0X

OUTPUT

iii xWfy

2.5.4.2 Neural Network Topologies2.5.4.2 Neural Network Topologies

2.5.4.2 Neural Network 2.5.4.2 Neural Network TopologiesTopologies

2.5.4.2 Neural Network Topologies2.5.4.2 Neural Network Topologies

TDNNTDNN

2.5.4.6 Neural Network Structures for 2.5.4.6 Neural Network Structures for Speech RecognitionSpeech Recognition

2.5.4.6 Neural Network Structures for 2.5.4.6 Neural Network Structures for

Speech RecognitionSpeech Recognition

3.1.1 Spectral Analysis Models3.1.1 Spectral Analysis Models

3.2 THE BANK-OF-FILTERS 3.2 THE BANK-OF-FILTERS FRONT- END PROCESSORFRONT- END PROCESSOR

3.2.1 Types of Filter Bank Used for 3.2.1 Types of Filter Bank Used for Speech RecognitionSpeech Recognition

Nonuniform Filter BanksNonuniform Filter Banks

HzbHzfFilter

1600,2400:4

800,1200:3

400,600:2

200,300:1

3.2.1 Types of Filter Bank Used for 3.2.1 Types of Filter Bank Used for Speech RecognitionSpeech Recognition

3.2.2 Implementations of Filter Banks3.2.2 Implementations of Filter Banks

Instead of direct convolution, which is Instead of direct convolution, which is computationally expensive, we assume computationally expensive, we assume each bandpass filter impulse response to each bandpass filter impulse response to be represented by:be represented by:

Where w(n) is a fixed lowpass filterWhere w(n) is a fixed lowpass filter

ienwnh )()(

3.2.2 Implementations of Filter Banks3.2.2 Implementations of Filter Banks

3.2.2.1 Frequency Domain Interpretation of the Short-3.2.2.1 Frequency Domain Interpretation of the Short-

Time Fourier TransformTime Fourier Transform

3.2.2.1 Frequency Domain 3.2.2.1 Frequency Domain Interpretation of the Short-Time Interpretation of the Short-Time

Fourier TransformFourier Transform

Linear Filter Interpretation of the Linear Filter Interpretation of the STFTSTFT

ns)(ns)(nw

)( 1jn eS

3.2.2.4 FFT Implementation of a 3.2.2.4 FFT Implementation of a Uniform Filter BankUniform Filter Bank

Direct implementation of an arbitrary Direct implementation of an arbitrary filter bankfilter bank

)(1 nh

)(nX Q

)(2 nh

)(1 nX

)(2 nX

3.2.2.5 Nonuniform FIR Filter Bank 3.2.2.5 Nonuniform FIR Filter Bank ImplementationsImplementations

3.2.2.7 Tree Structure Realizations of 3.2.2.7 Tree Structure Realizations of Nonuniform Filter BanksNonuniform Filter Banks

3.2.4 Practical Examples of Speech-3.2.4 Practical Examples of Speech-Recognition Filter Banks Recognition Filter Banks

3.2.4 Practical Examples of Speech-3.2.4 Practical Examples of Speech-Recognition Filter BanksRecognition Filter Banks

3.2.5 Generalizations of Filter-Bank Analyzer 3.2.5 Generalizations of Filter-Bank Analyzer

روش مل-کپسترومروش مل-کپستروم

Mel-scaling بندی فریم

|FFT|2

Low-order coefficientsDifferentiator

Cepstra

Delta & Delta Delta Cepstra

زمانی سیگنال

Logarithm

Time-Frequency analysisTime-Frequency analysis

Short-term Fourier TransformShort-term Fourier Transform Standard way of frequency analysis: decompose the Standard way of frequency analysis: decompose the

incoming signal into the constituent frequency incoming signal into the constituent frequency components.components.

W(n): windowing functionW(n): windowing function N: frame lengthN: frame length p: step sizep: step size

Critical band integrationCritical band integration

Related to masking phenomenon: the Related to masking phenomenon: the threshold of a sinusoid is elevated when threshold of a sinusoid is elevated when its frequency is close to the center its frequency is close to the center frequency of a narrow-band noisefrequency of a narrow-band noise

Frequency components within a critical Frequency components within a critical band are not resolved. Auditory system band are not resolved. Auditory system interprets the signals within a critical interprets the signals within a critical band as a wholeband as a whole

Bark scaleBark scale

Feature Feature orthogonalizationorthogonalization

Spectral values in adjacent Spectral values in adjacent frequency channels are highly frequency channels are highly correlatedcorrelated

The correlation results in a The correlation results in a Gaussian model with lots of Gaussian model with lots of parameters: have to estimate all the parameters: have to estimate all the elements of the covariance matrixelements of the covariance matrix

Decorrelation is useful to improve Decorrelation is useful to improve the parameter estimation.the parameter estimation.

CepstrumCepstrum Computed as the inverse Fourier transform Computed as the inverse Fourier transform

of the log magnitude of the Fourier of the log magnitude of the Fourier transform of the signaltransform of the signal

The log magnitude is real and symmetric -> The log magnitude is real and symmetric -> the transform is equivalent to the Discrete the transform is equivalent to the Discrete Cosine Transform.Cosine Transform.

Approximately decorrelatedApproximately decorrelated

Principal Component Principal Component AnalysisAnalysis

Find an orthogonal basis such that the Find an orthogonal basis such that the reconstruction error over the training set reconstruction error over the training set is minimizedis minimized

This turns out to be equivalent to This turns out to be equivalent to diagonalize the sample autocovariance diagonalize the sample autocovariance matrixmatrix

Complete decorrelationComplete decorrelation Computes the principal dimensions of Computes the principal dimensions of

variability, but not necessarily provide variability, but not necessarily provide the optimal discrimination among classesthe optimal discrimination among classes

Principal Component Analysis Principal Component Analysis ((PCAPCA))

MathematicalMathematical procedure that transforms a number of procedure that transforms a number of (possibly) correlated variables into a (smaller) number of (possibly) correlated variables into a (smaller) number of uncorrelateduncorrelated variables called variables called principal components (PC)principal components (PC)

Find an orthogonal basis such that the reconstruction error Find an orthogonal basis such that the reconstruction error over the training set is minimizedover the training set is minimized

This turns out to be equivalent to diagonalize the sample This turns out to be equivalent to diagonalize the sample autocovariance matrixautocovariance matrix

Complete decorrelationComplete decorrelation

Computes the principal dimensions of variability, but not Computes the principal dimensions of variability, but not necessarily provide the optimal discrimination among classesnecessarily provide the optimal discrimination among classes

PCA PCA (Cont.)(Cont.)

AlgorithmAlgorithm

Apply Transform

Output =

(R- dim vectors)

Input=

(N-dim vectors)

MNx * Covariance matrix

xxxxCov

EigVec

EigValNi ...1

Transform matrix

NEigVec

EigVec

...21 EigValEigVal

Eigen values

Eigen vectors

PCA PCA (Cont.)(Cont.) PCA in speech recognition systemsPCA in speech recognition systems

Linear discriminant Linear discriminant AnalysisAnalysis

Find an orthogonal basis such that the Find an orthogonal basis such that the ratio of the between-class variance ratio of the between-class variance and within-class variance is and within-class variance is maximizedmaximized

This also turns to be a general This also turns to be a general eigenvalue-eigenvector problemeigenvalue-eigenvector problem

Complete decorrelationComplete decorrelation Provide the optimal linear separability Provide the optimal linear separability

under quite restrict assumptionunder quite restrict assumption

PCA vs. LDAPCA vs. LDA

Spectral smoothingSpectral smoothing

Formant information is crucial for Formant information is crucial for recognitionrecognition

Enhance and preserve the formant Enhance and preserve the formant information:information: Truncating the number of cepstral Truncating the number of cepstral

coefficientscoefficients Linear prediction: peak-hugging Linear prediction: peak-hugging

propertyproperty

Temporal processingTemporal processing

To capture the temporal features of To capture the temporal features of the spectral envelop; to provide the the spectral envelop; to provide the robustness:robustness: Delta Feature: first and second order Delta Feature: first and second order

differences; regressiondifferences; regression Cepstral Mean Subtraction:Cepstral Mean Subtraction:

For normalizing for channel effects and For normalizing for channel effects and adjusting for spectral slopeadjusting for spectral slope

RASTA (RelAtive SpecTral RASTA (RelAtive SpecTral Analysis)Analysis)

Filtering of the temporal trajectories of Filtering of the temporal trajectories of some function of each of the spectral some function of each of the spectral values; to provide more reliable values; to provide more reliable spectral featuresspectral features

This is usually a bandpass filter, This is usually a bandpass filter, maintaining the linguistically important maintaining the linguistically important spectral envelop modulation (1-16Hz)spectral envelop modulation (1-16Hz)

RASTA-PLPRASTA-PLP

1 2.5.4.1 Basics of Neural Networks. 2 2.5.4.2 Neural Network Topologies.

Documents