signal processing via nn

8/13/2019 signal processing via nn

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PreparedRomil P


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The nonlinear nature of neural networks, the ability onetworks to learn from their environments in supervised as unsupervised ways, as well as the universal approximation pof neural networks make them highly suited for solving signal processing problems.

Basic Artificial Neural Network (ANN) Models1). McCulloch and Pitts

Neuron Model


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2). Multilayer Pe(MLP) Model

Finding the Weights of a Single Neuron MLP


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The objective is to adjust the weight matrix W to minerror E.The derivative of the scalar quantity E with respect to inweights can be computed as follows:

Wx

3). Radial Basis Networks


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... theory and application of filtering, coding, transmestimating, detecting, analyzing, recognizing, synthrecording, and reproducing signals by digital or analog devictechniques.

The term signal includes audio, video, speech

communications, geophysical, sonar, radar, medical, musicalother signals.(from the IEEE (Institute of Electrical and Electronics Engineering) Signal Process


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To find the signal component model and noise probabilidensity function (pdf).

The following assumptions, A1. The unknown signal model in vector form as

xp = sp + n p

Where, xp - N-dimensional random input vector p - M-dimensional random parameter vsp signal vector np - noise component of xp.


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A2. The elements (k) of are statistically independent

A3. The noise vector n has independent elements withGaussian pdf.

A4. The mapping s() is one-to-one.

Rewrite above equation as approximates of sp &

xp = sp + np

approximate the nth element of s p with an invnet ,

for 1 n


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Where, w o(n,k) - coefficient of f p(k,wi) in the approximation to s

f p(k,wi) - kth input or hidden unit in the network,

wi - a vector of weights connecting the input layer to a sin

hidden layer,

Nu - the number of units feeding the output layer.

f p(k,wi) can represent a multinomial function of parametin a functional link network or a hidden unit output in an

The error function for the nth output node,


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An MLPobtaininmodel

The signal model is determined from the noisy data by using aapproach, such as output weight optimization (OWO).

To minimize Ex(n) with respect to w, whose elements are denoted

by w(m). The gradient of En(n) is,


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The most general blind signal processing (BSP) probleformulated as, A set of signals from an MIMO nonlinear

system, where its input signals are generated from a numindependent sources.

The objective is to find an inverse neural system.


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Require a priory knowledge,

1) solvability of the problem (the existence of the inverse s

2) stability of the inverse model.

3) convergence of the learning algorithm and its speed with

related problem of how to avoid being trapped in local m

4) accuracy of the reconstructed source signals.


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The performance of the source separation is evaluated by the compmatrix,

T = W *H = PD

Where, D = Scaling diagonal matrixP = nn permutation matrix

So, y(t) = T (t) s(t)

The separation is perfect when it tends to a generalized permutamatrix which has exactly one nonzero element in each row and column.[1 0 0],[0 0 1]This corresponds to the indeterminacies of the scaling and ordeestimated signals.


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We can also use feedback model,

w

x(t) y(t)+

_

Relationship between feed-forward & feedback weights,


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Detailed architectumultichannel blinddeconvolution feedneural network

M ul tichannel Bl in d Deconvoluti on / Equali zation Problem

Now formulate a more general and physically realistic model wobserved sensors signals are linear combinations of multiply time-delay

of the original source signals and/or mixed signals.


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o

NEURAL NETWORK SIGNAL PROCESSING by, YU HEN HU & JENQ-NENG HWANG

o S. Amari Natural gradient works efficiently in learningComputation

o S. Amari, A. Cichocki, and H. H. Yang, A new learning algofor blind signal separation in Advances in Neural InformProcessing Systems, Vol. 8


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signal processing via nn

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