FIR Filter Design Using Neural Network Advisor: Dr.B.Mashoufi By: Mohammadreza Meidnai Urmia university, Urmia, Iran Spring 2015

Contents: Basic concepts of filter Digital filtering FIR filter Fir filter design using conventional methods Fir filter design using neural network Conclusion

Transfer functions of four standard ideal filters

Ideal low-pass filter approximation

The ideal filter frequency response can be computed via inverse Fourier transform. The four standard ideal filters frequency responses are:

Basic concepts of digital filtering The analog input signal must satisfy certain requirements. Furthermore, on converting an output digital signal into analog form, it is necessary to perform additional signal processing in order to obtain the appropriate result.

Calculations in digital filtering typically involve multiplying the input values by constants and adding the products together.

Types of digital filters: Filters can be classified in several different groups, depending on what criteria are used for classification. The two major types of digital filters are finite impulse response digital filters (FIR filters) and infinite impulse response digital filters (IIR).

FIR digital filter: In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. The impulse response of an Nth-order discrete-time FIR filter lasts exactly N + 1 samples (from first nonzero element through last nonzero element) before it then settles to zero.

FIR filters are digital filters with finite impulse response FIR filters are digital filters with finite impulse response. They are also known as non-recursive digital filters as they do not have the feedback. FIR filter transfer function can be expressed as:

FIR filter output samples can be computed using the following expression: h[k]: impulse response of system

FIR filter realization Direct realization

FIR Filter Design Using Conventional Methods: Rectangular window: w[n]=1 , 0 ≤ n ≤ N-1

Triangular (Bartlett) window:

Other windowing methods for designing FIR filter: Hanning window Hamming window Bartlet-Hanning Bohaman window Blackman window Kaiser window …

FIR Filter Design Using Neural Network Method(ADALINE): The output of neural network can be expressed as: Where, H is the output vector of the neural network, C is the transformation matrix of the hidden units of neural network, A is the weight vectors of the neural network. We define error function as:

We define the performance index P as: Wher J is: To minimize P we recursively calculated A as: Where, η is a learning rate. After substitution we have: In order to ensure the convergence of neural network, it is important to select a proper learning rate η

Design examples: The design parameters are as following: N=37,ωp=0.3, ωs=0.4 ,η=0.1. The proposed algorithm took 2000 iterations to converge to the magnitude response.

Conclusion: Designing FIR filter using neural network shows better characteristics than conventional design methods Defining proper amount for η, plays important role in designing filter To design FIR filter there are plenty methods and designer has to choose best method depending on his work

References: Keshab K.Parhi, , ‘VLSI Digital Signal Processing Systems: Design and Implementation’, January 1999, ISBN: 978-0-471-24186-7 Khushboo Pachori, Dr. Amit Mishra , ‘Design of FIR Digital Filters using ADALINE Neural Network’, 2012 Fourth International Conference on Computational Intelligence and Communication Networks Zoran Milivojevi.: 'Digital Filter Design', MikroElektronika 2009