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

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

3. Transfer functions of four standard ideal filters

4. Ideal low-pass filter approximation

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

6. 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.

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

8. 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).

9. 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.

10. 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:

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

12. FIR filter realization
Direct realization

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

14. Triangular (Bartlett) window:

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

16. 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:

17. 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

18. 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.

19. 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

20. References:
Keshab K.Parhi, , ‘VLSI Digital Signal Processing Systems: Design and Implementation’, January 1999, ISBN:
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