Design Band Pass FIR Digital Filter for Cut off Frequency Calculation Using Artificial Neural Network
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The document describes a study that uses artificial neural networks (ANN) to calculate cut-off frequencies for band pass FIR digital filters designed using different window methods. FDA Tool was used to design band pass FIR digital filters with Hamming, Hanning, and Kaiser windows. ANN algorithms including feedforward backpropagation and radial basis function were then used to estimate cut-off frequencies based on filter coefficients, and results were compared to actual frequencies from FDA Tool. The ANN approaches estimated cut-off frequencies accurately with low mean square errors.
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1367
Design Band Pass FIR Digital Filter for Cut off Frequency Calculation
Using Artificial Neural Network
Noopur Srivastava1, Vandana Vikas Thakare2
1,2Department of Electronics, Madhav Institute of Technology & Science, Gwalior-05, India
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - This paper presents a design approach of band
pass FIR digital filter for cut-off frequency calculation using
artificial neural network (ANN).In this work FDA Tool has
been used for design of FIR band pass digital filter with
hamming, hanning and Kaiser window because better
frequency response has been achieved by these window for
design of digital band pass filterthanotherwindowandANN
has been used for cut off frequency calculation with two
algorithms namely feedforwardback propagationandradial
basis function.
The cut-off frequencies have been compared byNN Tool and
FDA Tool, comparison has been done also for windows and
algorithms.
Key Words: Band pass FIR digital filter, FDA Tool,
NNTool, hamming, hanning, Kaiser Window, FFBP, and
RBF.
1. INTRODUCTION
A filter is a device that discriminates of its input accordingto
some attribute of the object. The digital filter can be
implemented in both software and Hardware.Digital filter is
a linear time invariant system (LTI) which does not vary
with time. Digital filter have high accuracy, easy to simulate
and design, flexible than analog filter [17]. Based on
frequency characteristics digital filter is divided into four
types-
Low pass filter (LPF)-Low pass filter only passes the low
frequency components (≤wc).
High pass filter (HPF)-High pass filter only passes the high
frequency components (≥wc).
Band pass filter (BPF)-Band pass filter only passes the
frequency components between two frequencies (wc1&wc2).
Stop band filter (SBF)-Stop band filter does not passes the
frequency components between two frequency (wc1&wc2).
In this section discussion has been done for the design of
band pass FIR digital filter. The band pass filter can also be
designed by combining of low and high pass filter.
There are two types of digital filter-
i. Finite impulse response filters (FIR).
ii. Infinite impulse response (IIR).
The impulse response of FIR filter is finitesothisisknown as
FIR digital filter. They do not use and feedback because they
depends on present input and past input so it is also known
as non recursive filter.FIR digital filter has linear phase
characteristics and they and inherently stable but IIR filter
do not have linear phase characterstics.The impulse
response of IIR digital filter is infinite so this is known as IIR
digital filter. They requires feedback because they depends
on present input, past input and past output so they are also
known as recursive filter[10].
The output sequence is given as for FIR filter-
Y(n)=
Y(n)=h(0)x(n)+h(1)x(n-1)+……+h(N)x(n-N)
This sequence of output is finite so this is known as finite
impulse response.
Figure 1. FIR digital filter
2. FIR DIGITALFILTERDESIGN USING WINDOW
METHOD
The window method is one of the simplest methods for
design of FIR filter among the two method i.e. fourier series
and frequency sampling. In the frequency sampling it only
works for particular frequency components and for other it
does not works. Window methodiseasymethodandvarious
windows can be used based on our application [5]. The
desired unit sample response is given by
hd(n)=
h(n)=w(n)hd(n)
Where hd(w) is desired frequency response
characteristics.hd(n) is of infinite duration so hd(n) is
truncated by finite length of window(M-1) which is w(n).so
h(n) will be of finite length duration.
In this paper three windows have been used which are-
Hamming window-hamming window is given by
wH(n)=
Hanning window-hanning window is given by
wHN(n)=](https://image.slidesharecdn.com/irjet-v4i6251-180201104501/85/Design-Band-Pass-FIR-Digital-Filter-for-Cut-off-Frequency-Calculation-Using-Artificial-Neural-Network-1-320.jpg)
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1368
Kaiser window- Kaiser Window is given as
wk(n)=
Where 1 and 2 is the ripple in pass band and stopband.wp
is pass band frequency and ws is stop band frequency. is a
shape parameter which is given as
And filter order is given by
N=
Attenuation A= -20
The Kaiser window is best among other window because
they have less transition band than other.
3. ARTIFICIAL NEURAL NETWORK (ANN)
Artificial neural network is comprised of a network of artificial
neurons (node) [15].neural network is an algorithmthat based on
the human brain works. They can build predicted model by
learning the pattern of historical data.ANN made by
interconnected processing element, these are known as node or
neuron. Each node processes the small part of the task. The most
common type of ANN is multi layer perceptron (MLP).in MLP
the nodes are organized in layer. It is also known as parallel
distributed processing system or connectionist system. The first
layer is the input layer, the outer most layer stands for output
layer. Between these two comes one or more layer known as
hidden layer. The entire node is fully connected with the
previous node. Input are multiplied by unique weight and added
together by a small value called bias. This total is processed is
by the function called the activation function.
f(u)=w1u1+w2u2+w3u3+b
Where w is weight is an input and b is a bias.
It leaves the node as output, this process proceeds till
information reached at the output layer and leaves it as the
prediction for the independent variable. The network compares
predicted and actual output. If these do not match it adjust all the
weight and repeat the process till the network produce an
accurate prediction for most of the observation.
There is various algorithms use in ANN this are-
Feed forward back propagation- a feed forward network has
feedback paths meaning they can have signals travelling using
loops. This system is nonlinear dynamic system because there is
a loop which changes until it reaches state of equilibrium. In this
the data flows in forward direction and error flows in reverse
direction.
Figure 2. Feed forward network
Feed forward distributed time delay algorithm-In this algorithm
whose basic function is to work on sequential data. Time delay
represents the time shift usually form part of a larger pattern
recognition system. It is mainly use to represent the relation
between time and input.
Radial basis function- It is a real value function whose value
depends only on the distance from the origin or alternatively on
the distance from some other point C, called a center. The norm
is usually euclidean distance although other distance function is
also possible. Radial basis function has more number of neurons
than other algorithm so it gives better result than another
algorithm.
4. FORMULATION OF PROBLEM
The objective of this paper is to be estimated the cut-off
frequency of proposed filter coefficients of band pass FIR
digital filter which is achieved by FDA Tool using hamming,
hanning and Kaiser Window. In this the input has been used
as filter coefficient and target has been used as cut off
frequency for which these filter coefficient have. Some filter
coefficients have been chosen which is worked as test input
and the cut off frequencies using NN Tool have been
estimated for this test input. The comparison has been done
between hamming, hanning, Kaiser Window. Feed forward
back propagation and radial basisfunctionalgorithmofANN
also have been compared.
5. EXPERIMENTATION
Cut-off frequencies of band pass FIR digital filter have been
calculated with three steps-
i. Step 1:
Band pass FIR digital filter has been designed by FDA Tool.
The order of the filter has been chosen 38 because for low order
the frequency response characteristics has not been properly
obtained. The cut-off frequencies have been used in the form of
normalized, varied from 0 to 1.
Two cut off frequencies have been used say fc1 and fc2.The
values have been selected as fc1=0.1 and fc2=0.3 and designed the
filter. The value of filter coefficients h(n) have been exported on
workspace. The same process have been repeated for fc1 from
0.1 to 0 .7 and fc2 from 0.3 to 0.9.Total 121 samples have been
achieved. Out of these 121 samples, 111 samples have been used](https://image.slidesharecdn.com/irjet-v4i6251-180201104501/85/Design-Band-Pass-FIR-Digital-Filter-for-Cut-off-Frequency-Calculation-Using-Artificial-Neural-Network-2-320.jpg)
![International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1374
testing. So we have seen ANN gives efficient result in less
time and it has been given result nearer to the actual one.
7. CONCLUSION
For finding that whichwindowgivesbetterresultthemean
square error (MSE) has been calculated for each window
and for each algorithm. After this and it has been found
that all window are given almost same result buthamming
window is given the more efficient resultthanhanningand
Kaiser Window. Out of two algorithms i.e. FFBP and RBF it
has been found from various error graphs that RBF is best
and better result is achieved by this almost same as actual
one.RBF has highly accurate algorithm than other.
8. REFERANCE
[1] Chonghua Li, “Design and Realization of FIR Digital
Filters Based on MATLAB”, IEEE 2010.
[2] Rohit Patel, .Mukesh Kumar, A.K. Jaiswal, Rohini
Saxena,” Design Technique of Band pass FIR filter using
Various Window Function” IOSR Journal ofElectronicsand
Communication Engineering (IOSR-JECE), Volume 6,Issue
6 (Jul. - Aug. 2013), PP 52-57.
[3]Gaurav Jain, R. P. Narwaria,”Designing of rectangular
window based FIR filter for cutoff frequency calculation in
artificial neural network”, International Journal of
Engineering Science &ResearchTechnology(IJESRT),etal.,
6(1): January, 2017.
[4] Alia Ahmed Eleti and Amer R. Zerek,
“FIR Digital Filter Design By Using Windows Method With
MATLAB”, IEEE 2013.
[5] John G. Proakis & Dimitis G. Manoakis, “Digital Signal
Processing Principles, Algorithms, and Applications”,
PRENTICE-HALLINTERNATINAL,INC.,ThirdEdition1996.
[6] Alan V. Oppenheim, and Ronald W. Schafer, “Discrete-
Time Signal Processing”.
[7] Yogesh Babu Indoriya, Anil Mourya, Karuna
Markam,”Design FIR digital filter using neural network”,
international journal of advanced and innovativeresearch,
vol. 4 issue 3.
[8] Suchi Sharma, Anjana Goen,”Analysis and Performance
Evaluation for Low Pass Filter Design Using Artificial
Neural Network “International journal ofinnovativetrends
in engineerining (IJITE), volume 19, nov. 02, 2016.
[9] M. A. Singh and V. B. V. Thakare,”Artificial Neural
Network Use for Design Low PassFIR Filtera Comparison”,
International Journal of Electronics and Electrical
Engineering Vol. 3, No. 3, June 2015.
[10] Sanjit K. Mitra, “Digital signal processing A computer-
Based Approach”, Department of Electrical and Computer
Engineering University of California, McGraw-Hill, Second
Edition 2002.
[11] Suruchi Sharma,” Design and Analysis of FIR Filter using
Artificial Neural Network”, et al International Journal of
Computer and Electronics Research ,Volume 4, Issue 2, April
2015.
[12] Aparna Tiwari, Vandana Thakre, Karuna Markam,”FIR
Filter Design Using Artificial Neural Network”, International
Journal of Computer & Communication Engineering Research
(IJCCER),
Volume 2 - Issue 3 May 2014.
[13]Ajeet Maheshwari, Karuna Markam,”Design A Bartlett
Window Based Digital Filter by Using GRNN”, International
Journal of Innovative Research in Science, Engineering and
Technology Vol. 3, Issue 7, July 2014.
[14] S. Haykins, “Neural Networks –A comprehensive
foundation”, Prentice –Hall of India Private Limited, New
Delhi, (2003).
[15] Artificial neural network by B.Yegnanarayana.
[16] Mathworks.com
[17]digital signal processing by Dr.J.S. Chitode.](https://image.slidesharecdn.com/irjet-v4i6251-180201104501/85/Design-Band-Pass-FIR-Digital-Filter-for-Cut-off-Frequency-Calculation-Using-Artificial-Neural-Network-8-320.jpg)
Design Band Pass FIR Digital Filter for Cut off Frequency Calculation Using Artificial Neural Network
- 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1367 Design Band Pass FIR Digital Filter for Cut off Frequency Calculation Using Artificial Neural Network Noopur Srivastava1, Vandana Vikas Thakare2 1,2Department of Electronics, Madhav Institute of Technology & Science, Gwalior-05, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - This paper presents a design approach of band pass FIR digital filter for cut-off frequency calculation using artificial neural network (ANN).In this work FDA Tool has been used for design of FIR band pass digital filter with hamming, hanning and Kaiser window because better frequency response has been achieved by these window for design of digital band pass filterthanotherwindowandANN has been used for cut off frequency calculation with two algorithms namely feedforwardback propagationandradial basis function. The cut-off frequencies have been compared byNN Tool and FDA Tool, comparison has been done also for windows and algorithms. Key Words: Band pass FIR digital filter, FDA Tool, NNTool, hamming, hanning, Kaiser Window, FFBP, and RBF. 1. INTRODUCTION A filter is a device that discriminates of its input accordingto some attribute of the object. The digital filter can be implemented in both software and Hardware.Digital filter is a linear time invariant system (LTI) which does not vary with time. Digital filter have high accuracy, easy to simulate and design, flexible than analog filter [17]. Based on frequency characteristics digital filter is divided into four types- Low pass filter (LPF)-Low pass filter only passes the low frequency components (≤wc). High pass filter (HPF)-High pass filter only passes the high frequency components (≥wc). Band pass filter (BPF)-Band pass filter only passes the frequency components between two frequencies (wc1&wc2). Stop band filter (SBF)-Stop band filter does not passes the frequency components between two frequency (wc1&wc2). In this section discussion has been done for the design of band pass FIR digital filter. The band pass filter can also be designed by combining of low and high pass filter. There are two types of digital filter- i. Finite impulse response filters (FIR). ii. Infinite impulse response (IIR). The impulse response of FIR filter is finitesothisisknown as FIR digital filter. They do not use and feedback because they depends on present input and past input so it is also known as non recursive filter.FIR digital filter has linear phase characteristics and they and inherently stable but IIR filter do not have linear phase characterstics.The impulse response of IIR digital filter is infinite so this is known as IIR digital filter. They requires feedback because they depends on present input, past input and past output so they are also known as recursive filter[10]. The output sequence is given as for FIR filter- Y(n)= Y(n)=h(0)x(n)+h(1)x(n-1)+……+h(N)x(n-N) This sequence of output is finite so this is known as finite impulse response. Figure 1. FIR digital filter 2. FIR DIGITALFILTERDESIGN USING WINDOW METHOD The window method is one of the simplest methods for design of FIR filter among the two method i.e. fourier series and frequency sampling. In the frequency sampling it only works for particular frequency components and for other it does not works. Window methodiseasymethodandvarious windows can be used based on our application [5]. The desired unit sample response is given by hd(n)= h(n)=w(n)hd(n) Where hd(w) is desired frequency response characteristics.hd(n) is of infinite duration so hd(n) is truncated by finite length of window(M-1) which is w(n).so h(n) will be of finite length duration. In this paper three windows have been used which are- Hamming window-hamming window is given by wH(n)= Hanning window-hanning window is given by wHN(n)=
- 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1368 Kaiser window- Kaiser Window is given as wk(n)= Where 1 and 2 is the ripple in pass band and stopband.wp is pass band frequency and ws is stop band frequency. is a shape parameter which is given as And filter order is given by N= Attenuation A= -20 The Kaiser window is best among other window because they have less transition band than other. 3. ARTIFICIAL NEURAL NETWORK (ANN) Artificial neural network is comprised of a network of artificial neurons (node) [15].neural network is an algorithmthat based on the human brain works. They can build predicted model by learning the pattern of historical data.ANN made by interconnected processing element, these are known as node or neuron. Each node processes the small part of the task. The most common type of ANN is multi layer perceptron (MLP).in MLP the nodes are organized in layer. It is also known as parallel distributed processing system or connectionist system. The first layer is the input layer, the outer most layer stands for output layer. Between these two comes one or more layer known as hidden layer. The entire node is fully connected with the previous node. Input are multiplied by unique weight and added together by a small value called bias. This total is processed is by the function called the activation function. f(u)=w1u1+w2u2+w3u3+b Where w is weight is an input and b is a bias. It leaves the node as output, this process proceeds till information reached at the output layer and leaves it as the prediction for the independent variable. The network compares predicted and actual output. If these do not match it adjust all the weight and repeat the process till the network produce an accurate prediction for most of the observation. There is various algorithms use in ANN this are- Feed forward back propagation- a feed forward network has feedback paths meaning they can have signals travelling using loops. This system is nonlinear dynamic system because there is a loop which changes until it reaches state of equilibrium. In this the data flows in forward direction and error flows in reverse direction. Figure 2. Feed forward network Feed forward distributed time delay algorithm-In this algorithm whose basic function is to work on sequential data. Time delay represents the time shift usually form part of a larger pattern recognition system. It is mainly use to represent the relation between time and input. Radial basis function- It is a real value function whose value depends only on the distance from the origin or alternatively on the distance from some other point C, called a center. The norm is usually euclidean distance although other distance function is also possible. Radial basis function has more number of neurons than other algorithm so it gives better result than another algorithm. 4. FORMULATION OF PROBLEM The objective of this paper is to be estimated the cut-off frequency of proposed filter coefficients of band pass FIR digital filter which is achieved by FDA Tool using hamming, hanning and Kaiser Window. In this the input has been used as filter coefficient and target has been used as cut off frequency for which these filter coefficient have. Some filter coefficients have been chosen which is worked as test input and the cut off frequencies using NN Tool have been estimated for this test input. The comparison has been done between hamming, hanning, Kaiser Window. Feed forward back propagation and radial basisfunctionalgorithmofANN also have been compared. 5. EXPERIMENTATION Cut-off frequencies of band pass FIR digital filter have been calculated with three steps- i. Step 1: Band pass FIR digital filter has been designed by FDA Tool. The order of the filter has been chosen 38 because for low order the frequency response characteristics has not been properly obtained. The cut-off frequencies have been used in the form of normalized, varied from 0 to 1. Two cut off frequencies have been used say fc1 and fc2.The values have been selected as fc1=0.1 and fc2=0.3 and designed the filter. The value of filter coefficients h(n) have been exported on workspace. The same process have been repeated for fc1 from 0.1 to 0 .7 and fc2 from 0.3 to 0.9.Total 121 samples have been achieved. Out of these 121 samples, 111 samples have been used
- 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1369 for training and 10 as testing. For Kaiser Window has been selected as, ii. Step 2: The MS excel file has been created for training input, target and testing input. These files have been loaded to MATLAB workspace. iii. Step 3: A neural network has been created by using nntool box. Training algorithms have been selected as feed forward back propagation and radial basis function. After training, the network has been simulated by testing input. Then the cut-off frequencies have been compared by data from FDA Tool. Figure 3. Filter designing by FDA Tool for hamming window Cut off frequency calculation of Band pass FIR digital filter using hamming window a) Feed forward back propagation (FFBP) Figure 4. Trained network Figure 5.1 Result of FFBP network for hamming window Figure 5.2 Result of FFBP network for hamming window Figure 6. Regression plot of FFBP for hamming window Figure 7. Performance plot for FFBP for hamming window b) Radial basis function (RBF) Figure 8.1 result of RBF for hamming window
- 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1370 Figure 8.2 result of RBF for hamming window Cut off frequency calculation of Band pass FIR digital filter using handing window a) Feed forward back propagation (FFBP) Figure 9. Trained network Figure 10.1 Result of FFBP network for hanning window Figure 10.2 Result of FFBP network for hanning window Figure 11. Regression plot of FFBP for hanning window Figure 12. Performance plot for FFBP for hanning window b) Radial basis function (RBF) Figure 13.1 Result of RBF network for hanning window Figure 13.2 Result of RBF network for hanning window
- 5. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1371 Cut off frequency calculation of Band pass FIR digital filter using Kaiser Window a) feed forward back propagation (FFBP) Figure 14. Trained network Figure 15.1 Result of FFBP network for Kaiser Window Figure 15.2 Result of FFBP network for Kaiser Window Figure 16. Regression plot of FFBP for Kaiser Window Figure 17. Performance plot for FFBP for Kaiser Window b) radial basis function (RBF) Figure 18.1 Result of RBF network for Kaiser Window Figure 18.2 Result of RBF network for Kaiser Window
- 6. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1372 Test input (Filter coefficient) hamming Window (actual cut off Frequency) Output of artificial neural network (calculated cut off frequency) Mean Square Error FFBP RBF FFBP RBF h(n) fc1 fc2 fc1 fc2 fc1 fc2 fc1 fc2 fc1 fc2 h1(n) .155 .355 .1557 .3557 .155 .355 .00000049 .00000049 0 0 h2(n) .215 .415 .21743 .41743 .215 .415 .0000059049 .0000059049 0 0 h3(n) .275 .475 .27453 .47453 .275 .475 .0000002209 .0000002209 0 0 h4(n) .335 .535 .33561 .53561 .335 .535 .0000003721 .0000003721 0 0 h4(n) .395 .595 .3951 .5951 .395 .595 .00000001 .00000001 0 0 h5(n) .455 .655 .45499 .65499 .455 .655 .0000000001 .0000000001 0 0 h6(n) .515 .715 .51485 .71485 .515 .715 .0000000225 .0000000225 0 0 h7(n) .575 .775 .574 .774 .575 .775 .000001 .000001 0 0 h8(n) .635 .835 .63556 .83556 .635 .835 .0000003136 .0000003136 0 0 h9(n) .695 .895 .69486 .89486 .695 .895 .0000000196 0000000196 0 0 Table 2. Result of hanning window using ANN Test input (Filter Coefficient) hanning Window (actual cut off Frequency) Output of Artificial Neural Network (calculated cut off frequency) Mean Square Error FFBP RBF FFBP RBF h(n) fc1 fc2 fc1 fc2 fc1 fc2 fc1 fc2 fc1 fc2 h1(n) .155 .355 .15528 .35528 .155 .355 .0000000784 .0000000784 0 0 h2(n) .215 .415 .21459 .41459 .215 .415 .0000001681 .0000001681 0 0 h3(n) .275 .475 .27504 .47504 .275 .475 .0000000016 .0000000016 0 0 h4(n) .335 .535 .33394 .53394 .335 .535 .0000011236 .0000011236 0 0 h4(n) .395 .595 .3895 .5895 .395 .595 .00003025 .00003025 0 0 h5(n) .455 .655 .4532 .6532 .455 .655 .00000324 .00000324 0 0 h6(n) .515 .715 .51187 .71187 .515 .715 .0000097969 .0000097969 0 0 h7(n) .575 .775 .57321 .77321 .575 .775 .0000032041 .0000032041 0 0 h8(n) .635 .835 .63453 .83453 .635 .835 .0000002209 .0000002209 0 0 h9(n) .695 .895 .69285 .89285 .695 .895 .0000046225 .0000046225 0 0 Table 3. Result of Kaiser Window using ANN Test input (Filter coefficient) Kaiser Window (actual cut off Frequency) Output of artificial neural network (calculated cut off frequency) Mean Square Error FFBP RBF FFBP RBF h(n) fc1 fc2 fc1 fc2 fc1 fc2 fc1 fc2 fc1 fc2 h1(n) .155 .355 .15567 .35567 .155 .355 .0000004489 0000004489 0 0 h2(n) .215 .415 .21418 .41418 .21498 .41498 .0000006724 0000006724 .0000000004 .0000000004 h3(n) .275 .475 .27404 .47404 .27499 .47499 .0000009216 .0000009216 .0000000001 .0000000001 h4(n) .335 .535 .33475 .53475 .335 .535 .0000000625 .0000000625 0 0 h4(n) .395 .595 .39593 .59593 .395 .595 .0000008649 .0000008649 0 0 h5(n) .455 .655 .45541 .65541 .455 .655 .0000001681 .0000001681 0 0 h6(n) .515 .715 .5145 .7145 .515 .715 .00000025 00000025 0 0 h7(n) .575 .775 .57232 .77232 .575 .775 .0000071824 .0000071824 0 0 h8(n) .635 .835 .63531 .83531 .635 .835 .0000000961 .0000000961 0 0 h9(n) .695 .895 .69439 .89439 .695 .895 .0000003721 .0000003721 0 0 Table 1. Result of hamming window using ANN
- 7. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1373 6. RESULT In this experiment three tables have been achieved. First is for hamming window second is for hanning window and last third one is for Kaiser Window. By help of the table 1, 2 and 3. Various error graphs between desired and obtained frequency are drawn for various windows. Figure 19. Error graph between desired cut-off frequencies and obtained cut-off frequencies for hamming window with FFBP Figure 20. Error graph between desired cut-off frequencies and obtained cut-off frequencies for hamming window with RBF Figure 19 and 20 shows error graph between desired cut-off frequencies and obtained cut-off frequencies for hamming window with FFBP and RBF. Figure 21. Error graph between desired cut-off frequencies and obtained cut-off frequencies for hanning window with FFBP Figure 22. Error graph between desired cut-off frequencies and obtained cut-off frequencies for hanning window with RBF Figure 21 and 22 shows error graph between desired cut-off frequencies and obtained cut-off frequencies for hanning window with FFBP and RBF. Figure 23. Error graph between desired cut-off frequencies and obtained cut-off frequencies for Kaiser Window with FFBP Figure 24. Error graph between desired cut-off frequencies and obtained cut-off frequencies for Kaiser Window with RBF Figure 23 and 24 shows error graph between desired cut-off frequencies and obtained cut-off frequencies for Kaiser Window with FFBP and RBF. The cut off frequencies have been calculated from ANN using NN Tool and it can be easily seen that there is very less difference between actual and calculated cut off frequency. In this 121 samples have been used for training and 10 for
- 8. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056 Volume: 04 Issue: 06 | June -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1374 testing. So we have seen ANN gives efficient result in less time and it has been given result nearer to the actual one. 7. CONCLUSION For finding that whichwindowgivesbetterresultthemean square error (MSE) has been calculated for each window and for each algorithm. After this and it has been found that all window are given almost same result buthamming window is given the more efficient resultthanhanningand Kaiser Window. Out of two algorithms i.e. FFBP and RBF it has been found from various error graphs that RBF is best and better result is achieved by this almost same as actual one.RBF has highly accurate algorithm than other. 8. REFERANCE [1] Chonghua Li, “Design and Realization of FIR Digital Filters Based on MATLAB”, IEEE 2010. [2] Rohit Patel, .Mukesh Kumar, A.K. Jaiswal, Rohini Saxena,” Design Technique of Band pass FIR filter using Various Window Function” IOSR Journal ofElectronicsand Communication Engineering (IOSR-JECE), Volume 6,Issue 6 (Jul. - Aug. 2013), PP 52-57. [3]Gaurav Jain, R. P. Narwaria,”Designing of rectangular window based FIR filter for cutoff frequency calculation in artificial neural network”, International Journal of Engineering Science &ResearchTechnology(IJESRT),etal., 6(1): January, 2017. [4] Alia Ahmed Eleti and Amer R. Zerek, “FIR Digital Filter Design By Using Windows Method With MATLAB”, IEEE 2013. [5] John G. Proakis & Dimitis G. Manoakis, “Digital Signal Processing Principles, Algorithms, and Applications”, PRENTICE-HALLINTERNATINAL,INC.,ThirdEdition1996. [6] Alan V. Oppenheim, and Ronald W. Schafer, “Discrete- Time Signal Processing”. [7] Yogesh Babu Indoriya, Anil Mourya, Karuna Markam,”Design FIR digital filter using neural network”, international journal of advanced and innovativeresearch, vol. 4 issue 3. [8] Suchi Sharma, Anjana Goen,”Analysis and Performance Evaluation for Low Pass Filter Design Using Artificial Neural Network “International journal ofinnovativetrends in engineerining (IJITE), volume 19, nov. 02, 2016. [9] M. A. Singh and V. B. V. Thakare,”Artificial Neural Network Use for Design Low PassFIR Filtera Comparison”, International Journal of Electronics and Electrical Engineering Vol. 3, No. 3, June 2015. [10] Sanjit K. Mitra, “Digital signal processing A computer- Based Approach”, Department of Electrical and Computer Engineering University of California, McGraw-Hill, Second Edition 2002. [11] Suruchi Sharma,” Design and Analysis of FIR Filter using Artificial Neural Network”, et al International Journal of Computer and Electronics Research ,Volume 4, Issue 2, April 2015. [12] Aparna Tiwari, Vandana Thakre, Karuna Markam,”FIR Filter Design Using Artificial Neural Network”, International Journal of Computer & Communication Engineering Research (IJCCER), Volume 2 - Issue 3 May 2014. [13]Ajeet Maheshwari, Karuna Markam,”Design A Bartlett Window Based Digital Filter by Using GRNN”, International Journal of Innovative Research in Science, Engineering and Technology Vol. 3, Issue 7, July 2014. [14] S. Haykins, “Neural Networks –A comprehensive foundation”, Prentice –Hall of India Private Limited, New Delhi, (2003). [15] Artificial neural network by B.Yegnanarayana. [16] Mathworks.com [17]digital signal processing by Dr.J.S. Chitode.