International Journal of Computer & Communication Engineering Research (IJCCER) Volume 2 - Issue 3 May 2014 Design Technique of Lowpass FIR filter using Various Function Aparna Tiwari, Vandana Thakre, Karuna Markam Deptt. Of ECE,M.I.T.S. Gwalior, M.P, India Abstract- There are various sophisticated Computer Aided Design tools are available to make the digital filter fast and power efficient. Filter design and analysis tool (FDA) is one of the Computer Aided Design tool available with MATLAB which enables design of the digital filter blocks faster and more accurate Finite Impulse Response, filters are one of the primary types of filters used in Digital Signal Processing. For the design of Low pass FIR filters complex calculations are required.mathematically, by substituting the values of Pass band, transition width, pass band ripple, stop band attenuation, sampling frequency in any of the methods from window method, frequency sampling method or optimal method we can get the values of filter coefficients h(n).for removing noise or cancellation of noise we use various type of digital filter.in this paper we propose design technique of lowpass FIR filter using various type of window function using Hamming, Hann,Rectangular window and Kaiser window and will analyse these windows behaviour in higher order. Kaiser window is the best window function in FIR filter design. Using this window we can realize that FIR filter is simple and fast. Keywords: FIR filter, LTI, lowpass filter, MATLAB. frequency passband and reject the frequency other than the passband specification. Then the filtered signal can be further used for the signal feature extraction. Filtering can also be applied to perform applications such as noise reduction, frequency boosting, digital audio equalizing, and digital crossover, among others. II. FIR DIGITAL FILTER 2.1 Basic Concept of FIR filte: The basic structure of FIR filter consists of multipliers, delay elements and adders to create the filter s output. The difference equation of N order of the recursive digital filters (FIR) can be represented as: Where, y (n) is the output signal, h(n) is the filter coefficients and k is the order of the filters. I. INTRODUCTION The developments in electronic technology are taking place at a tremendous speed. Recently, Digital Signal Processing (DSP) is used in numerous applications such as video compression, digital set-top box, cable modems, digital versatile disk, portable video systems/computers, digital audio, multimedia and wireless communications, digital radio, digital still and network cameras, speech processing, transmission systems, radar imaging, acoustic beam formers, global positioning systems, and biomedical signal processing. The field of DSP has always been driven by the advances in DSP applications and in scaled Very- Large-Scale-Integrated (VLSI) [1] technologies. In different areas digital filter design techniques are widely used. The digital filter consist of both software and hardware implementation. In the digital filter, the input and output signals are digital or discrete time sequence. Digital filters [3] are linear time invariant (LTI) systems which are characterized by unit sample response. These filters are portable and highly flexible. It has minimum or negligible interference noise and other effects. In storage and maintenance digital filters are easier. Digital filters reduce the failure time. Digital filters are categorized in two parts as finite impulse response (FIR)[6] and infinite impulse response (IIR)[2]. In comparison to IIR filters, the FIR filters have greater flexibility to control the shape of their 1 magnitude response. According to the frequency characteristics digital filter can be divided-lowpass, highpass, bandpass, and bandstop. The realization of FIR filter is non-recursive in comparison to IIR filter. Bandpass filtering plays an important role in DSP applications. It can be used to pass the signals according to the specified Figure.1: N-order FIR digital filter block diagram We can express the output signal in frequency domain by convolution of the input signal x(n) and the impulse response h(n). Y (n) = x (n)*h (n) The output signal is determined as, In differential equation, the coefficient equals to the successive value h (n) of unit-sample response. The system function H (z) can be expressed as: H (z) is polynomial of..this means that all poles are only plotted at the origin of the Z-plane. FIR filters can be designed in different ways, for exa mple window method, frequency sampling method, weighted least squares method, minimax method and http://ijccer.org e-issn: 2321-4198 p-issn: 2321-418X Page 130
equiripple method. Out of these methods, the window technique is most conventional method for designing FIR filters. 2.2 function method of FIR filter design: The basic design principles of window function are to calculate h (n) by the anti-fourier transform based on the ideal demanded filter frequency response formula of h (n) is shows as The Because h (n) is infinitely long, we have to deal with it by window function to get to the unit impulse response h (n). Now it is written as Where w (n) is the window function. Fixed window and adjustable window are the two categories of window function. Blackman window, Hanning, Hamming and rectangular window are mostly used fixed window function. Kaiser window is a type of adjustable window function. 2.2.1 Hanning window: The Hanning window is a raised cosine window and can be used to reduce the side lobes while preserving a good frequency resolution compared to the rectangular window. The hanning window is defined as The parameter β determines the shape of the window and thus controls the trade-off between main-lobe width and side-lobe amplitude. III. FIR FILTERDESIGN USING FDA TOOL The Filter Design and Analysis (FDA) tool works with MATLAB and the signal processing toolbox to provide a complete environment for start to finish filter design. The FDA tool supports many advanced techniques not available in SP tool. FDA tool is used to design filters, quantize filter, analyze filter, modify existing filter designs, realize simulink models of quantized direct form FIR filters. 3.1 Filter Specifications: Where W (n) is the window function. Fixed window, in proposed method we have taken Blackman window, Hanning, Hamming and rectangular window and Kaiser window.we analysed using different orders and compared all windows behaviour in higher order. Table 1: Filter Specification Paramaeters Filter Type Design method Filter order Cut-off frequency FIR w 2.2.2 Hamming window : The hamming window is, like the Hanning window, also a raised cosine window. The hamming window exhibits similar characteristics to the Hanning window but further suppress the first side lobe. The hamming window is defined as IV. RESULT AND SIMULATION From table 1 we analyzed the filter using Blackman window by FDA tool in the MATLAB and the response of the filter is given in figure 2,3 and 4 respectively at the order 35, 42 and 50. 2.2.3 Rectangular window: The rectangular window is sometimes known as a Dirichlet window. Its ideal frequency response is smeared out by a sinc-like function. 2.2.4 Kaiser window: The Kaiser window with parameter β is defined as Figure.2: FIR Rectangular window (N=35) http://ijccer.org e-issn: 2321-4198 p-issn: 2321-418X Page 131
Figure.3: FIR Rectangular window (N=42) Figure.5 FIR Hamming window (N=35) Figure.4: FIR Rectangular window (N=50) Figure.6: FIR Hamming window (N=42) 4.2 Hamming : We analyzed the filter using Hamming window or fixed widow by FDA tool in the MATLAB and the response of the filter is given in figure 5, 6 and 7 respectively at the order 35, 42 and 50. Figure 7: FIR Hamming window (N=50) http://ijccer.org e-issn: 2321-4198 p-issn: 2321-418X Page 132
4.3 Hanning : We analyzed the filter using Hanning window or fixed widow by FDA tool in the MATLA B and the response of the filter is given in figure 8, 9 and 10 respectively at the order 35, 42 and 50. Figure.8: FIR Hanning window (N=35) Figure.9: FIR Hanning window (N=42) Figure.10: FIR Hanning window (N=50) http://ijccer.org e-issn: 2321-4198 p-issn: 2321-418X Page 133
4.4 Kaiser : We analyzed the filter using Kaiser window by FDA tool in the MATLAB and the response of the filter is given in figure 11, 12 and 13 respectively at the order 35, 42 and 50. Figure.11: FIR Kaiser window (N=35) Figure.12: FIR Kaiser window (N=42) Figure.13: FIR Kaiser window (N=50) http://ijccer.org e-issn: 2321-4198 p-issn: 2321-418X Page 134
technique Rectangular Hamming Hanning Kaiser (β=3.2) Table 2: Comparison between different window techniques Order of the filter Normalised trainsition width of main lobe No. of side lobes Minimum stopband attenuation 35 0.0250 8-21 db 42 0.0209 10 50 0.01764 13 35 0.09166 10-53 db 42 0.07674 13 50 0. 06470 14 35 0.08611 9-44 db 42 0.07209 10 50 0.006078 11 35 0.06199 10 > -50db 42 0.05190 11 50 0.04375 14 From the table 2 we can see that as the order of the FIR filter increases the number of the side lobes also increases and width of the main lobe is decreased, that it is tending to sharp cut off that is the width of the main lobe decreased. If the width of the main lobe reduces then the number of the side lobes gets increased. So there should be a compromise between attenuation of side lobes and width of main lobe. On comparing all methods, the Hann has the smallest side lobes at any order but the width of the main lobe is increased. In the Kaiser window for the lower order the width of the major lobe is less than the other windows except rectangular window but as rectangular window passband gain is one and magnitude of sidelobes doesn t considerably suprresd (stopband attenuation near main lobe), it don t preferably used. For Kaiser window it is genrally greater than 50 db and depends on formula - 20log(δ), wher δ is stopband ripple. The Kaiser window gives best result. Therefore it is most commonly used window for FIR filter design. V. CONCLUSION Dig ital filter can play a major role in speech signal processing applications such as, speech filtering, speech enhancement, noise reduction and automatic speech recognition. The kaiser window gives the minimum Normalised transition width of mainlobe 0.04375 after Rectangular window but as it has lowest stopband attenuation cant preferably used and as Kais er window has better s topband attenuation (>50 db)for filter order 50 which means this window has less transition width and introduces more ripple. REFERENCES [1] S. Salivahanan, A. Vallavaraj, C. Gnanaapriya, Digital Signal Processing, Tata McGraw-Hill, 2000. [2] Sonika Gupta, Aman Panghal Performance, Performance Analysis of FIR Filter Design by Using Rectangular, Hanning and Hamming s Methods, International Journal of Advanced Research in Computer Science and Soft ware Engineering Volume 2, Issue 6, June 2012. [3] Chonghua Li, Design and Realization of FIR Digital Filters Based on MATLAB, IEEE 2010. [4] Saurabh Singh Rajput, Dr. S. S. Bhadauria, Implementat ion of FIR Filter using Efficient Function and its Application in Filt ering a Speech Signal, International Journal of Electrical, Electronics and Mechanical Controls Volume 1, Issue 1, November 2012. [5] IOSR Journal of Electronics and Communication Engineering (IOSR-JECE) Volume 6, Issue 6 (Jul. - Aug. 2013), Design Technique of Bandpass FIR filter using Various Function. [6] J.G. Proakis and D.G. Manolakis, Digital Signal Processing-Principles,Algorithms and Applications New Delhi: Prentice-Hall, 2000. [7] Magdy T. Hanna, Design of Linear Phase FIR Filters with a Maximally Flat Passband, IEEE Trans. Circuits Syst. II, 43 (2), 142 147, 1996. [8] Soo-Chang Pei and Peng-Hua Wang, Design of Equiripple FIR Filters With Constraint Using a Multiple Exchange Algorithm, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 49, NO. 1, JANUARY 2002 http://ijccer.org e-issn: 2321-4198 p-issn: 2321-418X Page 135