> z|opqrstuvwxy[ \bjbj dΐΐH06TT!!$$$$$$$P%\c%<$]%&(&&&K*K*K*\\\\\\\$1`b\]$K**")*"K*K*\!!&&.K]222K*^!&&$&\2K*\22.M#O& a$-M\a]0]Nec?/ec4O,2Oec$QK*K*2K*K*K*K*K*\\1K*K*K*]K*K*K*K*ecK*K*K*K*K*K*K*K*K*T ] : DESIGN OF FIR BSF USING MODIFIED HAMMING WINDOW
Smt.D.Swetha1, Ms.K.Suneetha Krishna2, Ms.A.Saritha3 & Ms.V.Shamily4
Asst.Professor, Asst.Professor, IV/IV ECE
Dept of ECE, Dept of ECE, BWEC
Bapatla Engineering College, BWEC Bapatla, Guntur
Bapatla, Guntur. Bapatla, Guntur. HYPERLINK "mailto:adapa.saritha@gmail.com"adapa.saritha@gmail.com
HYPERLINK "mailto:swethachand7@gmail.com"swethachand7@gmail.com HYPERLINK "mailto:suneethakrishna.kosaraju@gmail.com"suneethakrishna.kosaraju@gmail.com HYPERLINK "mailto:vadranam.shamily@gmail.com"vadranam.shamily@gmail.com
ABSTRACT: This report deals with design of Band Stop Filter (BSF) of FIR digital filter using modified hamming window technique. In the beginning, filter types and design techniques of FIR filter are discussed in detail with their advantages and disadvantages. FIR filter designed using modified coefficient of the Hamming window function provides smaller main lobe width and sharp transition band compare to Hamming window. Hence this type of filter plays very important role in spectral analysis of different types of signal. In spectral analysis applications a small main lobe width of the window function in frequency domain is required for increasing the ability to distinguish two closely spaced frequency components. This designed band-stop FIR filter using modified window technique is compared with Hanning window and Hamming window are shown in fig. window functions. Finally the simulation results show that the filter designed using modified window function is more efficient than Hanning and Hamming window function
Keywords Modified Hamming window, Hamming window, Hanning window, Band-stop filter.
I: Introduction
The digital signal processing has become an extremely important subject. A fundamental aspect of digital signal processing is filtering. A digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. There are two types of digital filters on the basis of the impulse response of the filter:
Infinite Impulse Response (IIR) filters, and
Finite Impulse Response (FIR) filters.
Digital filters with infinite duration impulse response referred to as IIR filters. IIR filters are recursive type filters where by the present output depends on the present input, past input and past outputs. Digital filters with finite duration impulse response referred to as FIR filters. FIR filters are non-recursive type filters where by the present output depends on present input and past inputs. FIR filters are widely used than IIR filters, because FIR digital filters have an exactly linear phase, always stable, non-recursive structure and arbitrary amplitude-frequency characteristic etc. [1], [3]. In view of the design and simulation analysis, the design of digital filter is quickly and efficiently achieved by using powerful computing capabilities of MATLAB [2].
FIR filter is described by the difference equation.
y(n)= QUOTE ..(1)
where x(n) is the input signal and h(n) is the impulse response of FIR system.
To design the FIR filters the simple and effective way is window method. In this method infinite impulse response of the ideal prescribed filter is truncated by using a window function. The main advantage of this design technique is that the impulse response coefficient can be obtained in closed form and can be determined very quickly. The window method is simple in operation, easy to understand and very convenient method for designing digital FIR filter [4].
The most popular and widely used window functions are; Rectangular window, Hanning window, hamming window and Kaiser window. The Rectangular window response provides sidelobes which gives rise to ripples in passband and stopband. The amplitude of the ripples is determined by the amplitude of the sidelobes. For the rectangular window, the amplitude of the sidelobes is unaffected by the length of the window. But the main lode width of rectangular window is narrower and higher. For the fixed length the Hanning window has significantly lower side-lobe amplitude but the main lobe width is wider compared to Rectangular window. The Hamming window also has the same main lobe width of Hanning window but it generates lesser oscillations in the side lobes than Hanning window. Hence Hamming window is generally preferred rather than Hanning window. The Kaiser window is a kind of adjustable window function which provides independent control of the main lobe width and ripple ratio but the Kaiser window has the disadvantage of higher computational complexity due to the use of Bessel functions.
With regard to these window methods a modified coefficient of Hamming window technique is developed here. FIR filter designed using modified coefficient of the Hamming window function provides smaller main lobe width and sharp transition band compared to Hamming window. This type of filter is very useful in spectral analysis of different types of signals. Further, we compare of the input and output signal in frequency and time domain using modified window, Hanning window and Hamming window functions. The simulation results show that the filter designed using modified window function is more efficient than Hanning and Hamming window function.
2. DESIGN METHODS OF FIR FILTERS
There are different methods for design of FIR digital filter.
Fourier series method
The window method
Frequency sampling method
Optimal filter design method
Fourier series method:
In this method from the desired frequency response specification Hd(w), corresponding unit sample response hd(n) is determined using the following relation
hd(n)= QUOTE 2
WhereHd(ejw)= QUOTE ....3
In general, unit sample response hd(n) obtained from the above relation is infinite in duration, so it must be truncated at some point say n= QUOTE to yield an FIR filter of length N. But abrupt truncation of the Fourier series provides oscillations in the passband and stopband, which is known as Gibbs phenomenon. These oscillations are due to slow convergence of the Fourier series.
Window method:
To reduce the oscillations in Fourier series method, the Fourier coefficients are modified by multiplying the infinite impulse response by a finite weighing sequence w(n) called a window. FIR filters design using window method is simple, effective and easy to understand. But this method is not suitable for any magnitude response and always integration computations are not easy. Hence the window method is not flexible.
Frequency sampling method:
In this method the given frequency response is sampled at a set of equally spaced frequencies to obtain N samples. Thus, sampling the continuous frequency response Hd(w) at N points essentially gives us the N-point DFT of Hd(2pnk/N). Thus by using the IDFT formula, the filter coefficients can be calculated using the following formula
h(n)= QUOTE QUOTE 4
The advantage of frequency sampling method is unlike the window method, this technique can be used for any given magnitude response.The disadvantage with this method is the frequency response obtained by sampling is equal to the desired frequency response only at the sampled points. At the other points, there will be a finite error present.
Optimal Filter design method:
To reduce the error in frequency sampling method this method is used and this method is best method to design the FIR filter. The basic idea of this method is to design the filter coefficients again and again until a particular error is minimized. But to determine the filter coefficients by using optimal filter design method is very complex.
The choice of technique to design the filter depends heavily on the decision of designer whether to compromise accuracy of approximation or ease of design. Optimal Filter design method is used for approximation where as window method is used for ease of design.
3. DESIGN PROCEDURE OF FIR FILTER USING MODIFIED WINDOW
Design steps of FIR band stop filter [3, 2]:
Specify the ideal frequency response
Hd (ejw) =1, when 0d"|w|d"wc1
Hd (ejw) =0, when wc1d"|w|d"wc2
Hd (ejw) =1, when wc2d"|w|d" ws/2
The cutoff frequency band of the ideal band stop filter is [wc1 wc2] and ws is sampling frequency.
The impulse response hd(n) of ideal filter was obtained by applying inverse Fourier transform to the ideal frequency response Hd(ejw) of digital filter.
The window function w(n) and window length N were identified according to the main lobe width and side lobe attenuation of the window function.
In this view of design of band-stop filter three common window functions are used. They are described as follows:
Hanning window function
w(n)=0.5-0.5cos QUOTE , 0d"nd"N-1
=0, otherwise
Hamming window function
w(n) =0.54-0.46cos QUOTE , 0d"nd"N-1
=0, otherwise
A Generalized Hamming window function
w(n)=-(1-)cos QUOTE , 0d"nd"N-1
=0, otherwise
Modified coefficient of Hamming window function for =0.72
w(n)=0.72-0.28cos QUOTE , 0d"nd"N-1
=0, otherwise
Obtain values of causal linear phase FIR coefficients h(n) by multiplying hd(n) and w(n).
h(n)=hd(n)*w(n)
The frequency response of designed FIR filter is obtained by taking Fourier transform of h(n).
H (ejw) = QUOTE
4. RESULT OF WINDOWS USING MATLAB
The frequency characteristic curves of Band-stop FIR filter with different window methods and their comparison plots are shown below. Fig1, 2, 3, and 4 represents the frequency characteristic curve of Hanning, Hamming, Modified Hamming and comparison of Hanning, Hamming and Modified window respectively. From the figures we can observe that the filter designed using modified hamming window has smaller main lobe width. Hence it can be used in spectral analysis
Fig 1: Hanning, window Fig2: Hamming window
Characteristic curve characteristic curve
Fig3: Modified Hamming Fig4: comparison of
Window characteristic curve Hanning, Hamming
and Modified window
5. CONCLUSIONS
In Signal processing applications digital filters are more preferable than analog filters. The digital filters are easily designed and also easy to use in various types of signal filtering applications. The choice of technique to design the filter depends heavily on the decision of designer whether to compromise accuracy of approximation or ease of design. In this view band-stop FIR filter has been designed using Modified coefficient of the Hamming window function and simulated with MATLAB programs. The results show that the filter design using Modified window function has a small main lobe width and sharp transition band compared to Hamming and Hanning window function. So that for same length this window function provides efficient results compare to Hanning and Hamming window function and this type of filters are very useful in spectral analysis and many other applications. On the bases of the desired filter characteristics/012>?lm|~
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6.REFERENCES:
J.G. Proakis and D. G. Manolakis, Digital Signal Processing Principles, Algorithms and Applications 3rd Edition Prentice-Hall, 2002.
Sanjit K. Mitra, Digital Signal Processing: A Computer-base approach, Tata McGraw-Hill, 2nd Edition 2001.
P. Ramesh Babu, Digital Signal Processing 4th Edition.
Sonika Gupta, Aman Panghal Performance Performance analysis of FIR Filter Design by using Rectangular, Hanning, and Hamming window methods International Journal of Advanced Research in Computer Science and Software Engineering Volume 2, Issue 6, June 2012.
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