Performance Analysis of Finite Impulse Response (FIR) Filter Design UsingVarious Window Methods

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					International Journal of Scientific Research Engineering & Technology (IJSRET)
Volume 1 Issue 5 pp 018-021       August 2012                              ISSN 2278 – 0882

 Performance Analysis of Finite Impulse Response (FIR) Filter Design Using
                        Various Window Methods
                                                       Era Singhal
                                                   Assistant Professor,
                                            IIMT Engineering College, Meerut

ABSTRACT                                                       areas.
Digital filters that incorporate digital-signal-processing      II. BASIC PRINCIPLE OF FIR FILTER
(DSP) techniques have received a great deal of                 Finite Impulse Response (FIR) digital filters have
attention in technical literature in recent years. Digital     attracted a great deal of interest because they are
filters offer features that have no counterparts in other      inherently stable structures which are much less
filter technologies. In this paper , design technique of       sensitive to quantization errors than filters of the
lowpass FIR filter using various window methods are            recursive type. The basic principle of FIR contains a
presented. The stability, filter order and the filter          series of multiplication and addition. The discrete
coefficients for different window methods are                  time-domain equation of the FIR filters can be
demonstrated. Among various window methods it is               expressed as (1):
shown that filter design by using hamming window
method is the best because it has fewer ripples in
passband, more stability and has a linear phase as
compared to other window techniques.

 Keywords: FIR Filter, Rectangular, Hanning and                where, y(n) is the current filter output, y(n-1) are
Hamming windows                                                previous filter outputs, the x(n-1) are current
                                                               corresponding to the zeros of the filter, or previous
  I. INTRODUCTION                                              filter inputs the ai are the filter’s feed forward
Filter is a device or process that removes from a signal       coefficients corresponding to the zeros of the filter, the
some unwanted component or feature. Filters are                bi are the filter’s feedback coefficients corresponding
widely employed in signal processing and                       to the poles of the filter, and N is the filter’s order. Its
communication systems in applications such as                  basic structure is shown in Fig.1 where the structure of
channel equalization, noise reduction, radar, audio            FIR filter in hardware is mainly composed of the shift
processing, video processing, biomedical signal                register, adder and multiplier.
processing, and analysis of economic and financial
data. In comparison to analog filters, digital filters are
having better stability, realibility, easy to design, more
flexible and high accuracy. Digital filters come in two
flavors: Finite Impulse Response (FIR) and Infinite
Impulse Response (IIR) filters. As the FIR filter have a
lot of good features such as only zeros, non-recursive
,the system stability, operation speed quickly, linear
phase characteristics and design flexibility, so that FIR
has been widely used in the digital audio, image                               Fig: 1 Structure of FIR Filter
processing, data transmission, biomedical and other

                                                     IJSRET @ 2012
International Journal of Scientific Research Engineering & Technology (IJSRET)
Volume 1 Issue 5 pp 018-021       August 2012                            ISSN 2278 – 0882

                                                                                  h(n) = hd (n) w(n)
There are essentially three well-known methods for            The FIR filter design process via window functions can
FIR filter design namely:                                     be split into several steps:
(1) The window method                                         1. Defining filter specifications;
(2) The frequency sampling technique                          2. specifying a window function according to the filter
(3) Optimal filter design methods                             specifications;
                                                              3. Computing the filter order required for a given set of
The design of FIR filters using windowing is a simple         specifications;
and quick technique. In the window method, the                4. Computing the window function coefficients;
desired frequency response specification Hd(w),               5. Computing the ideal filter coefficients according to
corresponding unit sample response hd(n) is                   the filter order;
determined using the following relation:                      6. Computing FIR filter coefficients according to the
                                                              obtained window function and ideal filter coefficients;
                                                              7. If the resulting filter has too wide or too narrow
                                                              transition region, it is necessary to change the filter
                                                              order by increasing or decreasing it according to needs,
  Where,                                                      and after that steps 4, 5 and 6 are iterated as many
                                                              times as needed.

                                                              The final objective of defining filter specifications is to
                                                              find the desired normalized frequencies (ωc, ωc1,
In general, unit sample response hd(n) obtained from          ωc2), transition width and stopband attenuation. The
the above relation is infinite in duration, so it must be     window function and filter order are both specified
truncated at some point say n = N-1 to yield an FIR           according to these parameters.
filter of length N (i.e. 0 to N-1). Then hd(n) the impulse    Most commonly used windows are rectangular,
response of a desired FIR filter is given by:                 Hamming, Hanning windows.

                                                              1. Rectangular window:

The Frequency response of the desired FIR filter is
obtained by truncating eq .(2) to length N.                   2. Hanning window:


Direct truncation of hd(n) to M terms to obtain h(n)
leads to the Gibbs phenomenon effect which manifests          Non-Causal:
itself as a fixed percentage overshoot and ripple before
and after an approximated discontinuity in the
frequency response due to the non-uniform
convergence of the Fourier series at a discontinuity.
Thus the frequency response obtained by using above
equation contains ripples in the frequency domain. In
order to reduce the ripples, hd(n) is multiplied by a
window function w(n) whose duration is finite.                 3. Hamming Window:

                                                     IJSRET @ 2012
International Journal of Scientific Research Engineering & Technology (IJSRET)
Volume 1 Issue 5 pp 018-021    August 2012                       ISSN 2278 – 0882



                                                            Fig.: 3 Magnitude Response of Hanning window
 4. Blackman Window:



                                                                Fig.: 4 Phase Response of Hanning Window

 5. Bartlett (Triangular) window:

Rectangular, Hamming , Hanning and Blackman are
the raised cosine windows.

IV. SIMULATION AND RESULT ANALYSIS                         Fig.: 5 Magnitude response of Hamming Window
In simulation, filter order=20, sampling frequency=
48000Hz, Cut-off frequency = 10800Hz

1. Magnitude response of rectangular window

                                                                Fig.: 6 Phase Response of Hamming windows

     Fig.: 2 Phase response of rectangular window

                                                IJSRET @ 2012
International Journal of Scientific Research Engineering & Technology (IJSRET)
Volume 1 Issue 5 pp 018-021        August 2012                     ISSN 2278 – 0882

                                                           [3] John. G. Proakis, Dimitris G. Manolaokis, “Digital
                                                           Signal Processing: Principles, Algorithms, And
                                                           Applications”, 4th Edition,Pearson Education , 2007
                                                           [4] Arojit Roychowdhury, “Fir Filter Design
                                                           Techniques”, Electronic System group,Nov 2002.
                                                           [5] Edmund Lai, “Practical Digital Signal Processing
                                                           for Engineers and Technicians” 1st Edition, 2003.
                                                           [6] Suvarna Joshi and Bharati Ainapure, “FPGA
                                                           Based FIR Filter”, 2010 International Journal of
   Fig.: 7 Magnitude response of Blackman window           Engineering Science and Technology
                                                           [7] Anthony G. Constantinides , “An Algebraic
                                                           Approach to the Estimation of the Order of FIR Filters
                                                           from Complete and Partial Magnitude and Phase
                                                           Specification” , IEEE 2005.
                                                           [8] Gennaro Evangelista, “Design of Optimum High
                                                           Order Finite Word length Digital FIR Filters with
                                                           Linear Phase”

    Fig.: 8 Phase Response of Blackman windows

                         Fig.: 9

FIR Filter design by using Hamming window is the
best because it has less ripples in passband and also
has the narrowest mainlobe and sidelobes as small as
possible compare to other window techniques. Also,
the stability is more and has a linear phase.

[1] Emmanuel      C.     Ifeachor,   “Digital    Signal
Processing”, 2nd Edition, Pearson Education Ltd., 2002.
[2] S. Salivahanan, A.Vallavaraj, “Digital Signal
Processing”, 2nd        Edition, Tata McGraw Hill
Educations Private Limited, 2010

                                                  IJSRET @ 2012

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