Design Technique of Low-Pass Filter Using Different Window

Design Technique of Low-Pass Filter Using Different Window

Manira Khatun

Assistant Professor, Department of Electronics and Communication Engineering, Mallabhum Institute of Technology P.S: Bishnupur, Dist: Bankura-722122, W.B, India

AbstractIn the field of signal processing and communication, digital filter plays pivotal role. Digital FIR filter designed by different window techniques perform better for reducing noise from signal. In this paper , we design low-pass filter by using various window methods such as Hanning, Hamming, Blackman, Kaiser .This paper also provides comparative study of lowpass filters using above window. It has been seen that Kaiser window is better with respect to Hanning, Hamming, Blackman window.

Keyword – Blackman window, FIR filter, Hamming window, Hanning window, Kaiser window, Lowpass filter, MATLAB .

1. INTRODUCTION

   In different areas digital filter design techniques are widely used. In the digital filter, the input and output signals are digital or discrete time sequence. Digital filters are categorized in two parts as finite impulse response (FIR) and infinite impulse response (IIR). According to the frequency characteristics digital filter can be divided-lowpass, highpass, bandpass, and bandstop. Filtering can be applied to perform

   1. The window method

   2. The frequency sampling technique

   3. Optimal filter design methods [2]

      • Window design method

        The window design method is first designs an ideal IIR filter and then truncates the infinite impulse response by multiplying it with a finite length window function. The result is a finite-

        impulse response filter whose frequency response is modified from that of the IIR filter. Multiplying the infinite impulse by the window function in the time domain results in the frequency response of the IIR being convolved with the frequency response of the window function.[3]

        Some of the windows commonly used are as follows:

        • Hanning window : The Hanning window is a raised cosine window . The hanning window is defined as

   0.5 0.5 2n

   applications such as noise reduction, frequency boosting, digital audio equalizing, and digital crossover, among others.

   w(n)=

   1

   0 , elsewhere

   , for n = 0 to M 1

2. FIR DIGITAL FILTER

   Finite impulse response (FIR) filter is a filter whose impulse response is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR)

   • Hamming window: The hamming window is also a raised cosine window. The hamming window is defined as

     0.54 0.46 2n

     filters, which may have internal feedback and may continue to respond indefinitely.

     w(n)=

     1

     0 , elsewhere

     , for n = 0 to M 1

     FIR filters offer the following advantages over the IIR filters:

     1. They can have an exact linear phase.

     2. They are always stable.

     3. The design methods are generally linear.

   • Blackman window: The Blackman window is defined as

     0.42 0.5 2n + 0.08 4n

     1. They can be realized efficiently in hardware. v.The filter start-up transients have finite duration. [1]

     w(n)=

     0 ,

     0 to M 1

     1

     elsewhere

     M 1

     , for n =

     A. Fir Filter design

     To design a filter means to select the coefficients such that the system has specific characteristics. The required characteristics are stated in filter specifications. Most of the

   • Kaiser window: The Kaiser window with parameter is defined as [2]

   1(n )2

   time filter specifications refer to the frequency response of the filter. There are essentially three well-known methods for FIR filter design namely:

   w(n)=

   0 to M 1

   ()

   0 , elsewhere

   , for n =

3. DESIGN TECHNIQUE OF LOWPASS FIR FILTER USING

   VARIOUS WINDOW FUNCTION :

   A. Filter Specifications:

   Parameters	Values
   Filter Type	Lowpass
   Design method	FIR windows(=0.37 for Kaiser window only)
   Filter order	30,40
   Sampling frequency	48000HZ
   Cut-off frequency	10800HZ

   Table.1 Filter specification

   0

   -5

   Phase (radians)

   -10

   -15

   -20

   -25

   -30

   Phase Response

   hann-40

4. RESULT AND SIMULATION

   1. Haanning window:

      From the table.1, we analyzed the lowpass filter using Hanning window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.

      -35

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.2b Phase response of LPF using Hanning window of order40

   2. Hamming window:

      From the table.1, we analyzed the lowpass filter using Hamming window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.

      Magnitude Response (dB)

      0

      -10

      -20

      Magnitude (dB)

      -30

      -40

      -50

      -60

      -70

      -80

      -90

      Magnitude Response (dB)

      				hann-30

      0 5 10 15 20

      Frequency (kHz)

      Fig.1a Magnitude response of LPF using Hanning window of order30

      0

      -10

      Magnitude (dB)

      -20

      -30

      -40

      -50

      -60

      -70

      -80

      							ham	-30
      				/td>

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.3a Magnitude response of LPF using

      Hamming window of order30

      0

      -5

      Phase (radians)

      -10

      -15

      -20

      -25

      Phase Response

      							ha	nn-30

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.1b Phase response of LPF using Hanning window of order30

      0

      -5

      Phase (radians)

      -10

      -15

      -20

      -25

      Phase Response

      								ha	m-30

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.3b Phase response of LPF using

      Hamming window of order30

      0

      Magnitude (dB)

      -20

      -40

      -60

      -80

      Magnitude Response (dB)

      							han	n-40

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.2a Magnitude response of LPF using

      Hanning window of order40

      0

      -10

      Magnitude (dB)

      -20

      -30

      -40

      -50

      -60

      -70

      Magnitude Response (dB)

      								ha	m-40

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.4a Magnitude response of LPF using

      Hamming window of order40

      0

      -5

      Phase (radians)

      -10

      -15

      -20

      -25

      -30

      -35

      Phase Response

      								ha	m-40

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.4b Phase response of LPF using

      Hamming window of order40

      0

      -5

      Phase (radians)

      -10

      -15

      -20

      -25

      -30

      -35

      -40

      Phase Response

      							blm	an-40

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.6b Phase response of LPF using Blackman window of order40

   3. Blackman window:

      From he table.1, we analyzed the lowpass filter using Blackman window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.

   4. Kaiser window:

      From the table.1, we analyzed the lowpass filter using Kaiser window in MATLAB and the response of the filter is given in fig.1 &fig.2 respectively at the order 30 &40.

      0

      -20

      Magnitude (dB)

      -40

      -60

      -80

      -100

      Magnitude Response (dB)

      							blm	an-30

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.5a Magnitude response of LPF using Blackman window of order30

      0

      -10

      Magnitude (dB)

      -20

      -30

      -40

      -50

      -60

      -70

      Magnitude Response (dB)

      								kai-	30

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.7a Magnitude response of LPF using

      Kaiser window of order30

      0

      -5

      Phase (radians)

      -10

      -15

      -20

      -25

      -30

      Phase Response

      blman-30

      0

      Phase (radians)

      -5

      -10

      -15

      -20

      							kai-	30

      Phase Response

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.5b Phase response of LPF using

      Blackman window of order30

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.7b Phase response of LPF using

      Kaiser window of order30

      0

      -20

      Magnitude (dB)

      -40

      -60

      -80

      -100

      Magnitude Response (dB)

      							blm	an-40

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.6a Magnitude response of LPF using Blackman window of order40

      0

      -10

      Magnitude (dB)

      -20

      -30

      -40

      -50

      -60

      -70

      Magnitude Response (dB)

      								kai	-40

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/sample)

      Fig.8a Magnitude response of LPF using

      Kaiser window of order40

      0

      -5

      Phase (radians)

      -10

      -15

      -20

      -25

      -30

      Phase Response

      								kai-	40

      0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

      Normalized Frequency ( rad/smple)

      Fig.8b Phase response of LPF using

      Kaiser window of order40

      Table-2

      Window technique	Ord er of the filter	Width of main lobe	No. of side lobes	Relative side lobe attenuati on (dB)
      Hanning window	30	0.09375	7	-31.5
      	40	0.070313	10
      Hamming window	30	0.085938	7	-41.7
      	40	0.0625	9
      Blackman window	30	0.10938	5	-58.1
      	40	0.082031	8
      Kaiser window	30	0.054688	9	-13.5
      	40	0.042969	11

      Comparison between various window:

      REFERENCES

      1. Digital Signal Processing; S.Salivahanan

      2. Digital Signal Processing; Sanjay Sharma, Katson Books.

      3. FIR Filter, Available: http://en.wikipedia.org/wiki/Finite_impulse_response

   AUTHOR:

   MANIRA KHATUN: She achieved her B.Tech (2007) and M.Tech (2010) degrees in Electronics & Communication Engineering under West Bengal University of Technology. She has nearly four years teaching experience in Electronics and Communication related subjects. She is presently serving as an Assistant Professor, Department of Electronics and Communication Engineering at Mallabhum Institute of Technology, Bishnupur, Bankura, West Bengal, India.

   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 Blackman 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. The Kaiser window gives best result. Therefore it is most commonly used window for FIR filter design.

5. CONCLSION

Digital filter plays a very important role in different digital signal processing applications. In Kaiser window, the main lobe width is 0.054688 for filter order 30 which means this window has less transition width and introduces more ripple. Digital filter can play a major role in speech signal processing applications such as, speech filtering, speech enhancement, noise reduction and automatic speech recognition.