Analysis of Shadow Filter With Hybrid Windows

Analysis of Shadow Filter With Hybrid Windows

Eppili Jaya Assistant professor DEPT. of ECE AITAM

Tekkali, INDIA

1. Krishna Rao Assistant professor

   DEPT. of ECE AITAM

   Tekkali, INDIA

   K Krishnam Raju Assistant professor DEPT. of ECE AITAM

   Tekkali, INDIA

   Abstract– A new concept of shadow filters are proposed by using hybrid windows which are obtained by combining the different conventional windows (Bartlett, hamming, hanning, Blackman, boxcar etc). The concept of shadow filter is that output of a base filter is giving to the input of another filter which is called feedback filter through feedback constant and the output of feedback filter is again given as input to main filter. By adjusting the value of feedback constant we can get response of main filter. We have to find the value of feedback constant for which the main filter response is good in terms of relative side lobe attenuation and bandwidth and which are compared with the filter without shadow mechanism. In this project LPF acts as the base filter and is tested with all other filters such as LPF, HPF, BRF and BPF in feedback path. Similarly this method is applied to HPF, BRF, and BPF as base filter. The base filter and feedback filters are being taken FIR filters applied with new hybrid windows. Finally shadow filters with conventional windows are compared with shadow filters with new hybrid windows in terms of RSA and BW.

   Index termsFIR filter, Hybrid windows, RSA, Shadow filter.

   1. INTRODUCTION

      A filter is linear time invariant system [1-3], used for removing undesirable noise from desired signal. It can be used in spectral shaping such as equalization of communication channels, signal detection in radar, sonar etc. A filter is designed to pass a band of desired frequencies without any distortion called pass band of the filter and to totally block a band of unwanted frequencies called stop band of the filter. The digital filters are available as low pass

      implementation of shadow mechanism using hybrid windows. Hybrid window is a new concept which is obtained by the combination of two different windows. We take the combinations of boxcar, hamming, hanning, bartlett windows. The shadow mechanism is to analyze and compare the frequency responses of Low pass, High pass, Band pass and Band reject filters for different feedback configurations with filters without shadow mechanism.

      The characteristics of FIR filters, the windowing technique and the required equations for the hybrid windows are explained.The shadow mechanism concept was also explained in next chapters. We used MATLAB tool for implementation of the filters.

      The frequency responses of different filters without shadow mechanism and with shadow mechanism are shown further. Tabular forms of the filters showing the data of Relative side lobe attenuation, main lobe width for different values of are also given.

   2. FIR FILTERS

      Impulse response of digital filters are computed for finite number of samples and hence called Finite Impulse Response filters. The transfer function is given by:

      H(n) 0, 0nM-1

      = 0, elsewhere (1)

      These filters are characterized by the system function which is not rational

      filters, high pass filters, band pass filters and band reject filters. A low pass filter blocks all frequencies above the specified cut off frequency similarly high pass filter passes

      H (Z) = M 1 BK ZK

      K=0

      A. Coefficients of linear phase filter: Low pass filter with cut off frequency

      (2)

      all frequencies above the specified cut off frequency.

      Theband pass filter allows a particular band of frequencies

      hd 0 =

      c for n =

      and the band reject filter rejects the particular band of frequencies and allows the other frequencies.

      Consider a basic second order filter, which is

      = sin c (n) for n (3)

      (n)

      High pass filter with cut off frequency c

      capable of realizing any of the four possible characteristics

      h n = 1 c

      d

      for n =

      viz. low-pass, high-pass, band-pass or band reject or a combination of these. Here we take FIR filters for

      = 1

      (n)

      sin n sin forn (4)

      Band Reject filter with cut off frequency 1,2

      d

      h n = 1 21

      for n =

      = 1

      (n)

      sin n 2 n + sin1 n

      for n (5)

      Band pass filter with cut off frequency 1, 2

      =

      2 1 for n =

      = 1

      2 1

      (6)

   3. TYPES OF WINDOW FUNCTIONS

      In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window, which describes the shape of its graphical representation. When another function or a signal (data) is multiplied by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap; the "view through the window".

      The following comes under the classification of the windows

      • Rectangular window

      • Triangular window

      • Hanning window

      • Hamming window

      • Blackmann window

      • Kaiser window

      A. Hybrid Windows:

      The hybrid window is a type of window formed by the combination of two different types of windows. The combining of the windows may be done by an operation like arithmetic operations. We take addition of two windows by multiplying a constant kwith each window.

      The windows which are taken are Boxcar window and Hanning window and constant as 0.5

      If wh is the function of Hybrid window, and k is the constant then the equqtions can be written as (7) & (8).

      Wn=k*Boxcar(n)+(1-k)*Hanning(n) (7)

      Fig 1: Block diagram for shadow mechanism

      The basic second order filter is capable of realizing any of the filters. We have to find the value of numeric constant for which the filter response is better in terms of relative side lobe attenuation and bandwidth compared to the filter without shadow mechanism. In this paper LPF acts as the base filter and is tested with all other filters such as LPF, HPF, BRF and BPF in feedback path. Similarly this method is applied to HPF, BRF, and BPF as base filter. The base filter and feedback filters are being taken FIR filters applied with new hybrid windows.

      1. RESULTS AND DISCUSSION

         Results are generated for all filters (LPF, HPF, BPF, BRF) using shadow mechanism with hybrid windows and applying different numerical (feedback) constants.

         Table 1.Response of filters Without shadow mechanism.

         or

         Wn=k*Hanning(n)+(1-k)*Boxcar(n) (8) If K=0.5

         Wn=0.5*Boxcar(n)+0.5*Hanning(n) (9)

         The hybrid window technique is used for improvisation of the signal response of the filter. If we consider only Boxcar window, a lot of Ripples and noise are added to the

         0.5

         0.4

         0.3

         Amplitude

         0.2

         0.1

         0

         -0.1

         Time domain

         0

         -20

         Magnitude (dB)

         -40

         -60

         -80

         Frequency domain

         signal.But by using this hybrid windows, the ripples are decreasedand the stop band attenuation increased without changing the other parameters, and the accuracy increases.

         -0.2

         5 10 15 20 25

         Samples

         -100

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         IV. SHADOW MECHANISM

         The concept of shadow filter is that output of a base filter is given as input to another filter which is in feedback section called feedback filter and again the output of feedback filter is given as input to base filter. By adjusting the value of numerical constant we can get response of the filter. The block diagram of the mechanism is shown in following figure (1).

         Fig 2. Responses of LPF with feedback LPF

         Time domain

         Frequency domain

         0.6

         20

         5

         15

         Samples

         20

         25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         10

         -100

         -0.1

         -80

         0

         0.1

         -60

         0.2

         -40

         0.3

         -20

         0.4

         0

         0.5

         Amplitude

         Magnitude (dB)

         Fig 3. Responses of LPF with feedback HPF

         Time domain

         Frequency domain

         Time domain

         Frequency domain

         0.5

         0.6 20

         0.6 20

         0.5

         0

         0.4

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         20 25

         15

         Samples

         5 10

         -80

         -0.4

         -60

         -0.2

         -40

         0

         -20

         0.2

         0

         0.4

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         20 25

         15

         Samples

         10

         5

         -100

         -0.1

         -80

         0.1

         0

         -60

         0.2

         -40

         0.3

         -20

         0.4

         0

         0.6 20

         Amplitude

         Amplitude

         Magnitude (dB)

         Magnitude (dB)

         Amplitude

         Magnitude (dB)

         Fig 4. Responses of LPF with feedback BRF

         Time domain

         Frequency domain

         0.3

         -20

         0.2

         -40

         0.1

         -60

         0

         -0.1

         15

         Samples

         20 25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         5 10

         -80

         Fig 5. Responses of LPF with feedback BPF

         Table 2. Responses of LPF with shadow mechanism for different numerical constant () values.

         Low pass filter with different feedback filters	Numerical constant	RSLA	MLW
         LPF with feedback LPF	0.01	-32.58189	0.95313
         	-0.01	-32.84274	0.95313
         LPF with feedback HPF	0.01	-31.820785	0.95313
         	-0.01	-33.0730	0.95313
         LPF with feedback BRF	0.01	-31.623215	0.95313
         	-0.01	-33.12427	0.95313
         LPF with feedback BPF	0.01	-31.506202	0.95313
         	-0.01	-33.105645	0.95313

         Time domain

         Frequency domain

         0.6 20

         0.4

         0

         0.2

         -20

         -0.2

         -60

         -0.4

         15

         Samples

         20 25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         5 10

         -80

         -40

         0

         Amplitude

         Magnitude (dB)

         Fig 6. Responses of HPF with feedback LPF

         Fig 7. Responses of HPF with feedback HPF

         Time domain

         Frequency domain

         0.6 20

         0.4

         0

         -20

         -0.2

         -80

         -0.4

         15

         Samples

         20 25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         -15

         <>-20

         5 10

         -100

         -60

         0

         -40

         0.2

         Amplitude

         Amplitude

         Magnitude (dB)

         Magnitude (dB)

         Fig 8. Responses of HPF with feedback BRF

         Time domain

         Frequency domain

         0.6 5

         0

         0.4

         -5

         0.2

         -10

         -0.2

         -25

         -0.4

         15

         Samples

         20 25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         5 10

         -30

         0

         Fig 9. Responses of HPF with feedback BPF

         Table 3. Responses of HPF with shadow mechanism for different numerical constant () values

         High pass filter with different feedback filters	Numerical constant	RSLA	MLW
         HPF with feedback LPF	0.01	-32.829777	1.9922
         	-0.01	-33.58795	1.9922
         HPF with feedback HPF	0.01	-31.2340	1.9922
         	-0.01	-32.986008	1.9922
         HPF with feedback BRF	0.01	-32.1453558	1.9922
         	-0.01	-33.115566	1.9922
         HPF with feedback BPF	0.01	-32.1162682	1.9922
         	-0.01	-33.2011589	1.9922

         Time domain

         Frequency domain

         0.2

         -30

         0.3

         -10

         -20

         0.4

         0.6 10

         25 0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         20

         15

         Samples

         5 10

         -70

         -0.4

         -60

         -0.2

         -40

         -50

         0

         -20

         -30

         0.2

         0.6 10

         0

         0.4

         -10

         Frequency domain

         Time domain

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         25

         20

         15

         Samples

         5 10

         -70

         -0.1

         -60

         0

         -50

         0.1

         -40

         0.2

         -30

         0.3

         -10

         -20

         0.4

         0

         0.5

         0.6 10

         Amplitude

         Amplitude

         Magnitude (dB)

         Magnitude (dB)

         Amplitude

         Magnitude (dB)

         Fig 10. Responses of BRF with feedback LPF

         Time domain

         Frequency domain

         0.5

         0

         15

         Samples

         20

         25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         -40

         0.3

         -20

         -30

         0.4

         0.6 0

         5 10

         -70

         -0.1

         -60

         0

         -50

         0.1

         -40

         Amplitude

         Magnitude (dB)

         Fig 11. Responses of BRF with feedback HPF

         Time domain

         Frequency domain

         0.5

         -10

         15

         Samples

         20

         25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         0.2

         -20

         0.3

         -10

         0.4

         0

         0.5

         0.6 10

         5 10

         -80

         -0.1

         -70

         0

         -60

         0.1

         -50

         0.2

         Amplitude

         Magnitude (dB)

         Fig 12. Responses of BRF with feedback BRF

         Time domain

         Frequency domain

         15

         Samples

         20

         25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         5 10

         -50

         -0.1

         -40

         0.1

         0

         -30

         Fig 13. Responses of BRF with feedback BPF

         <>Band reject filter with different feedback filters	Numerical constant	RSLA	MLW
         BRF with feedback LPF	0.01	-30.677184	1.9922
         	-0.01	-33.146347	1.9922
         BRF with feedback HPF	-0.01	-31.5048829	1.9922
         	-0.1	-27.0339084	1.9922
         BRF with feedback BRF	-0.01	-31.5048829	1.9922
         	-0.1	-27.0339084	1.9922
         BRF with feedback BPF	0.01	-30.445115	1.9922
         	-0.01	-30.868257	1.9922

         Table 4. Responses of BRF with shadow mechanism for different numerical constant () values.

         Fig 14. Responses of BPF with feedback LPF

         Time domain

         Frequency domain

         0.6 10

         0

         0.4

         -10

         0.2

         -20

         -30

         -60

         -0.4

         15

         Samples

         20

         25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         -40

         0

         5 10

         -70

         -0.2

         -40

         -50

         0

         Amplitude

         Amplitude

         Magnitude (dB)

         Magnitude (dB)

         Fig 15. Responses of BPF with feedback HPF

         Time domain

         Frequency domain

         0.6 20

         0.4

         0

         0.2

         -20

         -0.2

         -60

         -0.4

         15

         Samples

         20

         25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         5 10

         -80

         Amplitude

         Magnitude (dB)

         Fig 16. Responses of BPF with feedback BRF

         Time domain

         Frequency domain

         0.6 20

         0.4

         0

         0.2

         -20

         -0.2

         -60

         -0.4

         15

         Samples

         20

         25

         0 0.2 0.4 0.6 0.8

         Normalized Frequency ( rad/sample)

         5 10

         -80

         -40

         0

         Fig 17. Responses of BPF with feedback BPF

         Table 5. Responses of BPF with shadow mechanism for different numerical constant () values.

         Band pass filter with different feedback filters	Numerical constant	RSLA	MLW
         BPF with feedback LPF	0.01	-30.277925	1.9922
         	-0.01	-31.806377	1.9922
         BPF with feedback HPF	0.01	-30.954613	1.9922
         	-0.01	-32.635812	1.9922
         BPF with feedback BRF	0.01	-30.794920	1.9922
         	-0.01	-31.231530	1.9922
         BPF with feedback BPF	0.01	-29.504998	1.9922
         	-0.01	-30.381463	1.9922

      2. CONCLUSION AND FUTURE SCOPE

         The versatility of an interesting shadow filter, which can be electronically tuned by varying the gain of an amplifier, has been discussed in this paper. The advantages of shadow filters are same as filters but with better quality and can be quickly understandable for experimentation.

         The FIR filters are implemented using FIR with Hybrid windows, so that the ripples in the window can be decreased and attenuation of the stop band also increased. The relative side lobe attenuation has improved a lot using this concept. The input can be any real time signal and this concept can be applied for medical purpose that is for ECG because medical apparatus need accurate signals.

         It is observed from the Results and Tabular forms (1 to 5), the relative side lobe attenuation (RSA) has improved for all types of filters with shadow mechanism without altering the main lobe width (MLW) of filters, comparing with the filters without shadow mechanism. The extension for this paper can be done by new window types.

      3. REFERENCES

1. John G Proakis, DG Manolakis.,"Shadow filters-A new Family of Electronically Tunable Filters published in IETE journal Vol. 51, May-December 2010.

2. "Digital signal processing third edition", published byPrentice Hall. [3]P. Ramesh Babu,"Digital Signal Processing".

1. Y.Lakys, and A. Fabre, shadow filter-a new family of second order filters, electronics letter, vol 46, No. 4, pp.276-277, 2010.

2. Lakys, Y., Godara, B., Fabre, A.: `Cognitive and encrypted communications. Part 2: a new theory for frequency agile active filters and the validation results for an agile band pass in SiGe- BiCMOS', Invited paper, 6th Int. Conf. on Electrical and Electronics Engineering, ELECO 2009, November 2009, Bursa, Turkey, p. 16 29.

3. S.C. Dutta Roy, The many faces of the single tuned circuit, IETE journal of education, vol 41, NO. 4, PP. 101-104, 2000.

4. N. J. Fliege, Multiple biquads, ch. 13 in The circuits and Filters Handbook, W.K.chen(Ed), 2007, CRC Press.

5. Fabre, A., Saaid, O., Wiest, F., Boucheron, C.: `High frequency applications based on a new current controlled conveyor', IEEE Trans. Circuits Syst., 1996, 43, p. 82-9

6. Fabre, A.: Electronique analogique rapide, circuits et applications, 2009 (TechnoSup, Ellipses edit.Paris, France).