MODIFIED DESIGN OF DIGITAL COMB FILTER FOR HARMONIC ELIMINATION

R.POOVANNAN
Control and instrumentation
Anna University
Chennai-600025
INDIA

Dr.P.VANAJA RANJAN
Assistant Professor 
Anna University
Chennai-600025
INDIA

Abstract: - This paper presents the modified design method of digital comb filter so as to remove the harmonics interference that is contaminating the desired signals. The design technique by which the improvement in characteristics of the comb filter is designed and presented.

 Key-Words: comb filter-harmonics-filters-transfer function-signal processing 

1 Introduction
Harmonics elimination is the major problem in any power circuit and, filters play a vital role in the rejection of the harmonics. Filters are usually used to remove or attenuate an undesired portion of signal's spectrum while enhancing the desired portions of the signal. In the biomedical applications the elimination of harmonic interference should components that are present in the signal, the elimination of   single harmonic frequency can be easily rejected by the use of the general filters and in the case of multiple frequency harmonic rejection it is difficult and for this purpose the comb filters can be used.  And in many circuits, if the frequency component is not known then the task become so difficult and hence the comb filter should be designed in such a way that it should estimate the harmonic frequency of the circuit and it be precise and the signals should be fully free from the noise, so it is necessary to eliminate all the harmonics should eliminate the harmonic frequencies.

In the digital processing of communication signals the harmonic removal of harmonic interferences is desired while leaving the broadband signal unchanged. A typical one is to cancel power line 

Interference. When   the   single   notch filter is used
only single harmonic component is neglected and notch filter    produces  substantial  distortions of the
output response, which appear near its flat region due to the group delay variation. And hence the harmonics is not eliminated completely and also, in order to eliminate all of the harmonic frequency comb filters are used.

2. Problem formulation
Ideally, a comb filter has infinite attenuation at the notch frequencies (which are multiples of the center frequency), unity gain at all other frequencies and no effects on the phase of the signal. These characteristics cannot be approached using analog implementation, but a practical digital implementation is quite feasible.
The discrete transfer function of a conventional digital comb filter is given by

Where M-number of notch frequencies

The filter has zeros at frequencies
Where sampling frequency  k=1, 2, 3…M

The pole zero plot and its magnitude and phase response for the designed comb filter is shown in figure (1) and (2) respectively  

IMAGINAR
Y 

PART

           Z-PLANE 
	
                  REAL PART

Fig.1 Pole zero plot of comb filter

Fig.2 Magnitude and phase response of
Comb filter

The zeros can be used to provide the desired attenuation at the harmonic frequencies, but the other characteristics such as magnitude and phase response do not meet the desired requirements. so a filter should be designed in such a way that it should meet the desired specifications.

3. Problem solution
The desired comb filter characteristics can be met by placing the weaker poles at the frequencies of the zeros will modify the comb filter.
In the modified comb filter, in addition to the zeros placed at the unit circle in the complex z-plane

The additional poles are placed at

The discrete transfer function of the modified comb filter can be formed as

	

The pole zero patterns and its magnitude and phase response of the modified comb filter is shown in the Fig.3 and Fig.4 respectively.

Fig.1 Pole zero plot of modified comb
Filter

Fig.4 Magnitude and phase response of
Modified Comb filter

The filter is designed using the Signal processing tool box in the MATLAB.The r factor of the pole is varied and it is found that the r as close to unity the response is very much improved ,here it is taken as .98,since r=1 is not practically realizable.

CONCLUSION:
Thus the introduction of weaker poles provides the desired attenuation at the harmonic frequencies and also the magnitude and phase response is improved very much.

References:
[1]. Chang-Tar Tsai; Hsiao-Lung Chan; Chien
Cheng Tseng; Chien-ping Wu, Harmonic interference elimination by an active comb filter,
 Proceedings of 16th annual international conference of the IEEE (1994) Engineering in Medicine and Biology Society, 3-6 Nov.1994 Page(s):964-965 vol.2

[2].John g.proakis and dimitries.g.manolakis,, Digital Signal Processing principles Algorithms and Applications ,III edition prentice hall,Inc     company 1996  page 345-348.