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USE OF PHASE TO MEASURE LOWPASS FILTER BANDWIDTH

IP.com Disclosure Number: IPCOM000008267D
Original Publication Date: 1997-Sep-01
Included in the Prior Art Database: 2002-May-31
Document File: 2 page(s) / 92K

Publishing Venue

Motorola

Related People

Clement R. Copolillo: AUTHOR [+2]

Abstract

Electronic filters are used to remove noise from an input signal. In some applications, such as disk or tape drive read channels, the filter must not distort the shape of the original signal. This is accomplished with lowpass filters such as the Butterworth, Bessel, Chebychev filters and others, which have been used for many years in disk and tape drives. A primary requirement of such a filter is that it has the characteristic of a linear phase over the range of frequencies where the input signal is known to exist. The input is typically a complex non-repetitive signal often characterized by the con- volution of a Lorenzian pulse with randomly placed ones and minus ones, and such that the spacing between them is limited by the response of the heads and media used in the disk or tape drive. The bandwidth (or cutoff frequency) of these filters is defined as the point at which the magnitude response is -3dB down from that portion of the response which is flat (at low frequencies). The phase at the cutoff frequency is mathematically cal- culated and is often -180 degrees. The operation described herein utilizes the linear phase to determine the bandwidth of such lowpass filters. A measurement of phase is taken at a frequency equal to one half of the theoretical cutoff frequency (0.5T). Another is taken at the theoretical cutoff frequency (1 .OT).

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-A Technical Developments

@

USE OF PHASE TO MEASURE LOWPASS FILTER BANDWIDTH

by Clement R. Copolillo and Gaty L. Stuhlmiller

  Electronic filters are used to remove noise from an input signal. In some applications, such as disk or tape drive read channels, the filter must not distort the shape of the original signal. This is accomplished with lowpass filters such as the Butterworth, Bessel, Chebychev filters and others, which have been used for many years in disk and tape drives. A primary requirement of such a filter is that it has the characteristic of a linear phase over the range of frequencies where the input signal is known to exist. The input is typically a complex non-repetitive signal often characterized by the con- volution of a Lorenzian pulse with randomly placed ones and minus ones, and such that the spacing between them is limited by the response of the heads and media used in the disk or tape drive. The bandwidth (or cutoff frequency) of these filters is defined as the point at which the magnitude response is -3dB down from that portion of the response which is flat (at low frequencies). The phase at the cutoff frequency is mathematically cal- culated and is often -180 degrees. The operation described herein utilizes the linear phase to determine the bandwidth of such lowpass filters. A measurement of phase is taken at a frequency equal to one half of the theoretical cutoff frequency
(0.5T). Another is taken at the theoretical cutoff frequency (1 .OT).

The phase ~vs. frequency plot follows a straight line and can be thought of as:

@=m.f+@dc

where: $ is the phase at any point on the phase vs. frequency plot, m is the slope of the phase vs. frequency plot, f is the frequency where that phase exists, and Qdc is the projected phase at DC (0 Hz).

The actual cutoff frequency is determined by the calculation:

F,-$fc-@dc m

where:

   FC is the...