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Single Frequency Filter

IP.com Disclosure Number: IPCOM000062599D
Original Publication Date: 1986-Dec-01
Included in the Prior Art Database: 2005-Mar-09
Document File: 4 page(s) / 48K

Publishing Venue

IBM

Related People

Bonner, R: AUTHOR

Abstract

This article describes a new technique for extracting from a composite waveform the magnitude of a known single frequency, sinusoidal, noise component that is a part of the composite waveform. The purpose for this derivation is to apply corrections for this component either in hardware or in output interpretations (software). This technique applies when the frequency of the fundamental waveform is substantially different than the known single frequency sinusoidal noise component of the composite waveform. When the noise waveform is known to be 60 cycles, the new technique applies as follows: Sample the composite waveform at 250/sec for amplitude. Then sample the same composite waveform at 60/sec to determine the magnitude at each 1/60 of a second.

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Single Frequency Filter

This article describes a new technique for extracting from a composite waveform the magnitude of a known single frequency, sinusoidal, noise component that is a part of the composite waveform.

The purpose for this derivation is to apply corrections for this component either in hardware or in output interpretations (software).

This technique applies when the frequency of the fundamental waveform is substantially different than the known single frequency sinusoidal noise component of the composite waveform. When the noise waveform is known to be 60 cycles, the new technique applies as follows: Sample the composite waveform at 250/sec for amplitude. Then sample the same composite waveform at 60/sec to determine the magnitude at each 1/60 of a second. At this point we do not know what the noise contribution is, but we do know that the contribution at each of these points is constant. Since the magnitude of the composite wave is different at each of these same points, we are able to subtract these values to derive the magnitude of the noise component as follows: Consider the general situation at three sample points, with the middle point equidistant from the ones on each side, as shown in the figure. The signal f(t) is represented by a linear function kt and the deviation G from that function. The origin is taken to be the first point. The line kt is one drawn from the first point to the third point. The deviation of f(t) from this line at the middle sample is called G. The single frequency wave n(t) is defined as N cos - at the middle sample point. If the sample on one side of this point is n sample points away, the equivalent angular distance is given as a = 2fnTs radians __

Tp where TS = time between samples TP = period of single frequency wave The actual sample values at the three points are then S0 = N cos (- - a) first point S1 = N cos - + kt1 + G1 middle point S2 = N cos (- + a) + 2 kt1 third point Our goal is to find the value N cos -. To do this, we must find a way to reduce the effect of the signal f(t).

We do this by using the two samples on either side to predict the value of the middle sample and then subtracting this prediction from the actual middle sample as follows: B1 = S1 - (S0+S2)_______ 2 Substituting the values of S into this equation yields B1 = N cos - + kt1 + G1 = 1/2(N cos (--a) + N cos (--a) 2 kt1) Noting that l/2(cos (--a)) = cos- cosa, then B1 =

G1 + N cos -(1-cosa) (1) Therefore, B1 represents the deviation G1 of the signal f(t) from linearity and the single frequency wave value at the point N cos - multiplied by a constant (1-cosa) which is dependent on the sampling rate and the frequency of n(t). In the case where n=1 (three adjacent sample points), the expected deviation from linearity G1 ought to be minimal, since the sampling rate typically is much higher than the highest frequency present in f(t). Define a for n=1 as a1 . Now consider the same case of three samples as before;...