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White Noise, Linear, Passive, Gaussian Pulse, Matched Filter

IP.com Disclosure Number: IPCOM000096792D
Original Publication Date: 1963-Nov-01
Included in the Prior Art Database: 2005-Mar-07
Document File: 2 page(s) / 42K

Publishing Venue

IBM

Related People

Sierra, HM: AUTHOR

Abstract

This linear matched filter of purely passive components maximizes the signal to noise ratio S/N of a symmetrical Gaussian pulse in white noise.

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White Noise, Linear, Passive, Gaussian Pulse, Matched Filter

This linear matched filter of purely passive components maximizes the signal to noise ratio S/N of a symmetrical Gaussian pulse in white noise.

In the reproduction of a digital electromagnetic recording, an electromagnetic transducer, represented as a generator 10, delivers a signal of symmetrical Gaussian waveform s(i)(t) and noise n(i)(t). Such is to a resistive load element 20 at which the output S/R ratio R is maximized by interposed passive network 30.

Filter 30, of transfer function H(s) which maximizes the S/N ratio R, has an impulse response h(t) = s(i)(t(o) -t) for white noise n(i)(t). Mathematically, a wave form s(i)(t(o) -t) is the same as the waveform s(i)(t) but reversed about the zero time axis. The waveform s(i)(t) being symmetrical, the impulse response h(t) is exactly like s(i)(t).

The frequency spectrum of s(i)(t) is exactly like the frequency spectrum of h(t). Therefore, the LaPlace and also the Fourier transform of the waveform s(i)(t) is exactly like the LaPlace and Fourier transform of the impulse response h(t), which is H(s), the transfer function of filter 30.

For the Gaussian waveform, s(i)(t) = exp - (t)/2/ and the impulse response h(t) = exp - (t-d)/2/, where d is the time in passing through the filter 30.

Since the frequency response of h(t) is

F (j w) = pi exp - w/2/ /4, the transfer function

H(s) = sqrt(pi) exp s/2/ /4, where s = j w.

This transcendental transfer function i...