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Recovery of Diffusion-Deteriorated Signals

IP.com Disclosure Number: IPCOM000097154D
Original Publication Date: 1962-Jun-01
Included in the Prior Art Database: 2005-Mar-07
Document File: 3 page(s) / 40K

Publishing Venue

IBM

Related People

Miranker, WL: AUTHOR

Abstract

Signals that have been deteriorated with time according to a diffusion process are recovered by an iterative operation on the Fourier transform of the deteriorated signal. This type of deterioration of a time-varying signal may be found in the storage and retrieval of data that has been recorded on magnetic tape.

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Recovery of Diffusion-Deteriorated Signals

Signals that have been deteriorated with time according to a diffusion process are recovered by an iterative operation on the Fourier transform of the deteriorated signal. This type of deterioration of a time-varying signal may be found in the storage and retrieval of data that has been recorded on magnetic tape.

An analog signal f(x), within a band of frequencies Omega, may be stored on a magnetic tape as a function u(x) which describes the amplitude (positive or negative) as a function of the distance x along the tape. In addition to the deterioration that occurs during recording, further deterioration is caused by the interaction of the various magnetic peaks and troughs in the magnetic distribution of information. The total distortion may be considered to define a transformation of f(x) into the recorded version of u(x) according to u(x) = K >f(x)| as follows: see diagram where H is an experimentally-determinable property of the recording mechanism which characterizes the diffusion-distortion mechanism.

It is well known that transformation may be inverted to give F (omega), the Fourier transform of f(x) in terms of U (omega), the Fourier transform of u(x), as follows: F(omega) = e/H omega/2// u(omega)

However this inversion is unstable since a small disturbance in u(x) or U (omega) will be amplified exponentially. A more stable method for inverting the transformations makes use of:

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where the first iterate F(o) (omega) is chosen to be zero. This iteration scheme is obtained from the exact expression for F (omega), above, by multiplying the exact expression by e/-Homega/2/ and adding F (omega) to both sides of the equation. X is an operator which filters out frequencies outside the bandlwl < Omega . When the iterates converge we obtain F (omega) given by:

(Image Omitte...