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An impulse-response measurement apparatus for linear systems using a rectangular input with a Poisson distribution of zero crossings

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  • For many applications it is desirable to be able to experimentally determine the impulse response of a linear system while it is in operation. Use of correlation techniques allows this to be done without noticeably disturbing the quiescent output value of the system. An impulse response measurement apparatus is designed and constructed using correlation techniques. This device is based on the Input-Output Crosscorrelation Theorem. A Poisson rectangular wave is used as the input. The Poisson rectangular wave is a waveform which alternates between +Em volts and -Em volts at random intervals of time. The zero crossings of the wave, where it shifts from one value to the other, follow a Poisson probability distribution. An analytical method is developed which indicates the deviation of the apparatus output from the ideal impulse response. This error is expressed as a function of the characteristics of the Poisson rectangular input and the system under investigation. Results are obtained for the generalized second-order system, although the approach will work for any linear system. These results indicate that the error can be made sufficiently small to allow the use of a Poisson rectangular input. The Poisson rectangular input greatly simplifies the crosscorrelation circuitry. The multiplier circuit in the crosscorrelator is required to multiply the system output by +Em or -Em only. This permits the use of a very simple multiplication and averaging circuit. A closed-loop tape transport was found to be very satisfactory in achieving the variable delay required in the crosscorrelator. Delays in the millisecond range are obtained by the use of two sets of write-read heads.
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