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Determine and plot the response of an accumulator for an input sequence ๐‘ฅ[๐‘›] = ๐‘ข[๐‘›] + 2๐‘ข[๐‘› โˆ’ 1] โˆ’ 3๐‘ข[๐‘› โˆ’ 3]. Consider the system is at rest. use the function filter

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Kenisha Dcosta
Kenisha Dcosta on 27 May 2021
Answered: Mahesh Taparia on 4 Jun 2021
Consider the difference equation of an accumulator
๐‘ฆ[๐‘›] = ๐‘ฆ[๐‘› โˆ’ 1] + ๐‘ฅ[๐‘›]
The transfer function of this equation is given by taking z-transform as
๐‘Œ[๐‘ง] = ๐‘งโˆ’1๐‘Œ[๐‘ง] + ๐‘‹[๐‘ง]
๐‘‡[๐‘ง] = ๐‘Œ[๐‘ง]/X[๐‘ง] = 1/1 โˆ’ ๐‘งโˆ’1

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