A discrete-time system -S- with impulse response h-n-13n u-n- If system difference equation is h-n-kh-n-1- -n- then the value of k

Given, system difference equation, h[n] kh[n 1]=δ [n] (13)^n u[n] k(13)^u 1 u[n 1]=δ[n] δ[n]+(13)^n u[n 1] k(13)^n 1 u[n 1]=δ[n] (13)^n 1 u[n 1][1 3k]=0 ∴ ...

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A discrete-ti...

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$A discrete-time system 'S' with impulse response h [n] = {(\frac{1}{3})}^{n} u [n] . If system difference equation is h [n] - k h [n - 1] = δ [n], then the value of k$
0.33

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Solution

The correct option is A 0.33
Given, system difference equation,

$h [n] - k h [n - 1] = δ [n]$

${(\frac{1}{3})}^{n} u [n] - k {(\frac{1}{3})}^{u - 1} u [n - 1] = δ [n]$

$δ [n] + {(\frac{1}{3})}^{n} u [n - 1] - k {(\frac{1}{3})}^{n - 1} u [n - 1] = δ [n]$

${(\frac{1}{3})}^{n - 1} u [n - 1] [1 - 3 k] = 0$

$∴ 1 - 3 k = 0$

$∴ k = \frac{1}{3} = 0.33$

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A discrete-time system 'S' with impulse response h[n]=(13)nu[n]. If system difference equation is h[n]−kh[n−1]=δ[n], then the value of k0.33

The correct option is A 0.33Given, system difference equation, h[n]−kh[n−1]=δ[n] (13)nu[n]−k(13)u−1u[n−1]=δ[n] δ[n]+(13)nu[n−1]−k(13)n−1u[n−1]=δ[n] (13)n−1u[n−1][1−3k]=0 ∴1−3k=0 ∴k=13=0.33

$A discrete-time system 'S' with impulse response h [n] = {(\frac{1}{3})}^{n} u [n] . If system difference equation is h [n] - k h [n - 1] = δ [n], then the value of k$
0.33