A causal system produces the output sequence y(n)={1,0.7} when excited by the input sequence x(n)={1,-0.7,0.1}, then what is the impulse response of the system function?(a) [3(0.5)^n+4(0.2)^n]u(n)(b) [4(0.5)^n-3(0.2)^n]u(n)(c) [4(0.5)^n+3(0.2)^n]u(n)(d) None of the mentionedThis question was addressed to me by my school principal while I was bunking the class.Question is taken from Inverse Systems and Deconvolution topic in division Frequency Analysis of Signals and Systems of Digital Signal Processing

A causal system produces the output sequence y(n)={1,0.7} when excited

1.	A causal system produces the output sequence y(n)={1,0.7} when excited by the input sequence x(n)={1,-0.7,0.1}, then what is the impulse response of the system function?(a) [3(0.5)^n+4(0.2)^n]u(n)(b) [4(0.5)^n-3(0.2)^n]u(n)(c) [4(0.5)^n+3(0.2)^n]u(n)(d) None of the mentionedThis question was addressed to me by my school principal while I was bunking the class.Question is taken from Inverse Systems and Deconvolution topic in division Frequency Analysis of Signals and Systems of Digital Signal Processing
Answer» Right option is (B) [4(0.5)^n-3(0.2)^n]u(n) The best explanation: The system function is easily determined by taking the Z-transforms of x(n) and y(n). Thus we have H(z)=\(\FRAC{Y(z)}{X(z)} = \frac{1+0.7z^{-1}}{1-0.7z^{-1}+0.1z^{-2}} = \frac{1+0.7z^{-1}}{(1-0.2z^{-1})(1-0.5z^{-1})}\) Upon applying PARTIAL fractions and applying the INVERSE z-transform, we get [4(0.5)^n-3(0.2)^n]u(n).

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