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A discrete time signal with input as x[n] has impulse response h[n]=kδ[n] where k is constant. The output y[n] of the system is given as:
  • a)
    y[n]=x[n]* h[n]
  • b)
    Y(ω)=X(ω) x H(ω)
  • c)
    y[n]=kx[n]
  • d)
    All of the above
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A discrete time signal with input as x[n] has impulse response h[n]=k...
For a discrete time signal with input as x[n] has impulse response h[n] =kδ[n], the output y[n] of the system is given as:
y[n] = x[n] × h[n]
y[n] = x[n] ×kδ[n]
y[n] = k(x × δ)[n]
y[n] = kx[n]
Taking Fourier transform on both sides
Y(ω) = X(ω) x H(ω)
Therefore H(ω) = Y(ω)/X(ω)
This is known as the transfer function of the system.
h[n] = F-1[H(ω)].
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A discrete time signal with input as x[n] has impulse response h[n]=kδ[n] where k is constant. The output y[n] of the system is given as:a)y[n]=x[n]* h[n]b)Y(ω)=X(ω) x H(ω)c)y[n]=kx[n]d)All of the aboveCorrect answer is option 'D'. Can you explain this answer?
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