Multiple choice

Let y[n] denote the convolution of h[n] and g[n], where h[n]= (1/2)n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

  1. 0

  2. 1/2

  3. 1

  4. 3/2

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A Correct answer
Explanation

For causal convolution, y[n] = Σ h[k]g[n-k]. With y[0] = g[0] = 1 and y[1] = g[1] + h[1]g[0] = g[1] + 1/2. Setting y[1] = 1/2 gives g[1] = 0.

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