Question:
If \( x[n] = \{1, 0, -2, 3\} \) and \( y[n] = x[n] \ast x[n] \), the maximum value of \( y[n] \) is
If \( x[n] = \{1, 0, -2, 3\} \) and \( y[n] = x[n] \ast x[n] \), the maximum value of \( y[n] \) is
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When performing convolution, take the sum of the products of overlapping elements.
Updated On: May 5, 2025
- 4
- 9
- 2
- 6
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The Correct Option is B
Solution and Explanation
The convolution of \( x[n] \) with itself, \( y[n] = x[n] \ast x[n] \), is given by:
\[
y[n] = \sum_{k} x[k] \cdot x[n-k]
\]
Computing the convolution manually:
\[
y[0] = 1, \quad y[1] = 0, \quad y[2] = -2, \quad y[3] = 3
\]
Thus, the maximum value of \( y[n] \) is 9. Therefore, the correct answer is option (2).
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