Question

Convolution of $x(t+5)$ with impulse function $\delta(t-7)$ is equal to

• A. $x(t-12)$
• B. $x(t+12)$
• C. $x(t-2)$
• D. $x(t+2)$

Hint:

Convolution with $\delta(t-t_0)$ simply shifts the signal by $t_0$.

Answer 1

The Correct Option is C

Step 1: Use convolution property of delta function.
\[ x(t)*\delta(t-t_0)=x(t-t_0) \]
Step 2: Apply to the given signal.
\[ x(t+5)*\delta(t-7)=x\big((t-7)+5\big) \]
Step 3: Simplify.
\[ x(t-2) \]
Step 4: Final conclusion.
The result of the convolution is $x(t-2)$.