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## Homework Statement

Calculate the convolution of ##sinc(at)## and ##sinc(bt),## where ##a## and ##b## are positive real numbers and ##a>b.##

## Homework Equations

Convolution integral

## The Attempt at a Solution

The fact that ##a>b## tells us that the graph of ##sinc(at)## is ##a-b## times more "compressed" than that of ##sinc(bt).## So from the definition of the convolution integral:

$$sinc(at) * sinc(bt) = \int^\infty_{-\infty} sinc(a \tau).sinc(bt-\tau) d \tau = \int^\infty_{-\infty} \frac{\sin(a\tau)}{a\tau} \frac{\sin(bt-\tau)}{bt-\tau} d\tau \tag{1}$$

I've read that the convolution of two sinc functions at two different points is itself a sinc function located at the point of the difference between the two. So how exactly do I proceed from equation

**(1)**to arrive at this result?