1 1 vote Recall that \[\operatorname{sinc}(t)=\frac{\sin (\pi t)}{\pi t}\] and convolution of functions $x(t)$ and $y(t)$ is defined as \[x(t) \star y(t)=\int_{-\infty}^{\infty} x(t-\tau) y(\tau) d \tau .\] What is the necessary and sufficient condition on positive real numbers $f$ and $a$ such that the following is true for some non-zero real number $K$ (which may depend on $f$ and $a)$ ? \[\operatorname{sinc}^{2}(a t) \star \cos (2 \pi f t)=K \cos (2 \pi f t), \quad \text { for all real } t \text {. }\] $f<a$ $f>a$ $f<a^{-1}$ $f>a^{-1}$ None of the above Continuous-time Signals tifrece2021 continuous-time-signals convolution signals-and-systems + – admin 267 views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
