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