A function $s(t)$ is defined by $s(t)=\int_x p(t-cx)dx$ where $\tau = cx$ is a time variable and $t\neq \tau$. What is the Fourier transform, $S(\omega)$, of the function $s(t)$?
I know that for a function $f(t)=g(t-cx)$, the Fourier transform would be $F(\omega)=e^{i\omega cx}G(\omega)$, where $G(\omega)$ is the Fourier transform of $g(t)$. However, I don't think I can say that $S(\omega)=P(\omega)\int_x e^{i\omega cx} dx$.