I am a bit confused about some calculations of an example from a textbook:
Given: $$S_X(f)=N_0/2$$ $$S_Y(f)=|H(f)|^2 S_X(f) $$ with $$H(f) = e^{-j\pi fT}T\frac{sin(\pi Tf)}{\pi Tf}$$
From the textbook, the $S_Y(f)$ is: $$S_Y(f)= T^2 [\frac{sin(\pi Tf)}{\pi Tf}]^2 \frac{N_0}{2} $$
However, my result is: $$S_Y(f)= e^{-j2\pi fT}T^2 [\frac{sin(\pi Tf)}{\pi Tf}]^2 \frac{N_0}{2} $$ where does $e^{-j2\pi fT}$ go? Why did the text book emitted this term? I believe that there is a conversion but I am not sure about this.