Working on my communication class right now, and I'm having a bit of a problem with the matched filters.
As I see it the matched filters "eliminate" some of the noise. We project the received signal on our orthonormal base and everything that can't be generated by it is considered to be noise.
X(t) be our only signal we send, time-limited to
[0;T]. The matched filter at the receiver's end would have an impulse response of
h(t) = X(T-t).
After our received signal
R(t) passes through this filter we sample at
ts=T and we get our
After all that we can make our final decision based on
Y(t) and the expected
X(t), to see if the transmitter sent
X(t) or zero.
Now my question is why do we use a shifted time-reversed function, instead of just
X(t)? Someone told me that it's because having
h(t)=X(t) is too costly in the real world on the hardware level. But I'm not really sure it's this. Or maybe I'm completely wrong and and with
h(t)=X(t) it would work or be less effective.
Thank in advance for any answers.