10. Baseband digital transmission

Question 1

What is a matched filter?

Answer 1

Type of LTI filter used to maximize the SNR in the presence of additive random noise.

Question 2

Where is the matched filter found in digital modulation schemes?

Answer 2

At the receiver, used to detect the pulse signal of a digitally modulated signal in the presence of noise.

Question 3

What is the formula for peak SNR, and how does it relate to matched filters?

Answer 3

Peak SNR = instantaneous power of output due to pulse signal / average power of filter output noise.

The aim when designing the matched filter is to maximize the peak SNR.

Question 4

What is the formula for the impulse response for the matched filter?

Answer 4

h(t)=kg(Tb-t)
Tb: symbol period
g(t): transmitter pulse shape
k: gain

Note that the impulse response is a scaled, time-reversed, and shifted version of g(t), so duration and shape is determined by g(t).

Question 5

What is the peak SNR obtained by an optimal matched filter?

Answer 5

SNR = 2E/No = E/(No/2)
E: energy of the signal
No/2: PSD of white noise