This question is incomplete, the complete question is;
The signal m(t) = cos(400πt) is transmitted via FM.
There is an ideal band-pass filter passing 100 ≤ |f| ≤ 300 at the discriminator output.
Calculate the post-detection SNR given that kf =1 kHz per volt, and the pre-detection SNR is 500. Use Carson's rule to estimate the pre-detection bandwidth.
Answer: the value of the post detection SNR for FM system is 18750
Step-by-step explanation:
Given that;
the pre-detection SNR is 500
m(t) = cos(400πt)
filter; 100 ≤ |f| ≤ 300
kf = 1 kHz
from the signal m(t) = cos(400πt)
Amplitude (Am) = 1
ωm = 400π
2πfm = 400π
fm = 400π / 2π
fm = 200 Hz
Now lets consider the formula for modulation index of FM system
β = (KfAm / fm) ----------------equ 1
substitute the values in equation 1
β = (1 × 10³)1 / 200
= 1000 / 200
β = 5
Also lets consider the expression for Figure of merit ( FOM) for FM system
FOM = 3/2β²
so we substitute
FOM = 3/2 × (5)²
= 1.5 × 25
FOM = 37.5
Now lets consider another relation for FOM
FOM = Post detection SNR / Pre detection SNR
given that in the question; the pre-detection SNR is 500
so we substitute]
37.5 = Post detection SNR / 500
Post detection SNR = 37.5 × 500
= 18750
Therefore, the value of the post detection SNR for FM system is 18750