The signal is transmitted via FM. There is an ideal band-pass filter passing at the discriminator output. Calculate the post-detection SNR given that per volt, and the pre-detection SNR is 500. Use Carsonâs rule to estimate the predetection bandwidth.

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.

the value of the post detection SNR for FM system is 18750

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

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