Filtering of an AM signal at the reciever

Transfer function of a filter at the input of a receiver (synchronous demodulator of AM signal) is given with equation:

$$H(f)=e^\frac{-(f-f_0)^2}{B^2}+e^\frac{-(f+f_0)^2}{B^2}$$

$$B=10kHz$$

It is necessary to do the following:

-draw a diagram of this filter

-based on block diagram, determine the analytical expressions the signal after every part of the block diagram, if at the input, we have the following signal

$$u(t)=U_0(1+0.5cos(2\pi f_m))cos(2 \pi f_0)$$

$$U_0=1V$$

$$f_m=6kHz$$

$$f_0=10*B$$

find the index of modulation and mean power at the output of the receiver.

-find signal to noise ratio at the output of the receiver if, at the input, apart from our signal we have the noise with spectral density $$p_n=\frac{N_0}{2}=5*10^{-10} \frac{W}{Hz}$$

It is obvious that, in order to do this, i need to do the first part, which is the block diagram, but i am just not quite sure how i should do that, am i supposed to find fourier transform of $$H(f)$$ and then use time domain equation to create a diagram or should i use this expression i have in frequency spectrum?

• $H(f)$ is already in the frequency domain, so you do not need to take its Fourier Transform. I recommend sketching or plotting $H(f)$ in conjunction with the Fourier Transform of $u(t)$. This will allow you to see what the filter is doing to the signal. – Ill-Conditioned Matrix Jan 16 at 17:06