It looks like you want to implement a transfer function that has a periodic frequency domain response. Digital filters do that. If the transfer function you listed is |H(f)|^2, you could write H(f) as sin(w/40M), where w=2pi*f. This can be written as (exp(jw/40M)-exp(-jw/40M))/(2j). If you don't care about the j in the denominator, you could a z-domain block in VerilogA. I believe this would be

(z - z^-1)/2

where the sample rate is 40M.

If the transfer function you wrote is H(f), you might still be able to use a z-domain block. This time, the z-domain block is

-(z - z^-1)^2 / 4 .  The sample rate is again 40MHz. This time, the (-) in front takes care of the j.

The only snag might be if there is a restriction that the degree of the numerator be less than or equal to the degree of the denominator. I am not 100% sure but causality might impose this constraint. If that is true, this will not work. In that event, you might be able to take the IFFT of the target transfer function over the frequencies of interest, which gives you an impulse response, and then use the impulse response samples as taps in an FIR filter. Again, you would implement the FIR filter with z-domain blocks...or lossless transmission lines if you don't have VerilogA.

Thanks Eugene!

I would like to have a discrete time input x[k] feed into a continuous time filter H(f) to produce a coutinuous output y(t) (in frequency domain it's Y(f)).

Would you tell me more details on how to place the 40M sampling rate in the Verilog-A or show me where can I find the example?  I guess I might need some FIR filter with z-domain block examples.

Thank you very much!

Y(f)=(1/T)*|H(f)|^2*X(z)

where z=e^(-j6.28fT)
1/T=40MHz
H(f) is a 2nd-order noise shaped transfer function
H(z) = (1-z^-1)^2

Thanks! Eugene,

Following your instruction, I have done the H(f) noise shaped transfer function.

I am going to feed the discrete time pseudo-random noise in frequency domain to the input of the H(f) transfer function so that I expect most of the noise will be pushed to high frequency.

I know how to implement the pseudo-random noise generator in time domain.  However, I haven't figured out how to implement the discrete time pseudo-random noise in the frequency domain.  Would you give me some hints again?

I appreciate your help, Eugene.

Hi Eugene,

Very sorry to ask the syntax error.  Would you tell me where is my bug?

Thanks a lot!

Assume the random noise is (1/12)=0.083 over the frequency:

module test (vout);
output vout;
electrical vout;
     V(vout) <+ noise_table({1,0.083}, {100M, 0.083});
endmodule

Hi Eugune,

Thanks!  However, it looks that it complains the V(vout).  Looks that I should not use V().

"V(<<--? vout) <+ noise_table({1,0.083, 100M, 0.083});"

"V(<<--? vout) <+ noise_table({1,0.083}, {100M, 0.083});"

You need "analog begin" and "end":

module test (vout);
output vout;
electrical vout;
    analog begin //<<----
       V(vout) <+ noise_table({1,0.083, 100M, 0.083});
    end //<<----
endmodule

You can then drive your z-filter with V(vout).

I can't try it right now but I think your denominator coefficients should be {0,0,1}.

(1-z^-1)^2=(1-2z+z^2)/(0+0+z^2).

Maybe this helps.