How would this be implemented in practice

[David83]

Hello all,

I have the following mathematical equation, and I am wondering how would it be implemented in practice, and if it would be efficient. The equation is:

\[v_k=\sum_p H_p^*\int_{kT_s+\tau_p}^{(k+1)T_s+\tau_p}v(t)\,dt\]

where Ts is the symbol time, H_p is pth path's gain, and tau_p is the pth path's delay.

Thanks in advance

 

[ashugtiwari]

In analog, use op-amp integrator to run integral over value of input v(t) and then use inverting amplifier to multiply with Hp and find vk.
In digital, simply convert v(t) to digital using ADC in uC as fast as possible at periodic interval, do this for time t=[(k+1)Ts+taup]-[kTs+taup] using internal timer for uC and keep on accumulating value of v(t). Then simply multiply the completed value of v(t) i.e. accumulated value of v(t) with every value of Hp and add then all.

Hope that helps.

 

[zorro]

For each of the terms of the sum you have an integrate-and-dump block operating at cadence Ts and delays tau_p. The outputs (stored for example in hold capacitors or converted to digital form) are added with weights H*_p.
Regards

Z

 

[David83]

Thanks for the details ashugtiwari and zorro. I am not planning to implement it physically, but I am designing a system theoretically, and wanted to make sure the integral is not a practical issue, which both of you didn't mention. Is it? Also, I am more interested, how to implement the integral in MATLAB.

 

[David83]

Also, which is more complex in practice: an integrator or FFT operation? I have a system with a bank of integrators, and another with a bank of FFT blocks, and I want to make a comparison in terms of hardware complexity between them.

Thanks