# Implementing an analog approximation of an FIR filter given its impulse response

Problem:

I have the impulse response of a matched filter(therefore its phase and magnitude response. See figure below) of a filter, and I need to implement its response using only off-the-shelf components i.e low-pass filter, delay lines, multiplexers, etc.. I don't require extreme precision but I'd like to approximate its response as exact as possible.

Possible Solutions:

• Cascade low-pass and high pass filters to obtain the overall shape of the magnitude response. Use delay lines to implement two taps to give the magnitude response its "sinusoidal" nature as shown by the above figure.
• Use a multiplexers/splitters with delays, phase shifters, and attenuators with values according to the filter's frequency and phase response.

I am extremely new to signal processing so I don't know much of what is out there. So please, if anyone could guide me or give me an insight into how to achieve my goal, I'd really appreciate it.

• So this is originally an analog filter? Is it a standard form (low pass/high pass/ band pass etc)? Is it linear at least? Your plot is kinda noisy we can't really see... Also I imagine red is phase and blue is amplitude but could you confirm? – Florent Jul 25 '17 at 23:22
• I highly doubt that this is a filter at all... is this a sensor response? a channel response? How did you generate this so called FIR response? – Fat32 Jul 26 '17 at 16:12
• Yes the red curve is the phase and the blue one is the amplitude response. @Fat32 It is a filter. The way I obtained the tap coefficients of the filter was by reversing in time data of a single pulse, which acts as a matching filter if convoluted with the unfiltered data. Then by definition the time-reversed data is the impulse response of my desired filter. I am new to this so let me know if I need to elaborate more. – Agustin Pacheco Jul 26 '17 at 21:03
• ahaa! Yes this is the impulse response of a matched filter. Ok so you are right. Such a meaningless impulse response can be generated as a matched filter which is indeed a signal's waveform reversed. So you want to detect something with the matched filter? Why do you want to do that using analog technology? – Fat32 Jul 26 '17 at 21:15
• ok good but that requires more microwave engineering than DSP, I'm sure you'r aware of it. Coming to the approximation, analog approximation techiques is the least topic I could be talking of... sorry. You would need very high orders and comlplex transfer function to realize though. Unless you state explicitly what degree of approximation is acceptable. – Fat32 Jul 26 '17 at 22:06