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

Question

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.

Answer 1

FIR filters typically have a sinc^x type impulse response spectrum or something that looks like it, in some but not all cases. The sinc^x shape is mainly seen when the impulse response h(n), if plotted on cartesian coordinates, look like an even function time shifted where the coefficients are placed symmetrical about the origin. This is a simplistic answer based on a particular type of FIR filter such as a Type I or II. You have not given enough information to give a more specific answer.

So your analog filter would have to look like a sinc^x or some type of comb filter with lobes falling off faster than a typical comb filter. But again this is a simplified answer.

In short it is theoretically impossible to do what you want exactly, or even approximately, but I can't tell you that you cannot somehow come up with a crude approximation, say using delay lines

Answer 2

The plot shown has a frequency axis horizontally, so this is not an impulse response (which is the magnitude and phase of an impulse vs time), but is the Frequency Response.

From the comments it sounds like the OP would like to optimally detect very narrow time pulses (UWB?). Designing a static matched filter for this that would offer any benefit would have considerable challenges: a 0.1 ns pulse in time is a Sinc function in frequency with the first null of the main lobe out at 10 GHz! There will be significant phase dispersion and multipath propagation delay affects over this ultra-wide bandwidth extending over multiple GHz that will most certainly change with time, so unless this experiment is set up in a fixed and controlled environment such an "off-the-shelf components" based filter will likely not be able to offer any improvement.