I am reading a reseach paper "Joint Synchronization of Carrier Frequency, Symbol Timing and Sampling Rate in Digital Satellite Receivers" written by Suesser-Rechberger B and Gappmair W and have found an unknown for me type of matched filter.

What is derivative matched filter? What is a difference?


Take the matched filter (to the transmit filter, i.e. the time-inverse complex conjugate of the transmit filter), and calculate a derivative of it (in time domain).

That's your derivative matched filter! So, it's not a type of a matched filter, but something that can be calculated from a matched filter.

(the way you calculate a derivative of a finite-length discrete-time filter is up for discussion, too, but this might lead a bit too far)

I don't have that paper at hand, but using derivative filters is a common method in symbol synchronization: Note that convolution with a filter and derivation are both linear operations – so that convolution with a derivative filter allows for a "reordering" of these operations, and you get an output signal that is (an estimate of) the derivative of combined transmit filter + matched filter pulse shape.

Since that typically at least has a local maximum at the proper symbol instant, it can be used as base for symbol timing estimation.

The classical harris FLL band-edge filters can be used with it, too for frequency estimation (when you imagine the derivative of a typical low-pass pulse shaping filter, you'll find it will look like a high-pass filter, and if you compare the energy in the upper pass band with that in the lower pass band, you get an estimate for how to correct frequency) and phase estimation (this is where the actual derivative becomes useful). At GRCon, fred harris held a presentation on that (slides, video).


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