GNU Radio GMSK modulator

Question

I'm looking at the GNU Radio GMSK modulator block. The Gaussian taps are somehow convolved with a rectangular window with 4 * samples-per-symbol taps owing to the fact for GMSK, the filter spans four symbols. I was wondering if anyone could elaborate why do we convolve the Gaussian taps with the square wave?

self.gaussian_taps = filter.firdes.gaussian(
        1,             # gain
        samples_per_symbol,    # symbol_rate
        bt,            # bandwidth * symbol time
        ntaps                  # number of taps
        )
self.sqwave = (1,) * samples_per_symbol       # rectangular window
self.taps = numpy.convolve(numpy.array(self.gaussian_taps),numpy.array(self.sqwave))
self.gaussian_filter = filter.interp_fir_filter_fff(samples_per_symbol, self.taps)

Answer 1

Let's say you want to filter a signal $x[n]$ through a Gaussian filter with impulse response $h_g[n]$ and a Moving Average (the "sqwave") filter with impulse response $h_s[n]$. Then the resulting operation is

$$y[n] = h_s[n] * (h_g[n] * x[n]) = (h_s[n] * h_g[n]) * x[n]$$

So the a priori convolution of the two filter tap sets into one filter taps set, just reduces the two filtering operations into one filtering operation.

The Moving Average filter is just a low pass filter with a poor transition band and poor sidelobe supression. (The one used here isn't even normalized to unity gain.)

I can't definitely answer "why?", except to say that it looks like someone wanted to add a cheap low pass filter as a sort of channel filter. That moving average filter has been there since 2007, when GNURadio's git history starts. The old CVS repositories aren't on-line anymore, so the original rationale is probably lost to history.