Re: [Discuss-gnuradio] question on gmsk mod block

[Anastasopoulos Achilleas]

This does not seem right to me:

The instantaneous frequency of GMSK signal is supposed to be:
fi(t)=h sum_k a_k g(t-kT)
where a_k is the symbol (say +-1), g(t) is the Gaussian pulse
T is the symbol interval and h is the modulation index.
In a discertized model with oversampling factor of Q (ie, Ts=T/Q)
this equation becomes:
fi(n Ts)=h sum_k a_k g((n-kQ)Ts)
or in discrete time notation
fi(n)=h sum_k a_k g(n-kQ) = h    x(n) conv g(n) 
where
x(n) = [a0 0 0 0 a1 0 0 0 a2 0 0 0...]

I don't see where the need for the rectangular window is.
What am I missing?

Achilleas



On Wed, 9 May 2007, Matt Ettus wrote:

> Anastasopoulos Achilleas wrote:
> > Hi,
> >
> > I noticed that the Gaussian pulse is convolved with a rectangular window
> > in the GMSK modulator. Why is that so?
>
> The pulse is convolved with a rectangular window because the incoming data is 
> not. 
> For example, if you wanted to send 1011 and had 4X interpolated data, the 
> data stream into the gaussian filter would look like:
>
> 1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1
>
> however, the input to the block in question is:
>
> 1,0,0,0,-1,0,0,0,1,0,0,0,1,0,0,0
>
> It was easier to precombine the zero-order hold with the gaussian filter by 
> convolving it rather than having 2 separate filters in the real-time portion 
> of the code.
>
> Matt