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

From: Anastasopoulos Achilleas
Subject: Re: [Discuss-gnuradio] question on gmsk mod block
Date: Wed, 9 May 2007 14:09:57 -0400 (EDT)

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?


On Wed, 9 May 2007, Matt Ettus wrote:

Anastasopoulos Achilleas wrote:

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:


however, the input to the block in question is:


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.


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