Hi,

I noticed that the Gaussian pulse is convolved with a rectangular window

in the GMSK modulator. Why is that so?

Thanks

Achilleas

Hi,

I noticed that the Gaussian pulse is convolved with a rectangular window

in the GMSK modulator. Why is that so?

Thanks

Achilleas

If we need to truncate the Gaussian pulse, there are better windows!

Bob

Anastasopoulos Achilleas wrote:

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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

I guess I am answering my own question here.

Just realized that GMSK is defined with pulses that are

indeed the convolution of Gaussian and square pulses.

What a missnomer…

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

Anastasopoulos Achilleas schrieb:

Hi,

in the GMSK modulator. Why is that so?

Usually you would shape (that is) convolute your pulses with a rectangle

to get nice symbols, as a single spike won’t be detected at the

receiver.

But rectangles produce infinite bandwidth sinc spectra. You really like

to limit your bandwith (and thus save you trouble with other people and

power). This can be achieved by convoluting your (now rectangle) signal

with a Gaussian shape. This is known to achieve maximum bandwidth

efficiency.

Gaussian has an second interpretation/origin: yiu get the same signal

with an optimized phase shift modulation.

Patrick

Achilleas A. wrote:

I guess I am answering my own question here.

Just realized that GMSK is defined with pulses that are

indeed the convolution of Gaussian and square pulses.

What a missnomer…

Yeah, I was bothered by that for a while.

Matt

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