Hi, I noticed that the Gaussian pulse is convolved with a rectangular window in the GMSK modulator. Why is that so? Thanks Achilleas

on 2007-05-09 18:14

on 2007-05-09 18:46

If we need to truncate the Gaussian pulse, there are better windows! Bob Anastasopoulos Achilleas wrote: > Discuss-gnuradio mailing list > Discuss-gnuradio@gnu.org > http://lists.gnu.org/mailman/listinfo/discuss-gnuradio > -- AMSAT Director and VP Engineering. Member: ARRL, AMSAT-DL, TAPR, Packrats, NJQRP, QRP ARCI, QCWA, FRC. ARRL SDR WG Chair "If you're going to be crazy, you have to get paid for it or else you're going to be locked up." Hunter S. Thompson

on 2007-05-09 19:14

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

on 2007-05-09 20:13

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 2007-05-09 22:11

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

on 2007-05-09 22:14

Achilleas Anastasopoulos 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

on 2007-05-10 11:34

Anastasopoulos Achilleas schrieb: > Hi, > > I noticed that the Gaussian pulse is convolved with a rectangular window > 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