# Real parameters design and computation for a filter, modulator

I design in Gaussian filter for a modulator in MATLAB, which should be later implemented in FPGA. I have an implemented design of the filter and the modulator as well and now I have to determine some parameters: sampling rate, oversampling factor, spectral efficiency… (Did I miss something else?)

Oversampling factor is limited by a board specification I will use.

Sampling rate as I know should be two times more that max frequency of an input signal. I have seen in a publication if an operating frequency 2, GHz, this modulator has the sampling rate = 22MSps, 70 MHz to 6 GHz = 61,44 MSps. So I can assume the sampling rate as a parameter of filter should be computed somehow, right?

Spectral efficiency is a characteristic of the output of the modulator. I need to plot a spectrum of the output signal of the modulator and check if the desired value in dB is reached. Do I understand it correctly?

Could you please correct me if my assumptions are wrong?

• Did you choose a Gaussian filter because everyone does it, or do you need that filter specifically? Are you implementing it as an IIR, or an FIR filter? Apr 29, 2022 at 14:27
• @TimWescott I will do it as FIR. I implement gmsk modulation May 2, 2022 at 6:22

The design of a Gaussian filter allows for exactly one degree of freedom: The standard deviation of the pulse. The shape is already defined by the fact it's a Gaussian filter!

That standard deviation is a measure of how "wide" the pulse is in time (or, conversely, how narrow in frequency, since both are inherently inversely linked through the Fourier transform).

So, all you get to choose is the bandwidth or temporal extent of the Gaussian bell curve. That's it. Then you sample the continuous Gaussian function at times given by the sampling rate.

So I can assume the sampling rate as a parameter of filter should be computed somehow,

No.

Sampling rate, oversampling factor, spectral efficiency are parameters that are given for your system, so from these you need to compute the required bandwidth (or temporal structure) of your filter.

• bandwidth, i can compute from BT, right? I need only Ts Apr 29, 2022 at 11:26
• I don't know what BT or Ts are. you don't define these symbols anywhere. However, bandwidth is usually the most important externally defined requirement of any communications system, so I doubt you have to "compute" it at all. You just need to understand your requirements in context of your application. Apr 29, 2022 at 11:28
• Sorry ... BT -bandwidth-symbol time product where B is the −3 dB(half-power) bandwidth of the pulse/filter and T is the symbol duration. Apr 29, 2022 at 12:16
• Since the symbol duration is probably also defined by the external requirements, I think you've just answered your own question. (basic arithmetic.) Apr 29, 2022 at 12:38
• sampling rate ( oversampling rate) and sample per symbol, are two different value? May 2, 2022 at 8:57