filtering my received Signal by LPF

Question

I've received my transmitted signal that I sampled it on 20480000 frequency , transmitted frequency 868MHZ , bitrate 100KHZ , I see the "bits" that Im transmitting in my plot in matlab it looks like:

so what Im now going to do is doing LPF in the cutoff frequency = bit rate and that's in order to be able to do zero crossings, so my output signal of LPF must be like "sinusoidal", I mean by that "smearing the ups and downs that we see in the photo above to look like continues sinusoidal.

Any help how can I do that in matlab? thanks

attaching down a photo that I showed what I mean by "smearing" by dark marker..

eyediagram:

Answer 1

MATLAB has a lot of ways to design filters. You can try designfilt as a starting point: https://uk.mathworks.com/help/signal/ref/designfilt.html. You'd choose the options to set up a FIR LPF and give it your desired cutoff and other parameters (stopband attenuation, ripple allowance, method of filter design).

Choosing the cutoff frequency to be a function of the bit rate is not what you want though. Doing this will distort your signal which you are interested in. Instead, for GFSK, I'd recommend simply computing the 99, 95, or 90 percent bandwidth and setting the cutoff frequency to be half of that. MATLAB has an function called obw which gives the 99% bandwidth but you could write a function myObw(signal, percBandwidth) to calculate any percentage you'd like.

For something like this, it is a good idea to see if what you did actually makes sense. For example, plotting your filter's frequency response over the top of the signal's is a good place to start. The picture below illustrates what I mean and directly shows the problem with choosing the cutoff frequency to be half of your bit rate.

Answer 2

To add to the other good answer specific to designing filters, very importantly the OP must be careful to review the resulting time domain response of the filter to minimize inter-symbol interference (ISI), and design the filter with this purpose in mind specifically. Specifically the cascade of the transmitter filter and receiver filter (and the channel if it contributes distortion, but I don't see evidence of that in the OP's plots) should satisfy the Nyquist ISI criterion. (More on that here: https://www.google.com/search?q=nyquist+filtering&oq=nyquist+filtering&aqs=chrome..69i57j0.5511j1j7&sourceid=chrome&ie=UTF-8). If the transmitter and channel are not introducing ISI (as it appears to be from the plots), then in this case the receiver filter details are simplified, and the OP should design a filter such that the impulse response of the filter crosses 0 at successive symbol sampling locations, such that the time domain tails of prior symbols do not add errors to subsequent symbols. (Otherwise this design criteria is imposed on Tx+Rx, or Tx+Channel+Rx, where in the latter case channel equalization is involved).

One approach I would suggest overall is to create an eye diagram of the received symbols which can then readily show many performance metrics of the receiver waveform after filtering including ISI, jitter, SNR, etc... For further details on eye diagrams please see Eye pattern construction and interpretation