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Mishal Mohanlal
Last activity on 17 Nov 2023

Compression only spring mass system

Hi Guys

Posting this based on a thought I had, so I don't really ahve any code however I would like to know if the thought process is correct and/or relatively accurate.

Consider a simple spring mass system which only allows compression on the spring however when there is tension the mass should move without the effect of the spring distrupting it, thus the mass is just thrown vertically upwards.

The idea which I came up with for such a system is to have two sets of dfferential equations, one which represents the spring system and another which presents a mass in motion without the effects of the spring.

Please refer to the below basic outline of the code which I am proposing. I believe that this may produce relatively decent results. The code essentially checks if there is tension in the system if there is it then takes the last values from the spring mass differential equation and uses it as initial conditions for the differential equation with the mass moving wothout the effects of the spring, this process works in reverse also. The error which would exist is that the initial conditions applied to the system would include effects of the spring. Would there be a better way to code such behaviour?

function xp = statespace(t,x,f,c,k,m)
    if (k*x(1)) positive #implying tension
      **Use last time step as initial conditions**
      **differential equation of a mass moving""
    end
    if x(1) negative #implying that the mass in now moving down therefore compression in spring
      **Use last time step as initial conditions**
      **differential equation for a spring mass system**
    end
end

Ideas

Martin Ryba
Last activity on 12 Dec 2023

AWGN SNR calibration for band limited signals

Seeing a colleague make this mistake (one I've had to fix multiple times in other's work too) makes me want to ask the community: would you like the awgn() function/blocks to give the option for creating a SNR at the bandwidth of the signal? Your typical flow is something like this:

Create a signal, usually at some nominal upsampling factor (e.g., 4) such that it's now nicely over sampled, especially if you're using a RRC or similar pulse shaping filter.
Potentially add a frequency offset (which might make the sample frequency even higher)
Add AWGN channel model for a desired SNR
Put this into your detector/receiver model

The problem is, when someone says, "I'm detecting XYZ at foo SNR," it should not magically improve as a function of the oversample. The problem isn't that awgn() generates white noise, that's what it's supposed to do and the typical receiver has noise across the entire band. The problem is that SNR is most properly defined as the signal power over the noise power spectral density times the signal's noise equivalent bandwidth. Now I looked and there's no handy function for computing NEBW for an input signal (there's just a function for assessing analysis windows). In practice it can get a bit tricky. The occupied bandwidth or HPBW are often close enough to the NEBW, we're usually not haggling over hundredths of a dB. So, in my not so humble opinion, the "measured" flag for awgn() should give an option for bandwidth matching or at least document the behavior better in the help page. All too often I'm seeing 3-6 (or worse) dB errors because people aren't taking the signal's bandwidth into account.