6
$\begingroup$

I have a signal composed of the summation of a set of sine waves of different frequencies. The amplitude of these sub-signals can change so many times a second.

I have been told that, if I want to retain the ability to distinguish each of the frequencies, the time-frequency uncertainty principal means there will be a limiting relationship between the duration of the time window between amplitude changes and the smallest interval between frequencies.

I found a website which seems to deal with the problem, but as a non-mathematician, I'm not sure how to utilise the formulas it shows. To be honest, I'm not even sure if it's relevant.

My question then: What is the relationship between the time interval and the minimum frequency interval?

  • 0
    Roughly speaking, the relationship is that one is proportional to the inverse of the other. For a more precise answer, you might need to explicate what you mean by "the ability to distinguish each of the frequencies".2011-12-12
  • 1
    Are you familiar with the Nyquist rate?2011-12-12
  • 0
    Asking this question on the signal processing stack exchange dsp.SE instead might be worthwhile.2011-12-12
  • 1
    If you search for the sampling-theorem instead of the time-frequency uncertainty principle you find something more rigorous (a theorem) instead of just a principle.2011-12-12
  • 1
    Some related material is [here](http://dsp.stackexchange.com/q/432/235) on dsp.SE2011-12-12
  • 0
    are you looking for "intuitive insight" of the phenomena, an engineering rule of thumb, or a mathematical treatment ?2017-02-15
  • 0
    @GCab 'intuitive insight' is ALWAYS quite important.2018-03-27
  • 0
    [Incertainty Principle Energy vs. Time](http://www.phy.pku.edu.cn/~qhcao/resources/class/QM_panel_13/ajp_uncert_energy_time1.pdf)2018-03-27
  • 0
    @FelixMarin: thanks for inviting to answer. I posted what my engineering experience suggests in tackling this problem. The paper you suggest is quite interesting indeed, but if I understood properly the question we are in the field of signal analysis, far from quantum physics.2018-03-28

2 Answers 2