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Potential Fourier Analysis Metrics?

  1. Oct 7, 2012 #1
    So, my friend looked at this post and told me it's beyond confusing. So let me clarify.

    Suppose I have a neural network connected to various sensors. How best would I process the input data from the sensor such that a neural network could learn from it best. I'm assuming my network has many, many inputs, so perhaps I could input all types of processed input from my sensors. Forget about processing power limitations for now. I'm simply asking, what types of frequency input would be useful for a neural network to learn from?

    I thought of one metric. I was considering weighting recent inputs higher in a fourier integral as below.


    Continuous:

    [itex] {\bf{F}}_c(j\omega,\alpha,t) = \int^t_{t_0} f(\tau)e^{(\tau -t)\alpha}e^{-j\omega\tau}d\tau, \; \alpha >0 [/itex]

    and Discrete (which I would use on a comp):

    [itex] {\bf{F}}_d(j\omega,\alpha,n) = T\sum^n_{k=k_0} f_ke^{[k-n]\alpha T}e^{-j\omega Tk}, \; \alpha >0 [/itex]

    The idea is that they are weighted Fourier Transforms such that the exponential terms in the integrand and summand are such that since [itex] \tau -t \leq 0, k-n \leq 0 [/itex] ,then [itex] e^{(\tau -t)\alpha} \leq 1, e^{(k -n)T\alpha} \leq 1 [/itex] so that most recent terms are weighted exponentially more.

    Then, on the network inputs, I could input values of my weighted fourier transforms from several values of time and several frequency values, so perhaps a whole matrix of inputs from this frequency metric.

    I could even do the same thing for the continuous time inputs

    Continous:
    [itex] {\bf{f}}_c(\alpha,t) = f(t)e^{(\tau -t)\alpha} [/itex]

    Discrete:
    [itex] {\bf{f}}_d(\alpha,n) = f_ne^{[k-n]\alpha T}[/itex]

    and then, I can get a vector of inputs if I input the last so many sample values from this metric

    Would this be a good "feature selection"?
     
    Last edited: Oct 7, 2012
  2. jcsd
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