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Queries on Signal Processing - Cross Correlation

  1. Jan 3, 2012 #1
    I'm new to the field of signal processing and currently reading a paper which it uses cross-correlation of two signals for detecting some machine failures. But I'm confused with the complex conjugate in the equations. Take equation from wikipedia as example:

    [itex](f\star g)(t)\equiv \int_{-\infty }^{\infty }f^*(\tau)g(t+\tau)d\tau[/itex]

    Currently, I understood that they have significant contribution to the integral when some of their signals are aligned. But how does the complex conjugate involve and affect the function? And any recommended book on this topic?

    Any guidance will be much appreciated. And please correct me if I have made any fundamental misconceptions.
     
  2. jcsd
  3. Jan 3, 2012 #2

    rbj

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    It has to do with the inner product in a Hilbert space. This correlation, at [itex]t=0[/itex], could be a good definition of the inner product of [itex]f[/itex] to [itex]g[/itex]. as it is, it's the inner product of [itex]f[/itex] to [itex]g[/itex] slid apart by displacement [itex]t[/itex]. It's so that if a complex [itex]f()[/itex] is convolved with itself, when [itex]t=0[/itex] then it's the integral of [itex]|f|^2[/itex].
     
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