Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Binary Detection in Gaussian Noise

  1. Feb 7, 2013 #1
    I have a vector signal, [itex]\underline{x}(t)[/itex], which is afflicted with Gaussian noise [itex]\underline{n}(t)[/itex]. I take a finite number, [itex]L[/itex], of discrete observations and (based on those observations) want to determine whether:

    (1) Only Gaussian noise is present, [itex]\left[\text{i.e. } \underline{x}(t) = \underline{n}(t)\right][/itex]
    (2) Gaussian noise plus a "non-noise" term, [itex]\underline{a}m(t)[/itex], are both present. [itex]\left[\text{i.e. } \underline{x}(t) = \underline{a}m(t) + \underline{n}(t)\right][/itex]

    The scalar, [itex]m(t)[/itex], is zero-mean and has unknown power (variance). The elements of [itex]\underline{x}(t)[/itex] are independent of each other and also independent of [itex]m(t)[/itex].

    Given my observations, how can I estimate the probability that the signal is present?

    Many thanks for any help!
     
  2. jcsd
  3. Feb 7, 2013 #2

    chiro

    User Avatar
    Science Advisor

    Hey weetabixharry.

    I'm not an expert, but I do recall the subject of Kalman filters:

    http://en.wikipedia.org/wiki/Kalman_filter

    Basically you should check out these kind of things where you prefix a structure for your information that assumes some noise model (like White Gaussian) and then uses a filter to not only detect noise, but also the actual non-noisy information.

    There are also non-linear variants of the filter.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Binary Detection in Gaussian Noise
  1. Binary operation (Replies: 3)

  2. Binary Logic (Replies: 2)

  3. Binary operations (Replies: 12)

Loading...