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Welch's method

  1. Jun 9, 2010 #1
    Is this method good for analyzing a pulse?
    Why is the averaging of the spectra good for noise cleaning?
    What's the criteria for defining how much windows in a set of data one should take?

    Anyone who clarifies this has a big thanks from me.
     
  2. jcsd
  3. Jun 9, 2010 #2

    marcusl

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    Welch's method divides the data string into short segments, applies a window to each prior to the Fourier transform, averages the transforms, and takes the squared magnitude to produce a power spectrum. It reduces the variance of the DFT spectral estimate (just as Bartlett's method does) and at the same time smooths the estimate in the way windowing always does, at the expense of degraded resolution (also in the way windowing always does). Another advantage over the regular Bartlett periodogram is that the power spectrum is always positive. Most spectrum analyzers use this method.

    Answering your other questions requires a deeper understanding of spectral analysis. There are a dozen well-established methods of spectral analysis. DFT-based ones are the simplest and most common but not necessarily best. Model-based methods (AR, MA, ARMA, etc.) are better if you have a model and the time to develop the specific analysis. Non-linear methods (Capon method or minimum variance distortionless response, maximum likelihood, MUSIC, etc.) have far better resolution but are complicated and require a high state of knowledge to use wisely. Wavelets and so-called fractional Fourier transform methods are good for signals with components of varying finite durations (speech, say). Maximum entropy and Bayesian methods are at the top in terms of accuracy, resolution, freedom from artifacts, and also in terms of difficulty and required knowledge. They are seldom used.

    The wording of your questions suggests that you are not knowledgeable in these methods. Therefore, go ahead and use a simple FFT-based method. You have plenty of company--probably 90+% of engineers know of and use nothing else.
     
  4. Jun 9, 2010 #3
    Well,i didn't expect this much information :) ... but of course,your observation is very much correct.
    I had some assignments for class and i just wanted to know,on a whim,why these methods are suited for my task.
    MATLAB help points to the Introduction to Spectral analysis from Stoica and Moises,ill guess ill start there and then perhaps another time be more specific...But thanks anyway!
     
  5. Jun 9, 2010 #4

    marcusl

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    Sure thing.

    I can answer your last question in a general way, anyway. If your signal is repetitive and low in jitter (example: output of a radar transmitter), then averaging a lot of data is helpful. Overlap the windows so that all segments receive equal waiting on average. If the signal is variable (maybe receiving UHF radar pulses through the ionosphere during high solar activity), then you'll get a lot of smearing. This might be good if you want to characterize the average propagation channel. If you want to determine the spectrum of an individual pulse, on the other hand, the smearing is bad. Instead use a short data record.

    For a given data sequence, the trade between many short segments and fewer longer ones is the trade between lower variance in the spectral estimate, and finer spectral resolution.
     
  6. Jun 10, 2010 #5
    I'll be honest and say that i am not following everything you've said but at least you gave some pointers.

    And to be direct my problem was determining the amplitude response for a horizontal seimograph.
    In the picture on the left is the one obtained by forcing it with a current(via induction).While the right one is given by analyzing the spectral density of a pulse and then multiplying it with phase velocity squared to get the amplitude response.

    My problem is the difference that gets bigger with higher frequencies.

    Anyway,thanks for the effort,its much appreciated
     

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