Ortogonality prinsiple for noised sine vawes: solving amplitude and phase of sine vawe when frequenc

Discussion in 'MATLAB' started by juho salminen, Oct 6, 2009.

  1. Hi,

    is there any ready functions in matlab which solves amplitudes and phase of sine vawe when frequency is known. For example, in

    https://noppa.tkk.fi/noppa/kurssi/t-61.3040/viikkoharjoitukset

    exercise 24.9. problem 5 uses this method. (Click "Problem set in English" )

    Exercise starts as :

    You have observed the values x(0); x(1); x(2) from the real-valued sinusoidal signal
    x(n) = Asin(nw+a) + v(n); where v(n) is the noise term and a phase. Find the
    amplitude A and the phase that minimize the squared error...

    Thanks already for your answers/follow up-questions!
     
    juho salminen, Oct 6, 2009
    #1
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  2. juho salminen

    TideMan Guest

    No, but you can derive it pretty easily.
    First, use trig identities to expand the equation into a sin and cos
    Next, go:
    help mldivide

    BTW, just to be pedantic, it's wave, not vawe.
     
    TideMan, Oct 6, 2009
    #2
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  3. juho salminen

    Rune Allnor Guest

    If there is exactly one sinusoidal with *known* frequency,
    use DOT. If there are more sinusoidals amd/or the frequencies
    are unknown, things become quite a bit more cumbersome.

    Rune
     
    Rune Allnor, Oct 6, 2009
    #3
  4. If there is only one sampled sinusoidal, you may use the function sinfapm from
    http://www.mathworks.com/matlabcentral/fileexchange/19902
    even in case that the frequency is not known exactly.
    Mira
     
    Miroslav Balda, Oct 6, 2009
    #4
  5. Thanks for your answer.
    It seems this function is not effective for detecting amplitudes of noisy sine waves. Often it returns something completely different than original amplitude of noisy sine.
     
    juho salminen, Oct 11, 2009
    #5
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