Frequency spectrum with fft of a real valued array...?

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  • Holger
    #1

    Frequency spectrum with fft of a real valued array...?



    Dear all,

    I need to do a FFT on an array of 20k real values. Origin of the sampled
    data is a sinus wave with light harmonics.
    The goal is an frequency spectrum with the magnitudes of the first 50.
    harmonics.

    I addressed python like:

    test_arr = src_data_dict[ channel ][0:19599]
    target_data_dic t[ channel ] = FFT.fft(test_ar r,n=50,axis=-1)

    This results in an array of complex values but with unexpected big
    coefficients...
    (much higher than the original signal magnitudes)
    How do I get the absolute magnitudes of the harmonics, which are much
    lower than the
    resulting absolute values of the coefficients?

    The result should be like this:

    1.harmonic (50 Hz) 1,0
    2.harmonic (100 Hz) 0,01
    3.harmonic (100 Hz) 0,08
    4.harmonic (100 Hz) 0,0035
    etc.


    at the moment I get a resulting array like:

    CH1
    (1729.80103418+ 0j)
    (366.689810532+ 19.5196963754j)
    (370.688444025+ 32.162562652j)
    (372.122246668+ 46.9545880507j)
    (379.273599053+ 59.0724599622j)
    (369.889589421+ 75.9247281559j)
    (381.070551892+ 99.07345873j)
    (378.800462354+ 106.761629308j)
    (375.014128346+ 131.34177586j)
    (389.110601354+ 149.320740829j)
    (389.23247472+1 58.909042086j)
    (398.875237165+ 197.86980788j)
    (397.927158223+ 196.858459101j)
    (402.455325066+ 234.651276425j)
    (411.599088579+ 256.32156894j)
    (414.469935576+ 254.512014918j)
    (417.198515262+ 291.400509132j)
    (426.745545674+ 320.769421334j)
    (433.987466212+ 321.929780157j)
    (446.124386798+ 350.810581686j)
    (455.876025379+ 383.099789898j)
    (458.083277747+ 405.592129477j)
    (470.908512117+ 433.929598454j)
    (482.083855098+ 468.256188814j)

    What does it mean to me? How do I get to the wanted frequenca spectrum???
    ...

    btw The maximum magnitudes of the original data are app. 70 peak

    Thanks in advance for your help!!!

    Regards Holger
    Tags: python fftfreq
    • Robert Kern
      #2
      Re: Frequency spectrum with fft of a real valued array...?

      Holger wrote:
      What does it mean to me? How do I get to the wanted frequenca spectrum???
      It's packed in the conventional FFT format. Here is a function in numpy (the
      successor to Numeric, which I assume that you are using) that generates the
      corresponding frequencies in the same packed format:

      In [324]: import numpy

      In [325]: numpy.fft.fftfr eq?
      Type: function
      Base Class: <type 'function'>
      Namespace: Interactive
      File:
      /Library/Frameworks/Python.framewor k/Versions/2.5/lib/python2.5/site-packages/numpy-1.0.2.dev3507-py2.5-macosx-10.4-i386.egg/numpy/fft/helper.py
      Definition: numpy.fft.fftfr eq(n, d=1.0)
      Docstring:
      fftfreq(n, d=1.0) -f

      DFT sample frequencies

      The returned float array contains the frequency bins in
      cycles/unit (with zero at the start) given a window length n and a
      sample spacing d:

      f = [0,1,...,n/2-1,-n/2,...,-1]/(d*n) if n is even
      f = [0,1,...,(n-1)/2,-(n-1)/2,...,-1]/(d*n) if n is odd


      --
      Robert Kern

      "I have come to believe that the whole world is an enigma, a harmless enigma
      that is made terrible by our own mad attempt to interpret it as though it had
      an underlying truth."
      -- Umberto Eco

        Comment

        • Holger
          #3
          Re: Frequency spectrum with fft of a real valued array...?

          Hello Robert!

          Thank you for your tips. They were very useful.

          Bye Holger


          Am 11.01.2007, 19:08 Uhr, schrieb Robert Kern <robert.kern@gm ail.com>:
          Holger wrote:
          >
          >What does it mean to me? How do I get to the wanted frequenca
          >spectrum???
          >
          It's packed in the conventional FFT format. Here is a function in numpy
          (the
          successor to Numeric, which I assume that you are using) that generates
          the
          corresponding frequencies in the same packed format:
          >
          In [324]: import numpy
          >
          In [325]: numpy.fft.fftfr eq?
          Type: function
          Base Class: <type 'function'>
          Namespace: Interactive
          File:
          /Library/Frameworks/Python.framewor k/Versions/2.5/lib/python2.5/site-packages/numpy-1.0.2.dev3507-py2.5-macosx-10.4-i386.egg/numpy/fft/helper.py
          Definition: numpy.fft.fftfr eq(n, d=1.0)
          Docstring:
          fftfreq(n, d=1.0) -f
          >
          DFT sample frequencies
          >
          The returned float array contains the frequency bins in
          cycles/unit (with zero at the start) given a window length n and a
          sample spacing d:
          >
          f = [0,1,...,n/2-1,-n/2,...,-1]/(d*n) if n is even
          f = [0,1,...,(n-1)/2,-(n-1)/2,...,-1]/(d*n) if n is odd
          >
          >

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