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FFT question

Discussion in 'Electronics Homework Help' started by pump, Mar 30, 2013.

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  1. pump

    pump

    24
    0
    Nov 4, 2011
    Hey Guys,

    I am struggling to answer this question...

    When carrying out an FFT of a cosine wave whose frequency is 0.1Hz and whose amplitude is unity, explain why the peak amplitude measurement obtained in the range 9Hz to 0.11Hz should ideally have a value of 0.5?

    So the cosine's amplitude is unity why would it have an amplitude of 0.5 after conversion... There is something I am not understanding......
     
  2. Raven Luni

    Raven Luni

    798
    8
    Oct 15, 2011
    Are you sure thats the correct range that its asking for?
     
  3. Raven Luni

    Raven Luni

    798
    8
    Oct 15, 2011
    But anyway the 0.5 sounds about right. Remember an FFT gives you both positive and negative frequencies. You either add the corresponding bins or disregard one set and multiply by 2.
     
  4. pump

    pump

    24
    0
    Nov 4, 2011
    Hi Raven,

    Thanks for your reply.. the question does not specify the signals amplitude before conversion apart from being unity.. so after conversion how would I know the amplitude?

    Cheers in advance :)
     
  5. pump

    pump

    24
    0
    Nov 4, 2011
    oh yes that is the correct range.. just an academic question... :)
     
  6. Raven Luni

    Raven Luni

    798
    8
    Oct 15, 2011
    Unity means 1
     
  7. pump

    pump

    24
    0
    Nov 4, 2011
    yea sure unity means 1, but if I don't know the original magnitude how would I know its 0.5?
     
  8. pump

    pump

    24
    0
    Nov 4, 2011
    sorry it is 0.09Hz to 0.11Hz.... you were right questioning the range .. I read it wrong :)
     
  9. Raven Luni

    Raven Luni

    798
    8
    Oct 15, 2011
    For single frequencies, amplitude and magnitude are the same thing. The FFT spike has a magnitude of 1 because the time domain signal at that frequency has an amplitude of 1. The reason you get 0.5 is because the FFT is a form of the complex DFT. It shows a negative mirror image of the frequency domain. The magnitudes are split evenly between these and the phases are opposite.

    Read this book. It's free to download in PDF form, a bit dated but very good: http://www.dspguide.com/
     
  10. pump

    pump

    24
    0
    Nov 4, 2011
    Thank you ever so much for your reply it has really helped :) I'll take a look at the dsp guide right now... Thank you once again
     
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