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Math Help - Goertzel Reverse

  1. #1
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    Nov 2009
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    Goertzel Reverse

    Hi guys. This is probably a stupid question. If so, I guess at least it will be easy to answer quickly

    I have created a discrete power spectrum by running a Goertzel algorithm repeatedly. It does not have a window function. The algorithm was run over the normalised frequency range [0.01, 0.99]. The input sample only has 5 values.

    The implementation is standard, from here:
    Frequency Detection

    However I am scratching my head trying to figure out a way to calculate the reverse DFT using a similar algorithm. IE. I want to go from the spectrum back to the time domain.

    Intuitively it seems that it should be possible to construct a 'reverse Goertzel', but I can't see an obvious way. What do you think?

    P.S. I can provide source code and output info if it helps. I'm guessing the algorithm is irreversible since it discards some info while running (the 'd2' variable in the linked example)..
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  2. #2
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    Nov 2009
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    I have tried reconstructing using a formula like:

    1/N \sum r(f) . cos(2 \pi\ f) + i(f) . sin(2 \pi\ f)

    ..where r() is the real part and i() is the imaginary part, however I just get garbage back.

    Does anyone have ideas regarding how to inverse a power spectrum?
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