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dsplib: efficient fft computation of real input

Markus Grunwald
Expert 2060 points

Hello,

There is a great description for efficiently calculating the FFT of real valued input signals:

 http://processors.wiki.ti.com/index.php/Efficient_FFT_Computation_of_Real_Input

It's using dsplib, so I think this might be the right place to ask. Feel free to move the thread to a better place :)

I have a question for the math experts. The article describes how to calculate the spectrum of N real values using N/2 complex values. Part of the algorithm is to generate the second half of the spectrum by calculating the complex conjugated first half so that in the end there is a complete spectrum.

The inverse FFT is described there, too. As far as I understood (and read the example code), it uses the complete spectrum as it was calculated before.

Now, I'm really not interested at all in the second, complex conjugated part of the spectrum. For the "normal" FFT, I just leave it away as I can always reconstruct it, if necessary and I need half the memory.

Is there a way of calculating the inverse FFT, without reconstructing the second half of the spectrum? This would be great since I would have to allocate less memory…

Thank you,

Markus

  • 0
    Expert 2060 points

    Since I just have to "undo" the multiplication with the complex As and Bs of the algorithm it's in fact easy: I don't expand the second haf in the forward fft, so I just have to divide by the As and Bs in the inverse fft. That's actually multiplying by their complex conjugate and that is described in the mentioned document - you just have to find it :)