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## Main Question or Discussion Point

Hi all, I have a seemingly simple problem which is I'd like to efficiently evaluate the following sums:

[tex]

Y_k = \sum_{j=0}^{n-1} c_j e^{\frac{i j k \alpha}{n}}

[/tex]

for [itex]k=0...n-1[/itex]. Now if [itex]\alpha = 2\pi[/itex], then this reduces to a standard DFT and I can use a standard FFT library to compute the sums. But if [itex]\alpha \ne 2\pi[/itex] then I don't see how I can put this into standard DFT form to use a regular FFT library on this.

I guess this problem amounts to computing a DFT with harmonics that do not necessarily have periods of [itex]2 \pi[/itex].

Any help is appreciated!

[tex]

Y_k = \sum_{j=0}^{n-1} c_j e^{\frac{i j k \alpha}{n}}

[/tex]

for [itex]k=0...n-1[/itex]. Now if [itex]\alpha = 2\pi[/itex], then this reduces to a standard DFT and I can use a standard FFT library to compute the sums. But if [itex]\alpha \ne 2\pi[/itex] then I don't see how I can put this into standard DFT form to use a regular FFT library on this.

I guess this problem amounts to computing a DFT with harmonics that do not necessarily have periods of [itex]2 \pi[/itex].

Any help is appreciated!