I'm trying to understand this paper: http://academics.w

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I'm trying to understand this paper: http://academics.wellesley.edu/Physics/brown/pubs/effalgV92P2698-P2701.pdf

The author describes a way of calculating the Constant-Q Transform of a signal by calculating temporal kernels and finding their Fourier transforms to get the spectral kernels.

The part where the temporal kernels are calculated and graphed is where I'm lost. For whatever reason, there are 2048 samples on the graph, despite there being only 512 FFT bins implying the FFT from temporal to spectral kernels was done on a 1024 sample temporal kernel.

The angular frequencies appearing in Eq. 4 are all well over 2 pi rad/s, so these kernels are undersampled. I don't know if that's a problem or not.

I'm trying to write MATLAB code to calculate some spectral kernels of my own. It can be found at https://pastebin.com/dxUVx4Ar
Every so often, one of the center frequencies is a multiple of 2 pi, so the complex exponential is 1 across all frequencies, leaving the temporal kernel as simply the Hamming window. This never appears to happen in the attached graph.

Of course, I wouldn't be asking if my spectral kernels looked like those in the paper. They don't.

So what's going on? I'm stumped.