Considerations in the design of a ShortTimeFFT window?

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I was very excited by the new ShorftTimeFFT class, and am beginning to
introduce it into my workflow. My team is interested in audio simulation
and source waveform reconstruction from microphone arrays, and the inverse
STFT functionality is a big draw to the new class.

Our first use case is an integrator and differentiator. We implement this
with a forward/inverse stft pair, and the frequency domain calculus
definitions. We were surprised that the choice of window changes the
derivative result in particular, at a -50 dB level. Unexpectedly, it seems
that lower order windows work much better than higher order. For example,
the hann window computes a better inverse stft than the nuttall window.

We would like to get a better sense of why and get better insight into this
new class. The ShortTImeFFT example uses a Gaussian window, which is an
unusual window choice in my experience. Is there a good reference that can
guide the selection of a window with the application of an inverse stft in
mind?

Thank you,
Ned Richards

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<div dir=3D"ltr"><div>I was very excited by the new ShorftTimeFFT class, an=
d am beginning to introduce it into my workflow. My team is interested in a=
udio simulation and source waveform reconstruction from microphone arrays, =
and the inverse STFT functionality is a big draw to the new class.</div><di=
v><br></div><div>Our first use case is an integrator and differentiator. We=
 implement this with a forward/inverse stft pair, and the frequency domain =
calculus definitions. We were surprised that the choice of window changes t=
he derivative result in particular, at a -50 dB level. Unexpectedly, it see=
ms that lower order windows work much better than higher order. For example=
, the hann window computes a better inverse stft than the nuttall window.</=
div><div><br></div><div>We would like to get a better sense of why and get =
better insight into this new class. The ShortTImeFFT example uses a Gaussia=
n window, which is an unusual window choice in my experience. Is there a go=
od reference that can guide the selection of a window with the application =
of an inverse stft in mind?</div><div><br></div><div>Thank you,</div><div>N=
ed Richards<br></div></div>

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