Re: Sound Analysis Tools

[Thierry Rochebois <thierry@xxxxxxxxxxxxxxxxxxxxxx>]

Thierry Rochebois wrote:
>>What I have is a frequency sampled gaussian.
>>On a log scale a gaussian is a parabola.
>>So, the quadratic interpolation of this spectrum on a log scale gives
>>an accurate value of the frequency and amplitude.

James Beauchamp wrote:
>We are using a Kaiser window. Isn't a Kaiser close to a guassian? After all
>true guassians would require infinite time and frequency windows.

Julius O. Smith III wrote:
>We also like the Gaussian window because its transform is a parabola
>on a dB scale and so it is exactly interpolated by quadratic
>interpolation in the frequency domain. However, the Gaussian
>window must itself be windowed, so results are not exact.  What
>window do you use on the Gaussian window?  Have you quantified the
>resulting interpolation error?

I don't use any window on the gaussian (ie I use a square window).
I just adjust the ratio between the width of the gaussian lobe compared with
the width of the window. So, enlarging the window when keeping the same lobe
width is much like zero padding. But, unlike zero padding, as I add "nearly"
zero coefficient I decrease the side lobe amplitudes.

It must be very interesting to study the effects of windowing on a gaussian
window. It must be interesting to know how the side lobes and the accuracy of
the interpolation varies with the window type and window/gaussian lobe width
ratio.