08/2023
This visualization of sound is inspired by the Radon transform.
Step 1: Compute the usual spectrogram
- 16 kHz
- Frame size: 2048
- Num frames: 1024
Step 2: Compute the auto-correlation of each frame. This can be done by computing re*re+im*im of each component of the FFT, and then applying the inverse FFT.
Step 3: Following the idea of the Radon transform, re-arrange the auto-correlation frames as diameters of a circle.
There is a small improvisation here. If we were to follow the idea of the Radon transform strictly, each diameter of the circle would represent a different timeframe, so each column of the previous ACF image would become a diameter. The end result would be interesting, but not visually appealing. The improvisation is to re-arrange the ACF columns as circumferences.
Step 4: Apply the inverse FFT on the circular image.
In the Radon transform, this step restores the 3D/2D spatial data from a set of projections (CT scans), so an interpretation of this image is it's a 2D object whose average density at all angles look like the diameters of the image at step 3.
Other examples of vowel sounds:
A flute sound for comparison (the same sound at 16 kHz and 48 kHz):
Images are clickable.