# Cake Wavelets

Here the cake wavelets can be generated and are visualized.
The first collection of images shows the cake wavelets in the frequency domain.
In this domain it becomes clear why they are called cake wavelets: they look like pieces of a cake.
The last kernel in this collection is the direct sum of all the cake wavelets in the frequency domain,
and should look like a complete cake except with its center removed.
By taking the inverse discrete Fourier transform of the cake wavelets in the frequency domain
one gets the *complex-valued* cake wavelets in the spatial domain.
The second collection shows the *real* part of the cake wavelets in the spatial domain.
The real parts are *line* detectors.
The last kernel in this collection is again the direct sum of the kernels
and should look like a radial \(\operatorname{sinc}\).
The third collection shows the *imaginary* part of cake wavelets in the spatial domain.
The imaginary parts are *edge* detectors.
In every image the color black indicates the lowest value,
and white indicates the highest value.

The drawing illustrates how the settings influence the cake wavelets in the frequency domain.
The \(i_b\) and \(i_e\) labels in the figure correspond to the *inner taper begin* and *inner taper end* settings.
The \(o_b\) and \(o_e\) correspond to *outer taper begin* and *outer taper end*.
The \(a\) label indicates the *angle taper size*.

### Frequency

### Real Spatial

### Imaginary Spatial

## Input Image

Please choose an image. You can also drop any image onto the page.