Each section consists of two lollipop editors that display/modify a vector of complex numbers. In the cartesian view (default), these two represent the real (left) and imaginary (right) parts of the vector's elements. In polar view (switch using button to the left of the section) these two represent absolute values (left) and argument angels (right). Note that the polar view allows entering "negative absolute values", which are interpreted as positive absolute values with an additional argument angle offset of π. It also allows editing argument angles outside range [-π, +π[, which are renormalized into said range. Pressing the auralization button converts the associated complex vector into a stereo clip and continually loops over it with a sampling rate of 11025Hz, four times slower than usual in order to pitch down the waveforms by two octaves.
The lollipop waveform editors support the following editor modes: The pencil is designed to edit multiple values while keeping the mouse button pressed. The sticky pencil is designed to modify one sample in great detail, without loosing grip on it. The rotor tool allows the samples to be rotated to the left of right (single channel), while the mirror tool allows them to be mirrored at the horizontal axis. The eraser tool erases single values, while the reset button resets all values of both sections to zero.
The fold button causes a folding operation to be performed before Fourier transforming the values from the frequency to the time domain (top to bottom), and a corresponding unfolding operation after inverse Fourier transforming the values from the time to the frequency domain (bottom to top). This untangles the frequency domain values into a stereo spectrum, effectively using only a single O(N*logN) Fast Fourier Transform plus one O(N) folding operation. In fold mode, the left half of the complex values in the frequency domain (both editors) represent the spectrum of the left channel in the time domain (with ascending frequencies), while the right half of said values represents the corresponding spectrum of the right channel in the time domain (with descending frequencies); the values are best viewed in polar coordinates. The complex values at index zero and ½N combine 0Hz (real part) and the Nyquist Frequency (imaginary part) of their respective channel.
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