Generation of Trapezoidal Data

Generation of synthetic data sets, 1D signals and 2D images, are essential for the creation of test patterns, color maps, filter kernels, etc. In this experiment we want to create simple 1D signals and 2D images.

The Digital Impulse

The digital impulse delta(i) is defined as:

delta(i) = 1, for i = 0
         = 0, for other values of i

A sequence of impulses can be built from a summation of several impulses placed at different locations.

1D Impulses

1D Impulses: Amplitude (A=5), Number of Impulses (N=4), Spacing between impulses (k=3), Offset (o=5), Width dimension (W=26)

2D Impulses

Depicted below is an image with dimensions (W=128) and (H=100) consisting of 2D impulses. In the width direction there are (N=4) impulses separated by (k=32) pixels, and in the height direction (M=8) impulses separated by (l=10) pixels. The amplitude of each impulse is (A=255). The offsets for both width and height are (o=p=0).

Image with Impulses and generation formula

Trapezoidal Pulses

1D Pulses

There are several parameters that define a 1D-trapezoidal pulse. min and max are the minimum and maximum values. Other parameters are Rise duration (r), pulse Width (w), Fall duration (f) and pulse Period (t), where each control the length of each part of the pulse. Sampling (sampl) controls the number of samples. For most applications, ilt is easier to use sampl=1.

A sequence of almost two trapezoidal pulses, p(x), is shown below:

1D-trapezoidal pulses: min=0, max=10, r=2, w=3, f=4, t=14, sampl=1, signal width (W=26)

A particular cases of this function are the square wave (r=f=0), triangular wave (r=f, w=0) and ramp (w=f=0, r=t).

2D Trapezoidal Images

The images shown below correspond to a ramp, triangle and square waves in the width direction. The dimensions of all three images are (W=512, H=50) and sampl=1.

Ramp Image: r=512, w=f=0, t=W, min=0, max=256

Triangle Wave Image: r=f=256, w=0, t=W, mix=0, max=255

Square Wave Image: r=f=0, w=10, t=30, mix=100, max=200

Building a visual program (workspace) in cantata
Execute the visual program piecewise.wk

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