MacWavelets 2.00 User's Manual

5.2 Generating 2d Datasets

To generate 2d data, first create and select a 2d Image window by choosing the "New 2d Window" item of the Windows menu, or select an existing Image window.

Note that the following are displayed using the "Signed values" option of the Image window.

5.2.1 Random

To create a random dataset, choose the Generate Data... item from the Wavelets menu, and the Random item from the attached submenu. The random data generation function then presents the following dialog:

The distributions are as follows:

Uniform: points are chosen from a uniform distribution on an interval with a given mean and a range from mean - amplitude to mean + amplitude.
Normal: points are chosen from a normal distribution with given mean and a standard deviation equal to amplitude.

Here is an example of a random distribution:

5.2.2 Sine

To create a sine dataset, choose the Generate Data... item from the Wavelets menu, and the Sine item from the attached submenu. The sine data generation function then presents the following dialog:

The sine function generates a dataset using the following formula:

     z = amplitude * sin(x-frequency * x + x-phase)
                   * sin(y-frequency * y + y-phase)

Such a result looks like the following:

5.2.3 Sine * sine

To create a sine * sine dataset, choose the Generate Data... item from the Wavelets menu, and the Sine * sine item from the attached submenu. The sine * sine data generation function then presents the following dialog:

The sine * sine function generates a dataset using the following formula:

  z = amplitude * sin(x-frequency * x + x-phase) 
                * sin(x-frequency2 * x + x-phase2) 
                * sin(y-frequency * y + y-phase) 
                * sin(y-frequency2 * y + y-phase2)

Such a result looks like the following:

5.2.4 Chirp

To create a chirp dataset, choose the Generate Data... item from the Wavelets menu, and the Chirp item from the attached submenu. The chirp data generation function then presents the following dialog:

The chirp function generates a dataset using the following formula:

  z = amplitude * sin((x-acceleration * x) * x-frequency * x + x-phase)
                * sin((y-acceleration * y) * y-frequency * y + y-phase)

Such a result looks like the following:

5.2.5 Sine * chirp

To create a sine * chirp dataset, choose the Generate Data... item from the Wavelets menu, and the Sine * chirp item from the attached submenu. The Sine * chirp data generation function then presents the following dialog:

The sine * chirp function generates a dataset using the following formula:

  z = amplitude * sin((x-acceleration * x) * x-frequency * x + x-phase)
                * sin(x-frequency2 * x + x-phase2) 
                * sin((y-acceleration * y) * y-frequency * y + y-phase)
                * sin(y-frequency2 * y + y-phase2)

Such a result looks like the following:

5.2.6 Pulse

To create a pulse dataset, choose the Generate Data... item from the Wavelets menu, and the Pulse item from the attached submenu. The pulse data generation function then presents the following dialog:

The pulse function generates one or more Gaussian peaks such that:

The pulse locations can be evenly spaced or placed at random throughout the data array.
The pulse heights can be a constant value, or distributed uniformly between 0 and a maximum value.
The pulse widths can be a constant value, or distributed uniformly between 0 and a maximum value.

A typical pulse dataset looks like the following:

A more interesting pulse dataset (with 100 pulses, random locations, random heights, and random widths) looks like the following:

5.2.7 Ramp

To create a ramp dataset, choose the Generate Data... item from the Wavelets menu, and the Ramp item from the attached submenu. The ramp data generation function then presents the following dialog:

Presumably the function of the settings in the dialog are fairly obvious.

A typical ramp dataset looks like the following:

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