Douglas Goncz A.A.S. M.E.T. 1990

2023-04-16 06:35:36 UTC

Let us say we want the gradient of a Time series. For finite time series we

will be losing one data point at each end using most most methods. We

subtract each data point from its adjacent data point the one to either so

I'd let's say it's going to be the right side consistency consistently.

This gives us the time series which is the gradient of that original signal.

Let us say we want the gradient of a two-dimensional spatial series

otherwise known as an image. Buying analogous process I'm subtracting and

getting something like the gradient.

Symbolically the gradient is the partial derivative in each direction for

any number of dimensions.

Well I have been playing with the two dimensional spatial series data or

image format in mathcad and found a function called cfft which computes the

complex fast fourier transform of data in 2 dimensions. The icfft function

reverses that result to restore an image. Lowpass and high-pass filtering

are easy but not spectacularly easy in the cfft domain. They are

spectacular easy in the one-dimensional case.

Pixel data in two dimensions in space in grayscale our conventionally a

number of bits say 8 bits for 256 levels of Gray. And are analogous in

color spaces. Edge detection produces a result similar to an artist's

pencil drawing.

Well I collect pencil drawings and also pencil drawing software.

And I use mathcad.

I usually use the variable name capital m for matrix containing two

dimensional grayscale image data in mathcad. I compute the gradient several

different ways in method.

I have a new way to compute the gradient in mathcad and symbolically.

icfft (i * cfft (M))= grad(M).

Discussion?

Douglas

will be losing one data point at each end using most most methods. We

subtract each data point from its adjacent data point the one to either so

I'd let's say it's going to be the right side consistency consistently.

This gives us the time series which is the gradient of that original signal.

Let us say we want the gradient of a two-dimensional spatial series

otherwise known as an image. Buying analogous process I'm subtracting and

getting something like the gradient.

Symbolically the gradient is the partial derivative in each direction for

any number of dimensions.

Well I have been playing with the two dimensional spatial series data or

image format in mathcad and found a function called cfft which computes the

complex fast fourier transform of data in 2 dimensions. The icfft function

reverses that result to restore an image. Lowpass and high-pass filtering

are easy but not spectacularly easy in the cfft domain. They are

spectacular easy in the one-dimensional case.

Pixel data in two dimensions in space in grayscale our conventionally a

number of bits say 8 bits for 256 levels of Gray. And are analogous in

color spaces. Edge detection produces a result similar to an artist's

pencil drawing.

Well I collect pencil drawings and also pencil drawing software.

And I use mathcad.

I usually use the variable name capital m for matrix containing two

dimensional grayscale image data in mathcad. I compute the gradient several

different ways in method.

I have a new way to compute the gradient in mathcad and symbolically.

icfft (i * cfft (M))= grad(M).

Discussion?

Douglas