The `ed1D` program made 23 figures for this paper book,
many of them in chapters
and .
In the electronic book, the caption for
each of those 23 figures contains a pushbutton
that activates `ed1D` and initializes it to that figure.
`ed1D` has a built-in tutorial that will
enable you to operate it without this document.

`ed1D` is an interactive program
that shows two one-dimensional signals
related by various selectable mathematical transforms.
Using a pointer, you can edit either signal
and see the effect on the other one.
The signals can be **Fourier-transform** pairs,
or a wide variety of other pairs created by transformations
such as **Hilbert transform**s, spectral **factorization**,
autocorrelations, reflection coefficients, and impedance.
Some of these transformations are not described in this book,
but are described in chapter 8 of FGDP.

When you enter the program, you should move the pointer around the screen until you find the ``Tutor'' button and then click pointer buttons on it, all the while watching the message window for instructions.

You will see that there are several ways of editing a signal.
First, you can use the pointer simply to draw the signal you wish.
Second, you can draw a weighting function to multiply
any signal that you have previously prepared.
Third, there are a variety of preexisting analytic signals
that you can use as weights.
These mathematical weighting functions
have two adjustable parameters, the shift and the **bandwidth**,
which you select with the pointer.
Watch the message window for instructions for selecting these parameters.

As long as the number of ordinates is less than about 256, edited changes in one domain show up immediately in both domains. That is good for learning. With more ordinates (more computational work), you see the changes only in the domain you are editing, until later, when you move the cursor into the other domain.

The number of options in this program proved confusing to beginners, so I commented out a few in the source code. See Claerbout (1988) for more details. For example, there is a parabolic-shaped editing tool that can be pushed against any signal to deform it. The curvature of the parabola is adjustable. You can reinstall the parabolic pushing tool by uncommenting a few lines in the control panel. Another example is the huge number of transformations that can be studied with this program: I hid these, since they have no obvious interest and proved confusing to beginners.

10/21/1998