** **

**Electrical
Engineering Department**

IEEE Bucknell Student Branch

Speaker: EE Senior **Tom
Goodman**

Date: Thursday, November 18th

**Place: Dana 113**

Time: 12:00
noon

** **

*The Discrete Pascal Transform and its
Applications*

* *

Discrete
transforms, such as the Fourier, Cosine, Binomial, Laguerre, and Legendre
transforms, are commonly used in signal processing, communications, control
systems, and multimedia applications (image compression, JPEG, and MPEG
encoding, to name a few). The discrete Pascal transform (DPT) is a new
polynomial transform that shows promise in several areas of digital signal
processing, such as image processing, computer vision, and digital filter
design.

The transform matrix is a lower-triangular matrix
constructed from the rows of PascalĘs triangle. For example, the 4x4
transform matrix is

The transform defined by this matrix has
several interesting characteristics. For instance, the forward and
inverse transform computations are the same and the basis functions satisfy a
simple recursion. The transform matrix can be factored into binary
matrices, allowing for efficient implementation on an integrated circuit.
The lower-triangular nature of the transform matrix also produces a localization
characteristic not found in many other discrete transforms, making the DPT
highly useful for detection and pattern recognition
applications.

The talk will open with a discussion of discrete
transforms, followed by an introduction to the DPT and its properties.
Finally, applications of the DPT for image processing will be
discussed.