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.
Pizza and soda provided.