The discrete Pascal transform and its applications

We introduce a new discrete polynomial transform constructed from the rows of Pascal’s triangle. The forward and inverse transforms are computed the same way in both the oneand two-dimensional cases, and the transform matrix can be factored into binary matrices for efficient hardware implementation. We conclude by discussing applications of the transform in

The Modernity of la Mode: a History of the French Revolution Through the Lens of Fashion, Culture, and Identity

In my thesis, I explore the cultural history of the French Revolution and its relation to the modern era which ensued. Many historians have studied the French Revolution as it relates to culture, the rise of modernity, and fashion. I combine the unique histories of all three of these aspects to reach an understanding of the history of the French Revolution and fashion’s role in bringing about change. In the majority of literature of costume history, discussion of fashion surrounds its reflective properties. Many historians conclude fashion as a reflection of the broader cultural shifts that occurred during the Revolution. I, on the other hand, propose that fashion is an active force in bringing out cultural change during this time. In exploring fashion as a historical motivator, I examine the aesthetic world of fashion from 1740 to 1815, the modern system of cultural dissemination of fashion through particular historical heroes, and the rise of “taste” and its relation to modern identity. Through aesthetics, culture, and identity, I argue that fashion is a decisive force of culture in that it creates a visual world through which ideas form and communicate.

Pascal Filters

We introduce a new type of filter approximation method and call it the Pascal filter, which we construct from the Pascal polynomials. The roll-off characteristics of the Pascal, Butterworth, and the Chebyshev filters are compared.