Walsh

Walsh is a surname of Irish origin. It is an Anglicized form of the Gaelic Ó hUallacháin, meaning “descendant of Uallachán.” The personal name Uallachán is linked to a root associated with pride or boldness. Over time, the name acquired variants such as Walshe, and in some records O’Walsh appears as well. The surname is widespread in Ireland and among the Irish diaspora.

Historically, Walsh became established in Ireland and spread to other regions through emigration, especially to Britain, the United States, and other English-speaking countries. Today it ranks among the common Irish surnames and is carried by families across many counties, reflecting a long-standing presence in global populations.

In mathematics and information theory, Walsh refers to a family of square-wave, piecewise-constant functions introduced by Joseph L. Walsh in the early 20th century. These functions form an orthogonal basis and underpin the Walsh–Hadamard transform, which is used in digital signal processing and data compression. Related concepts include Walsh codes, used in channelization and spread-spectrum communications.

Beyond mathematics, Walsh appears as a surname in many cultures and is used for various place names and institutions in different countries. In encyclopedia-style writing, it serves as a general reference to people, places, and topics bearing the name. As a surname, Walsh continues to appear in literature, media, and public life around the world.