Signal processing is the science of identifying, analyzing, manipulating, and extracting physical signals such as audio, video, images, and sensory data in real-time. Digital Signal Processors (DSPs) are semiconductor chips that are the core engines of a diverse array of products including cell phones, digital cameras, high-definition televisions, network equipment, global-positioning systems, and communications satellites. DSPs account for $27 billion or 10 percent of global semiconductor revenues. Although DSPs are technologically and economically significant, the evolution of innovation in the signal processing industry is relatively unexplored. This paper traces the commercialization of signal processing since its inception in 1948, when the following three breakthrough innovations occurred. Information theory, a mathematical innovation, introduced a conceptual foundation for designing DSPs. Transistors, a material innovation, provided the physical building blocks for creating DSPs. Stored-program computing, an architectural innovation, offered an integrated framework for recombining mathematical and material innovations to produce functional DSPs. An analysis of sixty years of subsequent innovation in DSPs reveals that: (1) some fundamental mathematical innovations are actually rediscoveries of earlier inventions; (2) architectural innovations often lag mathematical innovations by decades due to the technological constraints of material innovations; and (3) architectural innovations frequently reconfigure industry alliances and open new markets.