In many ways, the late 1950s marked the beginning of the digital age, and with it, the beginning of a new age for the mathematics of signal processing. Highspeed analog-to-digital converters had just been invented. These devices were capable of taking analog signals like time series (think of continuous functions of time like seismograms which measure the seismic activity — the amount of bouncing — at a fixed location, or an EEG, or an EKG) and converting them to lists of numbers. These numbers were obtained by sampling the time series, that is, recording the value of the function at regular intervals, which at that time could be as fast as 300,000 times every second. (Current technology permits sampling at much higher rates where necessary.) Suddenly, reams and reams of data were being generated and new mathematics was needed for their analysis, manipulation and management.

So was born the discipline of Digital Signal Processing (DSP), and it is no exaggeration to say that the world has not been the same. In the mathematical sciences the DSP revolution has, among other things, helped drive the development of disciplines like algorithmic analysis (which was the impetus behind the creation of computer science departments), communication and information theory, linear algebra, computational statistics, combinatorics, and discrete mathematics. DSP tools have changed the face of the arts (electroacoustic music and image processing), health care (medical imaging and computed imaging), and, of course, both social and economic commerce (i.e., the internet). Suffice to say that the mathematics of DSP is one of the pillars supporting the amazing technological revolution that we are experiencing today.