Signal processing is the science of applying transformations to measurements to facilitate their use by an observer or a computer; and digital signal processing (DSP) is the enabling technology for applications across all disciplines and sectors. The study of sound and vibration is dependent on the use of special-purpose signal analysers or software packages which are easily installed on a variety of computing platforms. The accessibility and convenience of DSP analysis modules and procedures can sometimes create a deceptive air of simplicity in often complicated phenomena. It is important that practitioners, while availing themselves of the full range of DSP capabilities, should have a clear understanding of the fundamentals of the science of signal processing and so be fully aware of the assumptions, implications and limitations inherent in their analysis methods. The aim of this chapter is to provide an introduction to signal processing, emphasising the basis of the methodology.