Objectives

• Overview the concepts of systems and signals

• Give examples of systems and signals in engineering, nature, and mathematics

• Define the properties of linearity and shift invariance

• Introduce the mathematical concepts of convolution and impulse function

• Analyze input/output relationship of systems via impulse response and transfer functions

• Describe discrete-time and multidimensional linear systems

Systems in engineering, biology, and mathematics

The term system has many meanings in the English language. In engineering and mathematics, we think of a system as a “black box” that accepts one or more inputs and generates some number of outputs. The external observer may not know what takes place inside the black box; but by observing the response of the system to certain test inputs, one may infer certain properties of the system. Some systems in nature behave in a very predictable manner. For example, once we have seen a magnifying glass applied to any printed image, or a megaphone applied to any person's voice, we can reliably predict how these devices would perform given any other image or voice. Other systems are more complex and less predictable. For example, if we use fMRI to measure the response of the language areas of the human cortex to hearing short sentences, the output in response to hearing “the sky is blue” is not enough to predict the response to “I love you” or to “el cielo es azul,” since the brain responds quite differently to emotionally charged stimuli and unfamiliar languages.