Signals: Terms and basic concepts

The following definitions are kept relatively brief and are intended to form the basis for practical tasks: each concept should be visualised with practical examples.

1. Signal.
   Intuitively, a signal is a physical quantity that varies with time, space, or any other independent variable or variables.
   Formally, a signal is modelled as a function of one or more independent variables.
2. Examples ...
   Signals in time: Speech, music, other noises; atmospheric pressure, rainfall, hours of sunshine; heart beat rate measured by an electrocardiogramm, electrical brain activity measured by an electroencephalogramm breathing rate, blood sugar level; stock exchange rates, unemployment ratio; height of the sun, position of stars; ...
   Signals in space: Pictures, written text, input to scanner or fax; maps; height of terrain; temperature distribution over an area; atmospheric pressure over an area; ...
3. Continuous-time signals.
   If the physical quantity is known for arbitrary values of the independent variable, the signal is a continuous-time signal. Natural, or physical, signals vary continuously in time and space at very different speeds.
4. Discrete-time signals.
   If the physical quantity is only known at separated intervals or points in time, then the signal is a discrete-time signal.
5. Dimensionality of signals.
   If a signal is a function of one variable, such as time, it is one-dimensional. Speech signals are generally modelled as one-dimensional signals. This is an idealization, because the properties of acoustic signals, for examples, are dependent on the position and speed in space of the source relative to the observer.
6. Periodic and non-periodic signals.
   A periodic signal is a signal which repeats itself over contiguous intervals of the independent variable. Periodic signals are modelled by a function
   

   

   for all t where T is some positive value. A periodic acoustic signal, for example, will repeat itself during consecutive intervals of length T. If T = 200 msec, the signal will repeat itself 50 times per second.
   A non-periodic signals is called a noise. The term noise is also used to refer to unwanted components of a useful signal; the ration of signal level to noise level in this meaning of the term is referred to as the signal to noise ratio.

7. Simple and complex signals.
   A simple signal is a signal which can be modelled by a sine (or cosine) function; for this reason, a simple signal is called sinusoid. Signals which cannot be modelled by a sine function are complex. Ripples on a pond or on a cup of coffee, and the sound produced by a tuning fork, are approximately sinusoid.
   Complex signals are signals which cannot be modelled by a sine function. Complex signals can be approximated by regarding them as the sum, for any value of the independent variable, of the values of different sine functions. The values of the component sine functions which model components of the complex signal represents the spectrum of the complex signal.