Editing Analog signal processing (section)

==Signals==
While any signal can be used in analog signal processing, there are many types of signals that are used very frequently.

===Sinusoids===
[[Sine wave|Sinusoids]] are the building block of analog signal processing. All real world signals can be represented as an infinite sum of sinusoidal functions via a [[Fourier series]].  A sinusoidal function can be represented in terms of an exponential by the application of [[Euler's Formula]].

===Impulse===
An impulse ([[Dirac delta function]]) is defined as a signal that has an infinite magnitude and an infinitesimally narrow width with an area under it of one, centered at zero.  An impulse can be represented as an infinite sum of sinusoids that includes all possible frequencies.  It is not, in reality, possible to generate such a signal, but it can be sufficiently approximated with a large amplitude, narrow pulse, to produce the theoretical impulse response in a network to a high degree of accuracy.  The symbol for an impulse is δ(t).  If an impulse is used as an input to a system, the output is known as the impulse response.  The impulse response defines the system because all possible frequencies are represented in the input

===Step===
A unit step function, also called the [[Heaviside step function]], is a signal that has a magnitude of zero before zero and a magnitude of one after zero.  The symbol for a unit step is u(t).  If a step is used as the input to a system, the output is called the step response.  The step response shows how a system responds to a sudden input, similar to turning on a switch.  The period before the output stabilizes is called the transient part of a signal.  The step response can be multiplied with other signals to show how the system responds when an input is suddenly turned on.

The unit step function is related to the Dirac delta function by;

:<math>\mathrm{u}(t) = \int_{-\infty}^{t} \delta (s)ds</math>