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Tuesday, March 31, 2009

Domains electronicsjalil

Time domain
This is the domain that most people are familiar with. A plot in the time domain shows the magnitude of a signal at a point in time.
Frequency domain
This is the domain that engineers are glad exists. It's unfamiliar to most people, but makes the math associated with analog signal processing much easier than if it's analyzed in the time domain. A plot in the frequency domain shows either the phase shift or magnitude of a signal at each frequency that it exists at. These can be found by taking the Fourier transform of a time signal and are plotted similarly to a bode plot.
Signals
While any signal can be used in analog signal processing, there are many types of signals that are used very frequently.
Sinusoids
Sinusoids are the building block of analog signal processing. Theorem states that all real world signals can be represented by a sum of sinusoids. A sinusoid can be represented by a complex exponential, e^{st}.
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. This definition is really hard to use in real life, so most engineers conceptualize it to a signal that is one at zero and zero everywhere else. The symbol for an impulse is delta(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 step function is a signal that has a magnitude of zero before zero and a magnitude of one after zero. The symbol for a 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.

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