Step signal and impulse signal - Signals and Systems study notes


A. Singular signal


Strange signal, also known as transient signals . Singular point mutation portion and an irregular signal is often carries more important information, which is one of the important features of the signal:
for example, the image signal, the gray mutagenesis outline of an object.
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Function itself discontinuous point (trip point) or its derivative and integral with a class of functions collectively referred to as a discontinuous point of a signal singular or singular functions.

Singular signal comprises:
(1) a unit step signal
(2) unit impulse and impulse even signal
(3) ramp signal, also known as a ramp signal or a ramping signal


1. Unit ramp signal


Unit 1 slope ramp signal


2. The unit step signal


Unit step function t = 0 point No as defined or 1 2 \frac{1}{2} , Jump intensity is 1

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Gate function (or a combination of the essence of a step function)

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Unit Impulse signal


It is an "area" is equal to 1, the idealized narrow pulses. In other words, the amplitude of the pulse is equal to the inverse of its width.
Note impulse signal strength and height is not the same, the details may refer to:
the difference between the derivative and differential and contact

Impulse function of some important properties:

Impulse function for the derivative obtained impulse dual functions , unit impulse is a dual function: when t tends to zero from a negative value, the intensity of which is a positive infinite impulse function, as from t when the value goes to zero, it is a strength for the negative infinite impulse function.

Impact even function is an odd function, the integrated area to zero.


II. Intensity skip expressed by impulse function


By impulse signal strength and direction to indicate the degree of increase or decrease of the original function.
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