L2-Signal-rep

L2-Signal-rep - 1 Representation of signals Signals...

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Unformatted text preview: 1 Representation of signals Signals encountered in electronic communications are usually classified as: 1. Periodic or nonperiodic Periodic signal: its waveshape repeats after a duration or period T ; i.e., ) ( ) ( T t g t g = for all t . Examples: sinusoidal wave, repetitive pulse train, pseudo-random binary sequence. Nonperiodic signal: no repetition in waveshape. Examples: an isolated pulse, random signal. 2. Deterministic or random Deterministic signal: at any time (past, present or future), there is no uncertainty about its value. Examples: a specified sinusoidal wave, repetitive pulse train. Random signal: there is some degree of uncertainty about its value before it occurs. Examples: noise, speech, data. 2 3. Energy or power A signal may be represented by a voltage ) ( t v or a current ) ( t i and its instantaneous power, developed across a resistive load R , is defined as R t i R t v t p 2 2 | ) ( | or | ) ( | ) ( = . In communications, the instantaneous power ) ( t p is commonly referred to as 2 | ) ( | ) ( t g t p = per unit resistive load. It follows that the total energy of a signal ) ( t g is given by dt t g Lim E = 2 | ) ( | and the average power of a signal is given by . | ) ( | 2 1 2 dt t g T Lim P T T T = (i) Finite energy signal (i.e., < < E ) Examples: deterministic and nonperiodic signals like an isolated pulse. (ii) Finite power signal (i.e., < < p ) Examples: periodic signals like the sinusoidal wave, and random signals, like noise. 3 Types of signals Signals can be either continuous or discrete in both time and amplitude , and this leads to four types of signals: Continuous time, continuous amplitude (i.e., analogue) Continuous time, discrete amplitude Discrete time, continuous amplitude (i.e., sampled) Discrete time, discrete amplitude (i.e., digital) Continuous amplitude Discrete amplitude Continuous time Discrete time (Analogue) (Sampled) (No specific name) (Digital) time n time x Q ( t ) x Q [ n ] x ( t ) x [ n ] n 4 In communications, we often encounter functions in either the time-domain or the frequency domain. Question: What will happen to an input signal ) ( t v i after it has passed through a linear time-invariant system? The input signal, ) ( t v i is normally expressed in the time-domain, as observed on an oscilloscope. The system function, e.g., a linear filter, is more likely to be described in the frequency domain as ) ( f H . Sometimes, the system function is also expressed in the time-domain as ) ( t h , the impulse response of the system. The output signal is related to the input signal and the system function in the following ways: Frequency-domain: ) ( ) ( ) ( f H f V f V i o = where ) ( f V o and ) ( f V i are Fourier transforms of the signals, ) ( t v o and ) ( t v i , respectively....
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This note was uploaded on 05/09/2011 for the course ENGR 601 taught by Professor Kah-chung during the Three '11 term at Curtin.

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L2-Signal-rep - 1 Representation of signals Signals...

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