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Unformatted text preview: Purdue University: ECE438  Digital Signal Processing with Applications 1 ECE438  Laboratory 2: DiscreteTime Systems October 6, 2010 1 Introduction A discretetime system is anything that takes a discretetime signal as input and generates a discretetime signal as output. 1 The concept of a system is very general. It may be used to model the response of an audio equalizer or the performance of the US economy. In electrical engineering, continuoustime signals are usually processed by electrical cir cuits described by differential equations. For example, any circuit of resistors, capacitors and inductors can be analyzed using mesh analysis to yield a system of differential equations. The voltages and currents in the circuit may then be computed by solving the equations. The processing of discretetime signals is performed by discretetime systems. Similar to the continuoustime case, we may represent a discretetime system either by a set of difference equations or by a block diagram of its implementation. For example, consider the following difference equation. y ( n ) = y ( n 1) + x ( n ) + x ( n 1) + x ( n 2) (1) This equation represents a discretetime system . It operates on the input signal x ( n ) to produce the output signal y ( n ). This system may also be defined by a system diagram as in Figure 1. Mathematically, we use the notation y = S [ x ] to denote a discretetime system S with input signal x ( n ) and output signal y ( n ). Notice that the input and output to the system are the complete signals for all time n . This is important since the output at a particular time can be a function of past, present and future values of x ( n ). It is usually quite straightforward to write a computer program to implement a discrete time system from its difference equation. In fact, programmable computers are one of the easiest and most cost effective ways of implementing discretetime systems. While equation (1) is an example of a linear timeinvariant system, other discretetime systems may be nonlinear and/or time varying. In order to understand discretetime systems, Questions or comments concerning this laboratory should be directed to Prof. Charles A. Bouman, School of Electrical and Computer Engineering, Purdue University, West Lafayette IN 47907; (765) 494 0340; [email protected] 1 A more general behavioral view of systems is anything that imposes constraints on a set of signals. Purdue University: ECE438  Digital Signal Processing with Applications 2 y(n) x(n) D D D + + + Figure 1: Diagram of a discretetime system. (D = unit delay) it is important to first understand their classification into categories of linear/nonlinear, time invariant/timevarying, causal/noncausal, memoryless/withmemory, and stable/unstable....
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 Spring '08
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 Digital Signal Processing, Signal Processing, Purdue University, difference equation, discretetime systems

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