we shall demonstrate that such systems are characterized in the time domain simply by their response to a unit sample sequence.we shall also demonstrate that any arbitrary input signal can be decomposed and represented as a weighted sum of unit sample sequences.As a consequence of the linearity and time-in variance properties of the system,the response of the system to any arbitrary input signal can be expressed in terms of the unit sample response of the system.the general form of the expression that relates the unit sample response of the system and the arbitrary input signal to the output signal,called the convolution sum or the convolution formula,is also derived.Thus we are able to determine the output of any linear,time-invariant system to any arbitrary input signal.
Techniques for the analysis of Linear Systems
There are two basic methods for analyzing the behavior or response of a linear system to a given input signal.One method is based on the direct solution of the input-output equation for the system,which,in general,has the form
y(n)=F[y(n-1),y(n-2),.......y(n-N),x(n),x(n-1),....,x(n-M)]
where F[.]denotes some function of the quantities in brackets.
Resolution of a Discrete-Time signal into Impulses
suppose we
Techniques for the analysis of Linear Systems
There are two basic methods for analyzing the behavior or response of a linear system to a given input signal.One method is based on the direct solution of the input-output equation for the system,which,in general,has the form
y(n)=F[y(n-1),y(n-2),.......y(n-N),x(n),x(n-1),....,x(n-M)]
where F[.]denotes some function of the quantities in brackets.
Resolution of a Discrete-Time signal into Impulses
suppose we
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