2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
2. Time-Domain Representations of LTI Systems
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<strong>2.</strong>7 Relations Between <strong>LTI</strong>System Properties and the Impulse Response4. Invertible <strong>Systems</strong> and DeconvolutionA system is invertible if the input to the system can be recovered fromthe output except for a constant scale factor.(1) h(t) = impulse response <strong>of</strong> <strong>LTI</strong> system, Fig. <strong>2.</strong>24.(2) h inv (t) = impulse response <strong>of</strong> <strong>LTI</strong> inverse system(3) The process <strong>of</strong> recovering x(t) from h(t) x(t) is termeddeconvolution.(4) An inverse system performs deconvolution.x t h t h t x tin( ) ( ( ) v ( )) ( ).invh( t) h ( t) ( t)(<strong>2.</strong>30)inv(5) Discrete-time case: h[ n]h[ n] [ n](<strong>2.</strong>31)Continuous-timecase<strong>Time</strong>-<strong>Domain</strong> <strong>Representations</strong> <strong>of</strong><strong>LTI</strong> <strong>Systems</strong>45
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