Signals and Systems: Unit II: Analysis of Continuous Time Signals,,

Initial Value Theorem and Final Value Theorem

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Explanation about Initial Value Theorem and Final Value Theorem

INITIAL VALUE THEOREM AND FINAL VALUE THEOREM

Initial value theorem

If then initial value of x(t) is written as

Proof:

Differentiation property of Laplace transform is

Take limit δ → ∞ of the above equation

L.H.S of (2) can be written as

Substitute (3) in (2)

Final Value theorem

Proof:

Differentiation property of Laplace transform is given as,

L.H.S of (2) can be written as

Let us substitute (3) in (2)

Hence proved.

Signals and Systems: Unit II: Analysis of Continuous Time Signals,, : Tag: : - Initial Value Theorem and Final Value Theorem

Home | Department: ECE Department | Subject: Signals and Systems |

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Introduction of Continuous Time Signals - Representation of Fourier Series

Continuous Time Fourier Series - Cosine Fourier Series, Exponential Fourier Series

Properties of Fourier Series - Parseval's Power Theorem

Continuous Time Fourier Transform - Existence of Fourier Transform-Dirichlet Condition, Fourier Transform Properties

Problems Based on Fourier Transform - Inverse Fourier Transform

Laplace Transform - Laplace transform pair, Relationship Between Fourier Transform and Laplace Transform

Properties of Laplace Transforms

Initial Value Theorem and Final Value Theorem

Inverse Laplace Transform - Inverse Laplace Transform using Partial Fraction Expansion, Inverse Laplace Transform using Convolution Integral

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