# Inverse Laplace Transform

Inverse Laplace Transform using Partial Fraction Method $latex \displaystyle F(s) = \frac {N(s)}{D(s)} &s=2 &bg=ffffff$ $latex \displaystyle N(s) \rightarrow &s=2 &bg=ffffff$ Numerator Polynomial $latex \displaystyle D(s) \rightarrow &s=2 &bg=ffffff$ Denominator Polynomial $latex \displaystyle \Rightarrow &s=2 &bg=ffffff$ If degree of numerator polynomial $latex \displaystyle N(s) &s=2 &bg=ffffff$ is higher than the degree of $latex \displaystyle D(s) &s=2 &bg=ffffff$, than we should divide … Continue reading Inverse Laplace Transform

# Basics of Laplace Transform

$latex \displaystyle \Rightarrow &s=2 &bg=ffffff$ Laplace transform is used for the analysis of Stable, Unstable as well as Marginally stable systems. $latex \displaystyle \Rightarrow &s=2 &bg=ffffff$ Laplace transform is the generalized representation of Fourier Transform.  $latex \displaystyle \Rightarrow &s=2 &bg=ffffff$ Laplace transform converts any Linear differential equation into an algebric equation thats make analysis to be easy. $latex \displaystyle \Rightarrow &s=2 &bg=ffffff$ … Continue reading Basics of Laplace Transform

# Energy and Power Signals

Energy Signal A signal is said to be energy signal if it has a finite amount of energy associated with it. $latex \displaystyle E \rightarrow &s=2 &bg=ffffff$  Finite $latex \displaystyle P \rightarrow 0 &s=2 &bg=ffffff$ $latex \Rightarrow x(n) &s=2 &bg=ffffff$  is said to be energy signal if it is absolutely summable  $latex \displaystyle \sum_{n=-\infty}^{\infty} |x(n)| < \infty &s=3 &bg=ffffff$ … Continue reading Energy and Power Signals

# Properties of Z transform

Linearity $latex \displaystyle x_1(n) \rightleftharpoons X_1(z) &s=2 &bg=ffffff$ ROC : $latex \displaystyle a_1 < |z| < b_1 &s=2 &bg=ffffff$ $latex \displaystyle x_2(n) \rightleftharpoons X_2(z) &s=2 &bg=ffffff$ ROC : $latex \displaystyle a_2 <|z| < b_2 &s=2 &bg=ffffff$ According to property of Linearity \$latex \displaystyle a_1 x_1(n) + a_2 x_2(n) \rightleftharpoons a_1 X_1(z) + a_2 X_2(z) &s=2 … Continue reading Properties of Z transform