# 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

# Rank of a Matrix

Rank   $latex \rightarrow &s=2 &bg=ffffff$  No. of linearly independent rows or columns in a matrix $latex A &s=2 &bg=ffffff$ is called the Rank of $latex A &s=2 &bg=ffffff$ The rank is commonly represented by Rank (A) = rk (A) = $latex \displaystyle \rho (A) &s=2 &bg=ffffff$ $latex \Rightarrow &s=2 &bg=ffffff$  A fundamental result in linear algebra is that the … Continue reading Rank of a Matrix

# Memoryless LTI System

Consider an LTI system $latex \displaystyle x(t) \rightarrow &s=2 &bg=ffffff$  input to the system $latex \displaystyle h(t) \rightarrow &s=2 &bg=ffffff$  impulse response of the system $latex \displaystyle y(t) \rightarrow &s=2 &bg=ffffff$  output to the system $latex \displaystyle y(t) = \int_{-\infty}^{\infty} x(\tau) h(t - \tau) d\tau &s=3 &bg=ffffff$ $latex \Rightarrow &s=2 &bg=ffffff$ For an LTI system to be memory-less its … Continue reading Memoryless LTI System