2.1 Laplace Transformation

• Two-side or bilateral Laplace Transform:

• One-side or unilateral Laplace Transform:

• Convergence:

Re {s} is the real part of complex variable s

1.5 Higher Order Delta Function

• nth-order delta function:

• sampling property:

• sifting property:

1.4 Unit Impulse / Delta Function

• Unit Impulse function is the derivative of unit step u0(t):

• Two useful delta function properties are sampling & sifting property 
• Sampling property:

• Multiplication of any function f(t) by the delta function results in sampling the function at the time instants where the delta function is not zero. (foundation of discrete-time systems)
• Sifting property:

1.3 Unit Ramp Function

• Unit Ramp function u1(t) is defined as 

• u0(t) is the derivative of u1(t)

1.2 Unit Step Function

• A function is said to be discontinuous if it exhibits point of discontinuity
• A well known discontinuous function is called unit step function:

  

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