Properties of The Laplace Transform

Rishabh Dev — Sat, 22 Aug 2009 11:39:03 +0000

Here are some important properties of the Laplace Transform F(s) being the Laplace transform of f(t).










Initial Value Theorem
Final Value Theorem
periodic with a period T

Above, F₁(s) is the Laplace transform of f(t) for the first cycle.

Signal Operations - Time Shifting, Scaling & Inversion

Rishabh Dev — Thu, 13 Aug 2009 11:41:38 +0000

Signal Operations are simply modifications to the time variable of the signal to generate new signals. These are pretty similar to the mathematical graphical tranformations from our good old Calculus text.

The three kinds of Signal Operations are Time Shifting, Time Scaling & Time Inversion(or Time Reversal)

Time Shifting is simply shifting the signal in time. When we add a constant to the time, we obtain the advanced signal, & when we decrease the time, we get the delayed signal.

Time Scaling is compressing or dilating the signal.

Time Inversion is simply flipping the signal about the y-axis.

The above operations makes it easy to express a large domain of signals based on the fundamental signals by operation upon the basic signals.

Durofy » time scaling

Properties of The Laplace Transform

Signal Operations - Time Shifting, Scaling & Inversion