Properties of Continuous-Time Unit Impulse Signal Properties of a continuous-time unit impulse signal are given below − The continuous-time unit impulse signal is an even signal. That means, it is an even function of time (t), i.e., δ(t) = δ(-t). Sampling property:∫∞−∞x(...
We use these properties to now define the idealized unit impulse function. Definition 8.8 Unit impulse function The idealized unit impulse function (Dirac delta function) δ satisfies (8.15)δ(t−t0)=0,t≠t0,∫−∞∞δ(t−t0)dt=1. The Dirac delta function is not a real-valued functi...
The Dirac delta function is often used in applied problems for the description of impulse loading (impulse forces). The convolution of the k-th derivative of the delta function and f(t) is given by (2.151)∫−∞∞f(τ)δ(k)(t−τ)dτ=f(k)(t). Obviously, if p is a ...