Signals Basic Types
Here are a few basic signals: Unit Step Function Unit step function is denoted by u(t). It is defined as u(t) = { 1 0 t ⩾ 0 t < 0 It is used as best test signal. Area under unit step function is unity. Unit Impulse Function Impulse function is denoted by δ(t). and it is defined as δ(t) = { 1 0 t = 0 t ≠ 0 ∫ ∞ − ∞ δ ( t ) d t = u ( t ) δ ( t ) = d u ( t ) d t Ramp Signal Ramp signal is denoted by r(t), and it is defined as r(t) = { t 0 t ⩾ 0 t < 0 ∫ u ( t ) = ∫ 1 = t = r ( t ) u ( t ) = d r ( t ) d t Area under unit ramp is unity. Parabolic Signal Parabolic signal can be defined as x(t) = { t 2 / 2 0 t ⩾ 0 t < 0 ∬ u ( t ) d t = ∫ r ( t ) d t = ∫ t d t = t 2 2 = p a r a b o l i c s i g n a l ⇒ u ( t ) = d 2 x ( t ) d t 2 ⇒ r ( t ) = d x ( t ) d t Signum Function Signum function is denoted as sgn(t). It is defined as sgn(t) = ⎧ ⎩ ⎨ ⎪ ⎪ 1 0 − 1 t > 0 t = 0 t < 0 sgn(t) = 2u(...