Dirac delta function: Mathematics, Paul Dirac, Generalized function, Integral, Signal processing, Function (mathematics), Distribution (mathematics), Measure (mathematics), Weak topology -
Dirac delta function: Mathematics, Paul Dirac, Generalized function, Integral, Signal processing, Function (mathematics), Distribution (mathematics), Measure (mathematics), Weak topology
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Dirac delta or Dirac's delta is a mathematical construct introduced by theoretical physicist Paul Dirac. Informally, it is a generalized function representing an infinitely sharp peak bounding unit area: a 'function' ¿(x) that has the value zero everywhere except at x = 0 where ...Full description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Dirac delta or Dirac's delta is a mathematical construct introduced by theoretical physicist Paul Dirac. Informally, it is a generalized function representing an infinitely sharp peak bounding unit area: a 'function' ¿(x) that has the value zero everywhere except at x = 0 where its value is infinitely large in such a way that its total integral is 1. In the context of signal processing it is often referred to as the unit impulse function. The Dirac delta is not strictly a function, because any function that is equal to zero everywhere but a single point must have total integral zero. While for many purposes it can be manipulated as a function, formally it can be defined as a distribution that is also a measure. In many applications, the Dirac delta is regarded as a kind of limit (a weak limit) of a sequence of functions having a tall spike at the origin. The approximating functions of the sequence are thus "approximate" or "nascent" delta functions.