Howtosignalprocessing
- What is the Dirac delta function for Fourier Transform?
- Is Dirac delta function periodic?
- Why is the Dirac delta function not a function?
- Is the Dirac delta function continuous?
What is the Dirac delta function for Fourier Transform?
The Fourier transform of a function (for example, a function of time or space) provides a way to analyse the function in terms of its sinusoidal components of different wavelengths. The function itself is a sum of such components. The Dirac delta function is a highly localized function which is zero almost everywhere.
Is Dirac delta function periodic?
A function with periodic boundary conditions over an interval is equivalent to a periodic function over the entire real line. As such, what you have is a train of Dirac deltas.
Why is the Dirac delta function not a function?
The Dirac delta is not truly a function, at least not a usual one with domain and range in real numbers. For example, the objects f(x) = δ(x) and g(x) = 0 are equal everywhere except at x = 0 yet have integrals that are different.
Is the Dirac delta function continuous?
The Dirac delta function, often referred to as the unit impulse or delta function, is the function that defines the idea of a unit impulse in continuous-time. Informally, this function is one that is infinitesimally narrow, infinitely tall, yet integrates to one.
