Fourier transform and impulse function $\delta(\omega)$

1. What is the Fourier transform of an impulse function?
2. What is the Fourier transform of Delta function?
3. What does omega mean in Fourier transform?
4. What is the Fourier transform of impulse train?

What is the Fourier transform of an impulse function?

That is, the Fourier transform of a unit impulse function is unity. The magnitude and phase representation of the Fourier transform of unit impulse function are as follows − Magnitude,|X(ω)|=1;forallω

What is the Fourier transform of Delta function?

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.

What does omega mean in Fourier transform?

Continuous Fourier Equation

Note that these equations use a ξ (the Greek letter Xi) to imply frequency instead of ω (Omega) which generally refers to angular frequency (ω = 2πξ). The Fourier transform of a time dependent signal produces a frequency dependent function.

What is the Fourier transform of impulse train?

The Fourier series of the periodic impulse train is. s(t) = ∞ ∑ n=−∞