How to find inverse Fourier transform of summ of delta functions?

1. What is the inverse Fourier transform of a delta function?
2. How do you find the inverse of a discrete Fourier transform?
3. What is the inverse Fourier transform of δ pi * F?

What is the inverse Fourier transform of a delta function?

f(x) = e−i·0·x = 1. (17) Therefore, the inverse Fourier transform of δ(ω) is the function f(x) = 1. This time, the function δ(ω) in frequency space is spiked, and its inverse Fourier transform f(x) = 1 is a constant function spread.

How do you find the inverse of a discrete Fourier transform?

The IDFT is defined as(11.4. 2)an≡1N∑m=1NAme2πin−1m−1N≡IDFTAmnfor n=1 to N.

What is the inverse Fourier transform of δ pi * F?

Since ⟨δ,f⟩=f(0) (this is the definition of δ), the unitary inverse Fourier transform of the Dirac delta is a distribution which, given a function f, evaluates the Fourier transform of f at zero. In other words, ⟨F−1(δ),f⟩=1√2π∫∞−∞f(x)dx.