Topic 2

Question 1

When the x₀ of the Dirac Delta is equal to zero: What does the result mean?

Answer 1

The result states that the Fourier transform of a delta function centered at x₀ = 0 is equal to 1 for all frequencies.

This exhibits an inherent property of delta functions, that it needs waveforms at infinite frequencies for it to be represented.

Question 2

What do you need to remember about Fourier transform of odd and even functions?

Answer 2

The Fourier transforms of odd functions are imaginary.

The Fourier transforms of even functions are completely real.

Question 3

What is the FT of this equation?

What do you need to remember about the y?

Answer 3

y becomes Y(S).

Question 4

What is the general formula for the FT of any order derivative?

Answer 4

Start with s to the power of the derivative order multiplied with Y(s).

Following term is derivative with order 1 less than the previous term. For this derivative and any following derivatives, you need to find the values at t=0.