Howtosignalprocessing
- How do you use duality property in Fourier transform?
- What is the Fourier transformation of unit step function?
- Why do we use duality property?
- What is the Fourier transform of unit impulse function?
How do you use duality property in Fourier transform?
The Duality Property tells us that if x(t) has a Fourier Transform X(ω), then if we form a new function of time that has the functional form of the transform, X(t), it will have a Fourier Transform x(ω) that has the functional form of the original time function (but is a function of frequency).
What is the Fourier transformation of unit step function?
Therefore, the Fourier transform of the unit step function is, F[u(t)]=(πδ(ω)+1jω) Or, it can also be represented as, u(t)FT↔(πδ(ω)+1jω)
Why do we use duality property?
1. This duality property allows us to obtain the Fourier transform of signals for which we already have a Fourier pair and that would be difficult to obtain directly. It is thus one more method to obtain the Fourier transform, besides the Laplace transform and the integral definition of the Fourier transform.
What is the Fourier transform of unit 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
