Discrete-time Fourier Transform of the unit step sequence $u[n]$

1. What is the Fourier transform for unit step signal?
2. What is the formula of discrete-time Fourier transform?
3. What is the discrete Fourier transform sequence values?
4. What is the Fourier transform of step function?

What is the Fourier transform for unit step signal?

Its Fourier transform is ˆH(ω)=1/(α+iω), which converges to 1/(iω) pointwise as α→0, except at ω=0.

What is the formula of discrete-time Fourier transform?

The DTFT of the convolution sum of two signals x1[n] and x₂[n] is the product of their DTFTs, X₁(e^jω) and X₂(e^jω). That is: y [ n ] = x 1 [ n ] * x 2 [ n ] ⇔ Y ( e j ω ) = X 1 ( e j ω ) X 2 ( e j ω ) .

What is the discrete Fourier transform sequence values?

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.

What is the Fourier transform of 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)