Dtft of u(n)

1. What is the Fourier transform of u?
2. What is the DTFT of a constant?
3. How do you find the DTFT of a sequence?
4. What is DTFT equation?

What is the Fourier transform of u?

Find the Fourier transform of u(-t). We have F[u(-t)] = πδ(ω) – \frac1jω.

What is the DTFT of a constant?

Discrete Time

This function then periodically repeats with period 2π (as it must to be a DTFT). What this says is that a constant in the time domain is concentrated at zero frequency in the frequency domain (which should not be surprising). We can verify this answer easily by evaluating the inverse DTFT.

How do you find the DTFT of a sequence?

Find the DTFT of the sequence x(n)=u(n−k). ⇒F[u(n−k)]=e−jωk+e−jω(k+1)+e−jω(k+2)+... ⇒F[u(n−k)]=e−jωk(1+e−jω+e−j2ω+e−j3ω+...)

What is DTFT equation?

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 ) .