Dtft

Deriving expression for the DTFT of a rectangular window

Deriving expression for the DTFT of a rectangular window
  1. What is rectangular window in digital signal processing?
  2. How do you find the DTFT of a sequence?
  3. How do you find DTFT from DFT?

What is rectangular window in digital signal processing?

The rectangular window is the most common windowing technique to design a finite impulse response (FIR) filter. The frequency response of wR(n) is wR(ω) which is calculated as: wR(ω) = DTFT of wR(n), i.e. Main-lobe width = 2 × (zero-crossing points of sin c function), i.e.

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+...)

How do you find DTFT from DFT?

Correct Answer: Theoretical, Continuous-ω 2π-Periodic DTFT can be obtained by continuous Lagrangian-interpolation of the DFT Samples. So that the values at ω=2πk/N will be the DFT Samples X[k] for k=0,1,...,N−1 and the Interpolation-function's zero-crossings are at 2πk/N.

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