Dtft

Finding the discrete time Fourier series for signal

Finding the discrete time Fourier series for signal
  1. How do you calculate DTFT of a signal?
  2. How do i find DTFS?

How do you calculate DTFT of a signal?

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 i find DTFS?

x[n]=∑N−1k=0Ck⋅ej2πkn/N⋯(1), which is called the Discrete Time Fourier series (DTFS). The frequency range of DT signals is unique over the interval (−π,π) or (0,2π) . A DT signal of fundamental period N can consist of frequency components separated by 2πN radians or f=1N cycles.

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