5 The Discrete–Time Fourier Transform
5 The Discrete–Time Fourier Transform
5 The Discrete–Time Fourier Transform
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Example:<br />
Unit step x[n] = u[n]<br />
– Known<br />
and<br />
– Accumulation property<br />
X(e jω ) =<br />
Lampe, Schober: Signals and Communications<br />
=<br />
δ[n] F<br />
←→ 1 = G(e jω )<br />
u[n] =<br />
n<br />
m=−∞<br />
δ[m]<br />
1<br />
1 − e −jωG(ejω ) + πG(e j0 )<br />
1<br />
+ π<br />
1 − e−jω u[n] F<br />
←→<br />
∞<br />
k=−∞<br />
1<br />
+ π<br />
1 − e−jω ∞<br />
k=−∞<br />
δ(ω − 2πk)<br />
∞<br />
k=−∞<br />
δ(ω − 2πk)<br />
δ(ω − 2πk)<br />
152
Change language