Discrete Time Fourier Transform , Problems,Signals and Systems

1. Discrete Time Fourier Transform
Dr.K.G.SHANTHI
Professor/ECE
shanthiece@rmkcet.ac.in

2. 2
 Discrete Time Fourier Transform is mainly used for the analysis of
discrete signals and discrete LTI systems .
 If x(n) is the given discrete time sequence ,then X(ω)or X(ejω) is the
discrete Fourier transform of the signal x(n).
 The DTFT of x(n) is defined as
 The inverse DTFT is i.e. F–1[X(ω)] is defined as
 Then x(n) and X(ω)is called as Fourier Transform pair and the
relation is expressed as
F[x[n] = X(ω)= −∞
∞ x(n)e−jwn
F-I [X(ω)] = x(n) =
1
2𝜋 −𝜋
𝜋
𝑥 𝑛 e𝑗ω𝑛 dω

3. Existence of DTFT
3
The Fourier Transform exists for discrete time signal
x(n) if and only if the sequence is absolutely summable.
i.e. The sequence has to satisfy the following condition,
𝑛=−∞
∞
𝑥[𝑛] < ∞

4. Problems
4

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 13

14. THANK YOU ALL
14