UNIT 4: FOURIER REPRESENTATION FOR SIGNALS 1 – 1. State and prove the periodic time shift and periodic properties of DTFS. [ June 14 6marks] Solution: Periodicity: As a consequence of Eq. (6.41), in the discrete-time case we have to consider values of R(radians) only over the range0 < < 2π or < < while in the continuous-time case we Ω π Ω π, have to consider values of (radians/second) over the entire range < < 0 –∞ ω ∞. Time Shifting: 2. Find the inverse Fourier transform x [ n ] [ 6 marks] Solution: 3. State and prove the time shift and periodic time convolution properties of DTFS. [June 13, 6marks] Solution: 23
UNIT 4: FOURIER REPRESENTATION FOR SIGNALS – 1 1. State and prove the periodic time shift and periodic properties of DTFS. [ June 14 6marks] Solution: Periodicity: As a consequence of Eq. (6.41), in the discrete-time case we have to consider values of R(radians) only over the range0 < Ω < 2π or π < Ω < π, while in the continuous-time case we have to consider values of 0 (radians/second) over the entire range –∞ < ω < ∞. Time Shifting: 2. Find the inverse Fourier transform x [ n ] [ 6 marks] Solution: 3. State and prove the time shift and periodic time convolution properties of DTFS. [June 13, 6marks] Solution: 23
UNIT-4-SOLUTION.docx