Problem 5 4 Points Convolution Consider An Rc Filter With Impulse Response H T Encu T 1 Rc Where R 0 And C 0 A 1 (58.56 KiB) Viewed 42 times
Problem 5 [4 points] (Convolution) Consider an RC filter with impulse response h(t) = encu(t) 1 RC where R> 0 and C> 0 are the values of the resistance and the capacitance. i) Compute the output of the RC filter when the input is x(t) = rect +(²-D/²) where D> 0 is the duration of the rectangular pulse. ii) * Consider now the input signal +∞o T2(t) = rect ²-D/²) + Σ 6(t-kT₂) * k=-∞ where Tp > D and * denotes convolution. Compute the output of the RC filter when the input is r2(t). Draw the signals x2(t) and the output. iii) [1 bonus point] Consider the signal T3 (t) = rect (²-D/²) + Σ 26(t- kD). * k=-∞ Compute the output of the RC filter when the input is x3(t). Draw the signals x3 (t) and the output. +∞o
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²-D/²) + Σ 6(t-kT₂) * k=-∞ where Tp > D and * denotes convolution. Compute the output of the RC filter when the input is r2(t). Draw the signals x2(t) and the output. iii) [1 bonus point] Consider the signal T3 (t) = rect (²-D/²) + Σ 26(t- kD). * k=-∞ Compute the output of the RC filter when the input is x3(t). Draw the signals x3 (t) and the output. +∞o