EE150: Signals and Systems 2016-Spring QUIZ-5 EE150: Signals and Systems 2016-Spring

𝑥 𝑡 = sin 𝜋 𝑡 𝑇 0 𝜋 𝑡 𝑇 0 ⋅ sin 𝜋 𝑡 𝑇 0 𝜋 𝑡 𝑇 0 Continuous signal 𝑥 𝑡 = sin 𝜋 𝑡 𝑇 0 𝜋 𝑡 𝑇 0 ⋅ sin 𝜋 𝑡 𝑇 0 𝜋 𝑡 𝑇 0 is sampled at a sampling period of 𝑇 𝑠 = 𝑇 0 4 to get the discrete signal 𝑥 𝑠 𝑛 : 𝒙(𝒕) Sampling 𝑇 𝑠 𝒙 𝒔 [𝒏] Down-Sampling 𝑀 𝒙 𝒅 [𝒏] 1. (2 points) Plot the Fourier transform of 𝑥(𝑡) and the DTFT of 𝑥 𝑠 𝑛 ; 2. (1.5 points) Plot the DTFT of of 𝑥 𝑑 𝑛 when 𝑀 =2 3. (1.5 points) Plot the DTFT of of 𝑥 𝑑 𝑛 when 𝑀 =3