Question

blem 1. A signal varies as y(t) 1000sin(40Tt) + 500 sin(150rt). 1. Compu signal Compute Nyquist frequency for the signal. Does aliasing show up in the sampled signal provided a sampling frequency of 100 H Support your answer with appropriate calculations & using folding plot below. Compute the aliasing frequency. te the maximum frequency that can be represented in the resulting discrete 2. 3. 4. Sin 3.2 2.8 In-phase tofsf 2.6 2.4 2.2 Out-of phase 1.8 1.6 1.4 0.4 0.8 0.6 Input trequency.f 02

Answer 1

Given y (t) = 1000 sin (40 pi t) + 500 sin (150 pi t) The maximum frequency present in y (t) is f_m = 150 pi/2 pi = 75 Hz The discrete signal frequency is ohm = 2 pi f m/f_s for ohm to be maximum, f_s = 2 f_m So Ohm_max = 2 pi f_m/2 f_m ohm_max = pi radians/sample = pi/2 pi cycles/sample = 0.5 cycles/sample Nyquist frequency for the signal f_N = 2 f_m f_N = 2 (75) f_N = 150 Hz given sampling frequency f_s = 100 Hz The given sampling frequency f_s is less than the Nyquist frequency . So Aliasing occurs. The frequencies at the