Question

In an effort to digitize an analog signal Y(t), we would like to select the right sampling rate for the following signal: Y (t)= 4sin(251)t + 4sin (751) a) Select the right sampling rate for this signal. b) What will happen if the sampling rate from the above answer (a), is used to sample the following signal Y= 3sin(2507). c) Discuss if Aliasing is happening for answer (b) and if yes why? What will be the observing Aliasing Frequency?

Answer 1

y (+) = 4 sin (217 That means Y(t) = A sin (25 TT) + + 4 sin (75 17) a) Select the right sampling rate for this signal the minimum sampling rate to avoid alising effect, that is also called nyquist rate. know in Nyquist nate 23 =2fm ws=2wm Y(t) = 4 sin (wijft 4 sin (Wa)t to calculate wm we keed greater w. from two of them We ts=) 2T = 75 T Wm= wz Here, رالیا ل رکا Ws = 2xWm= 2x75 TT = 150 TT Now the sampling rate as 150T 2π - 75 Hz

nate b) what will happen if the sam sampling from the above answer cas, is used to sample the following signal Y=3sin (2507) Ans. From as we know fs = 75 Hz Y = 3 sin (2507)t => Y = 3 sin (2500) Wm= 250T => м an&m=2501 fr = 175 Hz a 2*m= 250 H2 seen that fs <2fm slynal will be oven damping. so so the

for answen (b) c) Discuss if Aliasing Aliasing is happening and if yes why? what will be the observing aliasing frequency we from by Am. seen that so, The the fska fm Its =) Sampling frequency aliasing is happening fm => measured frequency Because we know that the my quist pate 2fm = fs) is used to avoid aliasing effect. Here sampling frequency is less than Double of measured frequency so that's why aliasing is happening. to measured frequency, fm = 175 Hz Sampling frequency, ofs Nyquist IN ts/2 Aliasing fu= ? Han=0-5 = 75 Hz = 37.5 Hz NZ .. fa = 0.5 x fn = 0.5% 37.5 = 18.75 Hz