ECE 3512 - Signals Dr. Obeid Exam 3 November 17, 2017 1. (35 pts) A 10Hz cosine
ID: 2249890 • Letter: E
Question
ECE 3512 - Signals Dr. Obeid Exam 3 November 17, 2017 1. (35 pts) A 10Hz cosine a(t) is sampled at (a) Is there aliasing (undersampling). Explain why or why not. 25Hz to produce discrete-time signal n) (b) Compute the value of the discrete-time frequency . (c) How many samples per period are in n]? 0,1, ,5 (d) Sketch the plot of the first six samples of zln] for n e) Suppose you are just shown the plot from part (d) and told the sampling rate was F-100Hz What would you conclude is the frequency (in Hertz) of r(t)?Explanation / Answer
(A) According to the sampling theorem ,fs>= 2fm and for aliasing(undersampling) fs<2fm .
Therefore ,
fm= 10hz
fs =25 hz(given)
fs >= 2*10hz
>= 20hz(condition).
i.e fs> 2fm
Hence sampling theorem is satisfied.
(B) The discrete time frequency can be calculated as :
x(t) = cos (2*pi*f*t)
x(t)= x(nT)
=cos(2*pi*f*t *n)
Therefore, w= 2*pi*f*T (f is signal frequency and T is sampling interval i.e 1/fs)
=2 *pi *10/25
=4 Pi/5 radians
(c) Number of samples per period = 25*60 = 1500 i.e Fs = n/60
(e) When the sampling rate is doubled or increased, the frequency specture expands and higher frequencies can be recorded but if the sampling frequency is significantly higher than the nyquist rate than oversampling occurs.
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