44. Below is a graph of some samples taken from a sinusoid. 0.5 0.5 1.5 0.5 1.5

Question

44. Below is a graph of some samples taken from a sinusoid. 0.5 0.5 1.5 0.5 1.5 Time, (s) (a) What is the sampling rate fs? (b) If these samples have been taken properly (according to Shannon's sampling theorem), what is the fundamental frequency fo of the sinusoid? (c) The sinusoid from which the samples came can be expressed in the form A cos(2fo). What is the numerical value of (d) Specify the fundamental frequencies foi and fo2 of two other cosines of the same amplitude which, when sampled at the same rate, would yield the same set of samples.

Explanation / Answer

This is the simple question ,

We will begin by first understanding the sample frequency :

We know the sample frequency is the frequency at which the given continuous signal is sampled to get the discrete signal .

To find samplig frequency we shoul know the cotinuous structure of sinusoidal wave .

Now, by obsrving the above figure (from where the wave starts repeating we get )

a) fs(Sampling frequency )= 1/Ts

Ts=0.7 seconds(approx)

Hence , fs=10/7 Hz=1.43 Hz

b) It is mentioned that sample are taken properly , Hence fs=2fo from the Shanon Sampling theorem .

Hence , fo=1.43/2

fo= 0.715 Hz

c)

A is the magnitude at y axis .

Hence from figure it is given that

A=2

d)

fo1=fs+2fm

fo2=-fs-2fm

fo1=1.43 +2(0.715)=2.86 Hz

f02=-2.86 Hz

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