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Lab Exercise:

Signals, Sampling, Aliasing

This exercise should be done in Excel. Note that Excel has a built-in function pi( ) that returns the value of pi. It also has built in functions sin( ) and cos( ) that return the sine and cosine of real valued arguments. Be able to answer questions regarding all aspects of this exercise.

Consider the analog signals cos(2 pi 1000Hz t), cos( 2 pi 7000Hz t), and cos( 2 pi 9000Hz t). Use Excel to generate discrete-time samples of each of the three signals sampled at a rate of 8 KHz or 8000 Hz starting at t = 0. Generate the first 100 (or more) samples of each analog signal in separate columns of your worksheet:

n			x1(n)			x2(n)			x3(n)
0
1
. . .
99

Use three separate XY (scatter) graphs [from the menu: Insert >> Chart >> XY(scatter) ] to graph the resulting discrete-time signals x1(n), x2(n), and x3(n) against n on the horizontal scale.

What do you observed about the three graphs? How are they related? Why?

To demonstrate that you understand what is happening, generate your own example using the analog signals cos(2 pi f₁ t), cos( 2 pi f₂ t), and cos( 2 pi f₃ t), where f₁ is the frequency assigned to you [frequency assignments], and f₂ and f₃ are frequencies you may choose based on f₁. Keep the sampling frequency at 8000 Hz.

Using the same value of f₁ assigned to you, generate another example using the signals sin( 2 pi f₁ t), sin( 2 pi f₄ t), and sin(2 pi f₅ t) where f₄ and f₅ are frequencies you may choose based on f₁ . Keep the sampling frequency at 8000 Hz.

 

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