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Asked by Nalini Nadupalli on 12 Jan 2013

x(t)=cos(2π30t)+cos(2π70t+π) is sampled at 100 SAMPLE SECOND.

(a) Show algebraically (by substituting t= n/100 ) that the sampled signal is 0! (b) Plot the spectrum of the sampled signal. Show all of the components cancel.

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Answer by Walter Roberson on 13 Jan 2013

Edited by Walter Roberson on 13 Jan 2013

Hint:

plot(t, x(t))

## 6 Comments

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/58628#comment_122200

To do the first part by using MATLAB you would need to use the symbolic toolbox and do a bunch of manual algebraic manipulation.

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/58628#comment_122201

If this is a homework, what have you done so far?

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/58628#comment_122230

I have done the first part, for which i am unsure of the the method by which I have proved and the second part is where I am stuck at.

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/58628#comment_122239

Hint on part (a) if you are still unsure: You need the identity

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/58628#comment_122243

Interesting, I didn't know that identity.

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/58628#comment_122255

It's easy to prove using the two formulas for the cosine of the sum and the difference between two angles:

cos(A) = cos((A+B)/2+(A-B)/2) = cos((A+B)/2)*cos((A-B)/2)) - sin((A+B)/2)*sin((A-B)/2))

cos(B) = cos((A+B)/2-(A-B)/2) = cos((A+B)/2)*cos((A-B)/2)) + sin((A+B)/2)*sin((A-B)/2))

Adding these gives:

cos(A) + cos(B) = 2*cos((A+B)/2)*cos((A-B)/2))