How do I plot it? by hand or in matlab? if it can be done by both the how to do?

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.```

Roger Stafford

Roger Stafford (view profile)

on 13 Jan 2013

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

` cos(A) + cos(B) = 2*cos((A+B)/2)*cos((A-B)/2)`
Walter Roberson

Walter Roberson (view profile)

on 13 Jan 2013

Interesting, I didn't know that identity.

Roger Stafford

Roger Stafford (view profile)

on 13 Jan 2013

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))

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

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Walter Roberson (view profile)

on 13 Jan 2013
Edited by Walter Roberson

Walter Roberson (view profile)

on 13 Jan 2013

Hint:

`    plot(t, x(t))`

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