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February 17th, 2011, 05:32 PM   #1
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Trig Identities

I am studying for my DSP midterm, and I am stuck on some trig identities. I have this sample question:

If the difference equation is y(n)=x(n) + x(n-, and x(n)=cos(wn)*u(n), and w is equal to 2pi, and u(n) is the unit step, and n=8, express the answer in the form y(n)=A(cos(wn + B)).

I have...

y(=cos(w +cos(8w)^2 + sin(8w)^2

y(=cos(8w)+1

....

How can I simplify that further?
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February 19th, 2011, 02:25 PM   #2
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Re: Trig Identities

Hello Natalie,

Quote:
Originally Posted by You
y(=cos(8w)+1

....

How can I simplify that further?
The range of A(cos(w8 + B)) is [-A,A].
The range of cos(8w)+1 is [0,2]

-A=0 would imply A=0, but A=2 implies well, A=2. Contradiction, therefore,

You cannot write y(=cos(8w)+1 of the form y(n)=A(cos(wn + B)):=A(cos(w8 + B)).
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February 28th, 2011, 09:00 AM   #3
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Re: Trig Identities

Alright that makes sense as to why I cannot do that, but I still don't understand how to get it to that form.
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