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Question about 10.4 - "The Sampled Sinusoid"
dan_1
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January 26, 2021 - 2:54 pm
Member Since: January 26, 2021
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Hi all,

I have a question about equation 10.11, page 199 (2nd edition of the FX book)...

In short, the question is: is the equation correct?

It keeps puzzling me, as we are subtracting "M", which is a number of samples, from "nT" which is a value in seconds. I may be entirely missing the point, but it seems to me that equation 10.11 would work if M was a value in seconds, not number of samples.

In order to delay by a number of samples M, the exponent should be [j * omega * T * (n - M)] rather than [j * omega (nT - M)].

I thought this was perhaps a typo or something, but I see that the same equation is used multiple times later on so perhaps I'm just confusing myself...

Does anybody have any thoughts to share?

Thanks a lot!

Wutru
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March 21, 2021 - 6:03 pm
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I have this same question.

Have you found a solution yet, Dan?

I've asked my DSP teacher and he says it's probably a mistake in the book, but I would be surprised if it was, since it's used for a long time...

I hope Will could clear this up 🙂

W Pirkle
March 22, 2021 - 9:02 am
Member Since: January 29, 2017
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Hi - yes this is a typo of sorts. It actually has origins in the way I used to teach this, where I took some liberties mixing analog and sampled sinusoid equations. You are correct about it working for seconds rather than samples. I found that students from high-school had no problems with analog sinusoid equations, so I would start there and kind of blend the two together. In the 2nd edition of the book I tried to reconcile that with nT instead of just (t). Sorry for the confusion.

Will

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