Different Typs of Periodgram Comparison
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Different Typs of Periodgram Comparison

 
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ngeva0
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Posted: Wed Dec 14, 2005 1:16 am    Post subject: Different Typs of Periodgram Comparison Reply with quote

A WSS process x[n]=Acos(Bn+C) where C is uniformly distributed between
and 2pi and the other parameters are deterministic.

1. Is there an advantage to using the Barlett method over the Periodogram
Why or why not?

2. Is there an advantage to the Modified Periodogram over the Periodogram
Why or why not?

3. Does your answer to ques. 1 change if you are to estimate the PSD o
y[n]=x[n]+w[n], where x[n] is same as above and w[n] is a zero-mean whit
noise process? Why or why not?

I know, in general, Barlett's method uses avgeraging to reduce th
variance and Modified Periodogram uses a non-rectangular window to reduc
the bias. But I don't feel like they are sufficient to explain the abov
questions. Can anyone provide further details? Thanks!
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Peter K.
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Posted: Wed Dec 14, 2005 1:16 am    Post subject: Re: Different Typs of Periodgram Comparison Reply with quote

"ngeva0" <ngeva0@hotmail.com> writes:

Quote:
A WSS process x[n]=Acos(Bn+C) where C is uniformly distributed between 0
and 2pi and the other parameters are deterministic.

1. Is there an advantage to using the Barlett method over the Periodogram?
Why or why not?

2. Is there an advantage to the Modified Periodogram over the Periodogram?
Why or why not?

Think about what you're asking: does the periodogram of a cosine wave
of arbitrary phase depend on the phase?

Quote:
3. Does your answer to ques. 1 change if you are to estimate the PSD of
y[n]=x[n]+w[n], where x[n] is same as above and w[n] is a zero-mean white
noise process? Why or why not?

That's a different question, now you've added noise to the cosinusoid.

Quote:
I know, in general, Barlett's method uses avgeraging to reduce the
variance and Modified Periodogram uses a non-rectangular window to reduce
the bias. But I don't feel like they are sufficient to explain the above
questions. Can anyone provide further details? Thanks!

Think about what the "true" periodogram (spectrum) in each case SHOULD
look like, and then think about whether the estimators you're using
take account of each case.

Ciao,

Peter K.
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