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questions on FFT

Started by jeffxia March 29, 2006
Hi all,

I feel confused with some trivial questions and your help is highly
appreciated.

1. Suppose Y(k) is the N point FFT of the original data, for me, the power
spectrum is Y.*conj(Y). However, the example in "Matlab help" of fft tells
that the power spectrum is Y.*conj(Y)/N. 

2. I need to calculate the power of a specific band, for example 10-20Hz.
What I do is just to take FFT and sum up the power of frequency components
within 10-20Hz. I am wondering if it is a right way and if there is any
other better way.

3. Suppose I have N samples in time domain and the time interval is t. I
want to remove its low frequency components. So I desigh a K order FIR
highpass filter. The length of the resulting signal is N+K-1. Does the
time interval is still meaningful in the resulting signal? What if I still
want to keep N samples of the resulting data?

Thanks,

Jeff  



jeffxia wrote:
...
> 3. Suppose I have N samples in time domain and the time interval is t. I > want to remove its low frequency components. So I desigh a K order FIR > highpass filter. The length of the resulting signal is N+K-1. Does the > time interval is still meaningful in the resulting signal? What if I still > want to keep N samples of the resulting data?
Let's say you have two polynomials, one with degree N and the other with degree K. You multiply them together, the new polynomial has degree N+K. Can you throw away some terms to make it have degree N? Obviously, if N is the number of samples on a CD, and K is a third-order difference filter, then you won't lose too much information if you truncate the filtered output back to N samples. If you have to, make sure that you throw away the right part of the output signal (this depends on whether your FIR is linear- or minimum-phase or none of the above). Regards, Andor