# questions on FFT

Started by 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

```