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From my understanding PSD tries to give a good estimation on the power each frequency attributes to the overall signal power.

If I am only interested in a frequency range $(\omega_0 \leq \omega \leq \omega_1)$, could I put the signal through a band pass filter for that same frequency range then calculate the signal power using this formula:

$$P_x = \frac{1}{N_1 - N_0 + 1}\sum_{n = N_0}^{n=N_1} \left|x(n)\right|^2 $$

Would this technique give me what I am looking for, (the power of the signal from $N_0$ to $N_1$ for the specific frequency range)?

How does this compare to PSD estimation using any of the popular techniques?

Pros, Cons?

Thank you!

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  • $\begingroup$ i would say the answer is "yes, it should give you what you are looking for". Pros: simple and consistent. Cons: might be more expensive if $N_0 \ll N_1$ than an FFT. your BPF will likely need to be sharp on both left and right. $\endgroup$ – robert bristow-johnson Sep 7 '16 at 2:54
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You can switch to the frequency domain with regards to Parseval's theorem. I guess you can transform your problem via discrete-time fourier transformation.

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