I'm graduating in mechanical engineering and my monography is about audio analysis using python. And it might even evolve into cardiorespiratory disease analysis via python next semester. Your course is being very elusive for me in regard of signal analysis. Thank you very much, Dr. Cohen.
"the estimate of the statistic is independent of the size and location of the time window" What if the time window is only one data point long? For example with tzhe values -10 then 10 for another location. Do you scale the margin of error according to the size if the window?
Thank you for the video. Could you comment on if a deterministic signal can be regarded as stationary or not? My reasoning seems to give two contradictory results. On one hand, if the deterministic signal can be regarded as a signal with delta distribution. Its variance stays stable while mean will change over time depending on the functional form of the signal. This seems to suggest that a deterministic signal is non-stationary (although I have doubts on the result); On the other hand, the FFT of a function is a well-defined quantity and yields the energy distributions over frequency. I would appreciate that if you could help clarify that. Thanks.
Hi James. Stationarity and determinism are separate concepts, and with regards to interpreting the power spectrum, one has no effect on the other. The main point of this video is that non-stationarities make the power spectrum more difficult to interpret; the origin or mechanism of those non-stationarities don't matter. Also, I hope this point wasn't lost in the video, but the issue isn't whether the FFT is valid (it always is) or whether a system yields a well-defined power distribution; the issue is that making inferences about a system based on visual inspection of the power spectrum is straightforward for stationary signals, and increasingly difficult for non-stationary signals.
I'm graduating in mechanical engineering and my monography is about audio analysis using python. And it might even evolve into cardiorespiratory disease analysis via python next semester. Your course is being very elusive for me in regard of signal analysis. Thank you very much, Dr. Cohen.
Awesome, I'm glad it's useful!
wow, this is great content. looking forward to watching all of it. I'm a big fan of wavelets
I'm literally at this moment uploading dozens of new videos. This is one of them. Check back in a few days for the rest!
"the estimate of the statistic is independent of the size and location of the time window"
What if the time window is only one data point long?
For example with tzhe values -10 then 10 for another location.
Do you scale the margin of error according to the size if the window?
Thank you for the video. Could you comment on if a deterministic signal can be regarded as stationary or not? My reasoning seems to give two contradictory results. On one hand, if the deterministic signal can be regarded as a signal with delta distribution. Its variance stays stable while mean will change over time depending on the functional form of the signal. This seems to suggest that a deterministic signal is non-stationary (although I have doubts on the result); On the other hand, the FFT of a function is a well-defined quantity and yields the energy distributions over frequency. I would appreciate that if you could help clarify that. Thanks.
Hi James. Stationarity and determinism are separate concepts, and with regards to interpreting the power spectrum, one has no effect on the other. The main point of this video is that non-stationarities make the power spectrum more difficult to interpret; the origin or mechanism of those non-stationarities don't matter. Also, I hope this point wasn't lost in the video, but the issue isn't whether the FFT is valid (it always is) or whether a system yields a well-defined power distribution; the issue is that making inferences about a system based on visual inspection of the power spectrum is straightforward for stationary signals, and increasingly difficult for non-stationary signals.
Find someone that talks about you the way Dr. Cohen talks about the FFT. 😍
Awww :P
doesn't cover the part of the title "and their effect on the power spectrum"...?