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Help with Nyquist's Frequency 
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#1
Mar2114, 04:16 PM

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Hi everyone!
Struggling to get my head about Nyquist's Frequency.. Have I got this right? The Nyquist Frequency is 1/2 of the sampling rate of a discrete signal, and is the highest frequency that will allow a signal to be fully reconstructed without aliasing, at a given sampling rate. The standard framerate for a certain video camera is 30 frames per second. Therefore the camera is sampling at 30Hz. This means that the Nyquist Frequency is 15 Hz. Any vibrations applied to the camera about 15Hz will therefore not be visible in the footage. Or is that completely wrong? Is it 60Hz rather than 15Hz? Any help would be much appreciated! Thanks, JJ. 


#2
Mar2114, 04:57 PM

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It means that a vibration at 17 Hz would be indistinguishable from a vibration at 13 Hz. Or a vibration at 19 Hz would be indistinguishable from a vibration at 11 Hz. Or a vibration at 29 Hz would be indistinguishable from a vibration at 1 Hz. To avoid aliasing you would need to ensure that there were no vibrations above 15 Hz. 


#3
Mar2114, 05:00 PM

P: 5

Thanks for the reply. Does this mean that if I isolate the vibrations below 15Hz, no other vibrations will be apparent? 


#4
Mar2114, 05:20 PM

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Help with Nyquist's Frequency
Have you ever seen a film or video of a rotating wheel where the wheel gives the illusion of rotating backwards? (Wagonwheel effect) A rotation of 29 spokespersecond clockwise would look like a rotation of 1 spokepersecond anticlockwise. 


#5
Mar2114, 05:45 PM

P: 308

Aside from the problem of aliasing from higher frequencies there is another consideration. The accuracy of the amplitude estimate of the lower frequencies can be very bad if the data used is not over infinite time. Given an infinite data sample, the amplitude of anything below 15 Hz can be determined precisely (assuming no aliasing from higher frequencies). But shorter sample times give much larger amplitude errors. The Nyquist frequency is often misinterpreted as being adequate to reconstruct signals even though the amplitude calculations are based on data taken over a short time. There are formulas for the amplitude error limits if the data sample is not infinite.



#6
Mar2114, 05:57 PM

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PF Gold
P: 12,135

Factchecker is right about the time for the sampling. The contribution of noise from the sampling circuit is affected by the time taken for the sample to be made. It is common to use a sample time equal to the interval between samples (boxcar) and this then requires an appropriate equalisation to adjust for the resulting effect on the frequency response. 


#7
Mar2114, 06:37 PM

P: 5

OK, thanks.
Going right back to basics  I've been told that there is a relationship between the frame rate which the camera is recording at, and an upper boundary of vibration frequencies, above which they will not be visible, explained(?) by Nyquist. Is this correct? Sorry for the ignorance  this is definitely not my area of expertise! 


#8
Mar2314, 05:46 AM

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Thanks
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#9
Mar2314, 07:26 AM

P: 308




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