An aliasing example

 Yesterday I had the pleasure of visiting the Measurement Standards Lab at Lower Hutt. We were talking about making measurements of electrical impedance. In practice, if you want a decent measurement, it’s rather less straightforward than whacking on a multimeter. It was interesting to have a look at their labs, including several New Zealand ‘standard’ things (such as resistors) – and apparatus for measuring them really, really accurately. 

But that’s another blog entry. On the flight from Hamilton to Wellington we had a fantastic view of the snow-capped Tongariro volcanoes, in some really great visibility conditions.  There was a fair bit of photography  going on. The guy in front of me got out his cellphone, but before snapping his picture noted a rather interesting phenomenon. He was viewing the image on his phone screen partly through a rotating propellor. For the eye, since the propellor was rotating so fast, all this meant was that the background viewed through it was simply slightly darker than the rest. However, the camera screen told a different story. On this one could see almost stationary propellor blades. They were rotating very slowly and a little distorted in shape.  

I assume this would be an example of aliasing. The rotation rate of the propellor, and the refresh rate of the camera screen, would be close to integer multiples of each other. So every time the screen refreshed, the propellor had rotated such that there was a blade in approximately the same position. Consequently, a blade shape appeared on the screen. However, on the final photograph, with a long exposure time, no such blade was apparent. 

With a given sampling rate (in this case that of the camera screen) there is a maximum frequency of oscillation which one can detect. This is half the sampling rate, called the Nyqvist frequency. Anything that is oscillating more quickly than that won’t appear at its true frequency – instead it will be aliased to a frequency that lies between the negative of the Nyquist frequency or the positive of it. So the oscillating thing will appear to move either forward or backwards at a slower frequency. One sees it on movies with accelerating cars – the wheels can appear to be rotating slowly backwards (or forwards) or even be stationary.  Here’s a nice example from YouTube. Very disturbing visually. Fortunately the eye doesn’t have a regular refresh rate and so isn’t susceptible to aliasing – it just fails to see the rotation at all once it gets to fast.

 

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