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I sampled frequencies of 400, 500, and 600 Hz at a sampling frequency of 1 kHz. My oscilloscope showed aliasing at 400 Hz, nothing at 500Hz, and then a lot of aliasing at I saw some aliasing

aliasing should not occur when the sampling frequency is more than two times the max frequency of the signal. so why was aliasing occurring at 400 Hz?

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What you are seeing is not aliasing. It's simply an artifact of the way your scope is rendering the data it had captured.

When you sample a 400 Hz sinewave at 1000 sps, you're only capturing 2.5 samples per cycle. Obviously, most of these samples aren't going to be at the peaks of the waveform. Therefore, when your scope draws simple straight lines to connect the points, you see a waveform whose amplitude varies periodically.

In order to properly reconstruct the waveform for display, the scope really should be oversampling the data and passing it through a low-pass filter with a sharp cutoff.1 But this is computationally intensive, and so most scopes skip it. They usually just tell you to use a sample rate that's at least 10x the highest frequency of interest.

1 This is just another way of saying "interpolate with a sinc function".

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  • \$\begingroup\$ To add to Dave Tweed's answer, the sampling theorem just tells you how often (at minimum) you need to sample a bandlimited signal to get all of the information contained in the signal. If you want to reconstruct/view the original signal correctly you need to interpolate the samples using the sinc function. \$\endgroup\$ – GummiV Sep 8 '12 at 10:34
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    \$\begingroup\$ When you display high frequencies on a scope at a slow display rate, that's aliasing, too. Whether because time base settings impacted the scope's sample rate, or the screen resolution makes little difference. In the day of the digital scope, there's more sampling errors that you need to keep track of than in the old days \$\endgroup\$ – Scott Seidman Sep 8 '12 at 10:47

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