Say I have a signal which has a component above 50kHz.. and I sample that signal at a rate lower than the Nyquist Frequency ( which is 100kHz ? correct me if i'm wrong).. As a result, aliasing occurs , and the component above the 50Khz appears to be within the 0 - 50kHz range.. Can someone please explain to WHY that happens?

Thanks

 

quick addition,

Can we calculate what "low frequency" alias value the component will be located at ? ( so that I can basically ignore it once i see it )

 

Say I have a signal which has a component above 50kHz.. and I sample that signal at a rate lower than the Nyquist Frequency ( which is 100kHz ? correct me if i'm wrong).. As a result, aliasing occurs , and the component above the 50Khz appears to be within the 0 - 50kHz range.. Can someone please explain to WHY that happens?

Thanks

Sampling is "equivalent" to multiplication in the analog world. Take a mathematical look at the product of two sine waves of different frequencies.
Also, think of this: Mentally, take a sine wave at 50kHz. Mentally sample and hold it at 50kHz. You will get a DC voltage which is a function of the phase of the sampling. Now, change the sampling frequency by 1kHz. The phase of the sampling will precess at a 1kHz rate, giving you a 1kHz sine wave (with stairsteps superimposed).
If you try to ignore the aliased product, you will also ignore legitimate signals of the same frequency.
Also, look up convolution.

 

aliasing is when different frequencies look the same when sampled at any given frequency. if you draw a sine wave (several cycles) on paper above and below a horizontal center line. now draw another sine wave of less frequency on top, and make landmarks (zero crossovers and peaks)coincide. for example start both at zero, make the slower sine wave meet the second peak of the faster waveform, then continuing that wave shape it meets the faster wave again at zero, etc.. so if the sampling rate is that of the coincident values, you have aliasing. a problem with dsp, but easily removed with filters.