Finding the aliased version of a signal

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SUMMARY

The discussion focuses on the concept of aliased signals and how to identify the aliased version of a function at a specific sampling rate, particularly using the example of a time-varying voltage function V=sin(1/t) sampled at 100 Hz. The conversation highlights the importance of understanding the Nyquist theorem, which states that frequencies above half the sampling rate will be aliased back into the Nyquist band. Participants discuss methods for interpolating data points during rapid signal changes and the implications of performing a Fast Fourier Transform (FFT) on such signals.

PREREQUISITES
  • Understanding of Nyquist theorem and aliasing
  • Familiarity with Fast Fourier Transform (FFT) techniques
  • Basic knowledge of signal processing concepts
  • Experience with time-varying functions and their behaviors
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  • Research the Nyquist-Shannon sampling theorem in detail
  • Learn about interpolation techniques for non-uniformly sampled data
  • Explore advanced FFT applications in signal analysis
  • Study the effects of sampling rates on signal integrity and reconstruction
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Electrical engineering students, signal processing practitioners, and anyone interested in understanding the implications of sampling rates on signal analysis and reconstruction.

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Hey everyone. I've got a question pertaining to aliased signals. Is there a general method for finding what signal a function would alias to at a certain sampling rate? For example, suppose that you have a time-varying voltage V=sin(1/t), and you take data at a rate of 100 Hz, starting from when t=0. I picked this function because the initial frequency is infinite, and subsequently decreases.Therefore, what should happen is that at some point in time, whatever doing the sampling should eventually "get" the correct function. However, I'm more interested how one would interpolate the data in those first few moments when the signal does all kinds of crazy stuff. Is it possible to interpolate a function which "fits" those data points? Thanks!
 
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If you perform an FFT of the signal, the power that really exists in bins past half the sampling rate will appear folded back into the Nyquist band.

- Warren
 
Could you elaborate on that? I'm only a first year EE student, and I'm not clear on what you mean when you say "folded back into the Nyquist band."
 

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