anachem@silver.ucs.indiana.edu (|mehcana| (undersampled)) (02/16/91)
In article <21978@duke.cs.duke.edu> sza@physics.phy.duke.edu (Eric Szarmes) writes: > >of the signal spectrum, and if the sampling rate is more than twice the >highest frequency component, we see (as below) that there is no aliasing, >or overlap, of spectral components. Filtering the sampled signal with the ^^^^^^^ or "foldover" see my "alias" in the "From" field of the header.... :*) -- Mark Gilstrap Analytical Chemist Department of Geosciences Indiana University gilstrap@iubacs
tomb@hplsla.HP.COM (Tom Bruhns) (02/18/91)
sza@physics.phy.duke.edu (Eric Szarmes) writes: >... > This convolution essentially replaces each delta function with a copy >of the signal spectrum, and if the sampling rate is more than twice the >highest frequency component, we see (as below) that there is no aliasing, >or overlap, of spectral components. Filtering the sampled signal with the >appropriate lowpass filter then exactly reproduces the original signal. >... Note: that "_more_than_" is crucial. If we sample a sinewave at exactly twice its frequency, and happen to sample it at its zero crossings, we get a stream of zeros out. And if we sample it at any other phase, we still have no way of knowing its amplitude. Note also that to satisfy the Nyquist theorem, the sinewave must go on forever, else it will have other (including higher) frequency components. Note also that you can extend the Nyquest theorem to allow `perfect' sampling of any band whose _width_ is less than 1/2 the sampling frequency, so long as it does not contain a frequency that is a harmonic of 1/2 the sampling frequency (since all such harmonics suffer the same problem). This assumes instantaneous, jitter-free sampling, of course.
smithj@hpsad.HP.COM (Jim Smith) (02/20/91)
Mark Gilstrap writes: >see my "alias" in the "From" field of the header.... :*) Well, if you hadn't been undersampling, you wouldn't have aliased! -Jim Smith (alias "Jim Smith")