james@phred.UUCP (JAMES Taylor) (02/06/90)
In article <7973@charlie.OZ> peter@aragorn.UUCP (Peter Horan) writes: >In article <1990Jan25.194133.4503@athena.mit.edu> ashok@atrp.mit.edu (Ashok C. Popat) writes: >>Conservative sampling rates are used not because the sampling theorem >>has a ">" instead of a ">=" (it doesn't); instead, they are used >>because real-life information-carrying (i.e., non-degenerate) signals >>are not (and cannot be) strictly bandlimited. >> > >Actually, it is a practical matter. To recover a sinusoid >of say 495Hz sampled at 1KHz requires a 70 pole Butterworth >filter. However, if sampling is done at 2KHz, a 3 pole filter >will do. (I forget what the criterion of performance was - the >error may have been 30 to 40dB down). Note, it is also worthwhile >interpolating before recovery (so-called oversampling in the CD >world). > >Peter Horan >peter@aragorn.cm.deakin.oz Another pratical matter is involved here - Nyquist said not only 1> a band limited signal, of bandwidth "B" say 2> sampling rate of > 2*B *BUT ALSO* 3> ALL of the samples to provide an exact reconstruction. It is also trivially easy to show that arbitrary time limited signals are NOT bandlimited. The major consequence in an Engineering sense is to provide one more trade off in determining the required over-sampling factor r, where W==(sample rate)=r*(2*B), ie, for the process, f(t) -> f(n/W) -> f'(t), what time interval is required in order to bring the estimate error max(f'(t)-f(t)) to within some particular design criteria. Another factor is the fact that over-sampling can give some immunity to non-linear noise sources, such as sample jitter or missing samples. For more information Dr. Robert Marks II at the University of Washington has published several papers (in the Journel of Optic, I believe) which deal with the Popoulis Sampling Theorem (an extention of the Shannon ST), and reconstuction algorithms.