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It is the maximum frequency of the signal (not the maximum frequency
of interest) that dictates sampling requirements. The reason for
this is noise, which is often broad-spectrum (e.g. white or pink).
Any noise in the signal above the Nyquist frequency (1/2 the sampling
frequency) will be aliased back to lower frequencies, probably
overlapping with the signal of interest and leading to signal
distortion. Once aliasing has occurred, there is no way to remove
the noise with digital filtering.
So, the proper way to match sampling frequency to desired bandwidth
is to limit signal bandwidth to the frequencies of interest via
analog "antialiasing" filters, and then sample the data at a minimum
of 3-5 times the filter cutoff frequency. It is important to
remember that the "2X" sampling rule is a theoretical ideal, assuming
a perfect filter. In real life, analog filters have gradual roll-
offs, so a higher oversampling rate is required.
The observation that these guidelines have not been followed in some
published work (e.g. 1 kHz filter with 1 kHz sampling) does not
necessarily imply that undersampling is generally acceptable or that
any published data is erroneous. It is often possible to get by
without "proper" antialiasing filters if you have very clean signals,
or if your application is such that the effects of high-frequency
noise do not alter data interpretation significantly. But, it is
always preferable to know the effects of noise in your signals. A
good way to characterize the frequency content of your signal is to
acquire some data under realistic conditions using a very high
sampling rate (several times the expected highest frequency, e.g.
10X), and check for the presence of high-frequency noise using an FFT
power spectral analysis. Most signal processing software (e.g.
Matlab) has tools for this kind of analysis.
___________________________
Scott Tashman, Ph.D.
Associate Professor
Dept. of Orthopaedics
University of Pittsburgh
phone: (412) 260-7102
E-mail: sct8@pitt.edu
of interest) that dictates sampling requirements. The reason for
this is noise, which is often broad-spectrum (e.g. white or pink).
Any noise in the signal above the Nyquist frequency (1/2 the sampling
frequency) will be aliased back to lower frequencies, probably
overlapping with the signal of interest and leading to signal
distortion. Once aliasing has occurred, there is no way to remove
the noise with digital filtering.
So, the proper way to match sampling frequency to desired bandwidth
is to limit signal bandwidth to the frequencies of interest via
analog "antialiasing" filters, and then sample the data at a minimum
of 3-5 times the filter cutoff frequency. It is important to
remember that the "2X" sampling rule is a theoretical ideal, assuming
a perfect filter. In real life, analog filters have gradual roll-
offs, so a higher oversampling rate is required.
The observation that these guidelines have not been followed in some
published work (e.g. 1 kHz filter with 1 kHz sampling) does not
necessarily imply that undersampling is generally acceptable or that
any published data is erroneous. It is often possible to get by
without "proper" antialiasing filters if you have very clean signals,
or if your application is such that the effects of high-frequency
noise do not alter data interpretation significantly. But, it is
always preferable to know the effects of noise in your signals. A
good way to characterize the frequency content of your signal is to
acquire some data under realistic conditions using a very high
sampling rate (several times the expected highest frequency, e.g.
10X), and check for the presence of high-frequency noise using an FFT
power spectral analysis. Most signal processing software (e.g.
Matlab) has tools for this kind of analysis.
___________________________
Scott Tashman, Ph.D.
Associate Professor
Dept. of Orthopaedics
University of Pittsburgh
phone: (412) 260-7102
E-mail: sct8@pitt.edu