Scott Tashman

11-01-2006, 06:22 AM

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