Smooth Differentiation

A smoothed differentiation filter (digital differentiator).

A smoothed differentiation filter (digital differentiator).

Such a filter has the following advantages:

First, the filter involves both the smoothing operation and differentation operation. It can be regarded as a low-pass differention filter (digital differentiator). It is well known that the common differentiation operation amplifies the high-frequency noises.Therefore, the smoothded differentiation filter would be valuable in experimental (noisy) data processing.

Secondly, the filter coefficients are all convenient integers (simple units) except for an integer scaling factor, as may be especially significant in some applications such as those in some single-chip microcomputers or digital signal processors.

Usage:
h=smooth_diff(n)
n: filter length (positive integer larger no less than 2)
h: filter coefficients (anti-symmetry)

Examples:
smooth_demo

Author:
Jianwen Luo <[e-mail], [e-mail]> 2004-11-02
Department of Biomedical Engineering, Department of Electrical Engineering
Tsinghua University, Beijing 100084, P. R. China

References:
Usui, S.; Amidror, I.,
Digital Low-Pass Differentiation for Biological Signal-Processing.
IEEE Transactions on Biomedical Engineering 1982, 29, (10), 686-693.
Luo, J. W.; Bai, J.; He, P.; Ying, K.,
Axial strain calculation using a low-pass digital differentiator in ultrasound elastography.
IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 2004, 51, (9), 1119-1127.