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Smooth Differentiation

4.2 | 6 ratings Rate this file 40 Downloads (last 30 days) File Size: 65.6 KB File ID: #6170 Version: 1.0
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Smooth Differentiation


Jianwen Luo (view profile)


02 Nov 2004 (Updated )

A smoothed differentiation filter (digital differentiator).

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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.
  n: filter length (positive integer larger no less than 2)
  h: filter coefficients (anti-symmetry)
  Jianwen Luo <,> 2004-11-02
  Department of Biomedical Engineering, Department of Electrical Engineering
  Tsinghua University, Beijing 100084, P. R. China
  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.


This file inspired Generation Of Random Variates.

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Comments and Ratings (7)
30 May 2012 UMP

UMP (view profile)

Jianwen Luo: I have go through this m.file. This is a nice work and good reference to me but I really want to know how I can find the maximum and minimum peak from this graph?I want to use [pks locs]=peakfind() but I do not know how to manipulate it. I need your help.

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19 Jun 2008 ridzan djafri

19 May 2008 Hakan Demir

Can you also draw the bode plot of the differentiator as a transfer function.

[h, w] = freqz(h);
plot(w/pi*30, (abs(h)), 'r-');

This doesn't seem like a differentiator.

12 Oct 2006 veera puthiran

10 Oct 2006 Ho Hung-jung

18 Aug 2005 Tomas Ward

Very useful

26 Feb 2005 Martin Ferguson-Pell

This is a very handy tool for differentiating signals eliminating the common problem of spikey differentials due to suble noise fluctuations in the signal

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