How can I filtrate recorded time acceleration signal with 4th order Butterworth low and high pass filter ??

Discription of the problem:

I need to apply a 4th order Butterworth low and high pass filter of 0.1-100 Hz to filter the integrated velocity out from both low frequency and high frequency.

Parameters are listed below: (time frame is 10 Sec. with 0.01 Sec. increament).

Answer 1

[Mathieu NOE]

hello

below a script you can use / modify to fit your own needs ;

You may have to change the way you load the time data (example here for txt / ascii files using the readclm function)

the filter is applied on the time data using the filtfilt function

you need the signal processing toolbox

enjoy !

Mathieu

-------------------------------------------------------------------------------------------------------------------------------------------------
clc
clear all
close all

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
file = 'test3.txt';
% time indexes ;
time_min = 0;
time_max = 5;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Nclm = 2; % nb of columns : 1 = time , 2 = vibration
[outdata,HEAD] = readclm(file,Nclm,1);   
t = outdata(:,1);   % time
Data = outdata(:,2);    % vibration channel # 1
clear outdata
ind = find(t>=time_min & t<=time_max); % use only data between the two time indexes
t = t(ind);
Data = Data(ind);
samples = length(t);
Fs = round((samples-1)/(max(t)-min(t)));    % Sampling frequency
Filename_title = file(1:length(file)-4);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% decimation 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
decim = 2; %;
Data2 = decimate(Data,decim);
Fs2 = Fs/decim;
t2 = min(t)+ (0:length(Data2)-1)/Fs2;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% band pass filtering
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f_low = 150;
f_high = 300;
Wn = 2*[f_low f_high]/Fs2;
N = 2;
[B,A] = BUTTER(N,Wn);
% apply band pass filter to data
Data_filtered = filtfilt(B,A,Data2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% plot
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1);
subplot(2,1,1),plot(t2,Data2);xlabel('Time (s)');ylabel(' amplitude (g)');legend('unfiltered');
title(' Time signal - Accelerometer ');
subplot(2,1,2),plot(t2,Data_filtered);xlabel('Time (s)');ylabel(' amplitude (g)');legend('filtered');

max_amplitude_g = max(abs(Data_filtered));
disp(['Max g level : ' num2str(0.01*round(max_amplitude_g*100)) ' g']);

[Mohamed Abdelkareem]

Dear Sir,

Thank you very much for your help.

I need to inquiry about some points:

1. Is it a 4th order Butterworth filter?
2. Is it filtering the low and high frequences in terms of 0.1-100 Hz?
3. What should I change if I have differnt time sampling for example 0.005, where to change the sampling time

Thank you very much!

[Mathieu NOE]

hello

I change the parameters for the Butterworth filter (N = 2 changed to 4)

same for the low and high cut off frequency (look for f_low and f_high ) in the attached m file

Sampling frequency : how do you get you data ? do you have a file ? format ? could you send it to me ?

If your sampling frequency is known , then you can specify it dirctly in your file

see the attaced file : I have created a dummy signal (random numbers) for example

Also keep in mind that filters cut off frequencies cannot be above the Nyquist frequency ( = half of the sampling frequency). In the practice , we usually set the sampling frequency at least as 2.56 times above the highest frequency for analysis (true also for filters cut off frequencies)

so if you are interested to filter out your signal above 100 Hz (and set your filter accordingly) , your recommended lowest sampling frequency is 256 Hz

there is no need for very high frequency sampling if you are only interested in the 100 Hz range; oversampling will just make your data file bigger and the slow down your processing time

all the best

Mathieu