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Lesson 5: More Formulae Basic Data Filtration

Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

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Page 1: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Lesson 5: More Formulae

Basic Data Filtration

Page 2: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Today's Lesson

Filtering Data with MatlabRoot Means SquaredButterworth Filters

Basic Statistical Analysis of DataMean, Mode, MedianStandard DeviationCross Correlation

    

Page 3: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Root Means Squared

• When used with a sliding window, smoothes data.

• RMS = sqrt(sum(all x^2)/n)

Page 4: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Using Root Means Squared

Page 5: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

RMS With a Sliding Window

Page 6: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Filtering Data

Goal of removing unwanted frequencies from signal data.

Butterworth filters produce no ripple, but slowest roll-off.

Elliptical filters produce steepest roll-off, but ripples in the pass and stop band.

Typically, Butterworth Filters are the Filters of Choice.

Page 7: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Different Filters

Page 8: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Creating a Butterworth Filter

Page 9: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Effect of Order on the Filter

Page 10: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Rectification of Data

Abs absolute value function

Page 11: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Statistical Functions

Mean, std, xcorr

Page 12: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Programming Tips: Error CatchingA program's Achilles Heel is unexpected data:    Extra Data    Missing Data    Wrong Data Type

It is easy to protect your programs from these sorts of errors by adding data checking loops.

Page 13: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Example:  Array Length Check

%Imagine that for this function, we know that there %should be only two numbers in the input array.

function[sum] = addThemUp(summands)

    %If there aren't 2 numbers in the array, exit nicely.    if(length(summands) ~= 2)            disp('There weren't exactly 2 numbers in the input.')            return;    end

    sum = summands(1) + summands(2);

Page 14: Lesson 5: More Formulae Basic Data Filtration. Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis

Example:  Data Type Check%Now, let us add something to the previous function to %further ensure that it will work.

function[sum] = addThemUp(summands)

    %If there aren't 2 numbers in the array, exit nicely.    if(length(summands) ~= 2)            disp('There weren't exactly 2 numbers in the input.')            return;    end     %If one of the 2 "numbers" isn't a number, exit nicely.    if(~(isnumeric(summands))            disp('One of the summands was not a number.')             return;    end

    sum = summands(1) + summands(2);