Lesson 5: More Formulae

Basic Data Filtration

Today's Lesson

Filtering Data with MatlabRoot Means SquaredButterworth Filters

Basic Statistical Analysis of DataMean, Mode, MedianStandard DeviationCross Correlation

    

Root Means Squared

• When used with a sliding window, smoothes data.

• RMS = sqrt(sum(all x^2)/n)

Using Root Means Squared

RMS With a Sliding Window

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.

Different Filters

Creating a Butterworth Filter

Effect of Order on the Filter

Rectification of Data

Abs absolute value function

Statistical Functions

Mean, std, xcorr

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.

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);

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);