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Lesson 5: More Formulae Basic Data Filtration

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Today's Lesson Filtering Data with Matlab Root Means Squared Butterworth Filters Basic Statistical Analysis of Data Mean, Mode, Median Standard Deviation Cross Correlation

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Root Means Squared When used with a sliding window, smoothes data. RMS = sqrt(sum(all x^2)/n)

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Using Root Means Squared

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RMS With a Sliding Window

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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.

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Different Filters

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Creating a Butterworth Filter

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Effect of Order on the Filter

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Rectification of Data Abs absolute value function

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Statistical Functions Mean, std, xcorr

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Programming Tips: Error Catching A 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.

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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);

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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);

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STATISTICS Chapter 2 and 11. 2.1 and 2.2: Review of Basic Statistics Topics covered today: Mean, Median, Mode 5 number summary and box plot Interquartile.

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