Resample and Filter a Nonuniformly Sampled Signal

A person recorded their weight in pounds during the leap year 2012. The person did not record their weight every day, so the data are nonuniform. Use theSignal Analyzerapp to preprocess and study the recorded weight. The app enables you to fill in the missing data points by interpolating the signal to a uniform grid. (This procedure gives the best results if the signal has only small gaps.)

Load the data and convert the measurements to kilograms. The data file has the missing readings set toNaN. There are 27 data points missing, most of them during a two-week stretch in August.

wt = datetime(2012,1,1:366)'; loadweight2012.datwgt = weight2012(:,2)/2.20462; validpoints = ~isnan(wgt); missing = wt(~validpoints); missing(15:26)

ans =12x1 datetime09-Aug-2012 10-Aug-2012 11-Aug-2012 12-Aug-2012 15-Aug-2012 16-Aug-2012 17-Aug-2012 18-Aug-2012 19-Aug-2012 20-Aug-2012 22-Aug-2012 23-Aug-2012

Store the data in a MATLAB® timetable. Remove the missing points. Remove the DC value to concentrate on fluctuations. Convert the time information to adurationarray by subtracting the first time point. For more details, seeData Types Supported by Signal Analyzer.

wgt = wgt(validpoints); wgt = wgt - mean(wgt); wt = wt(validpoints); wt = wt - wt(1); wg = timetable(wt,wgt);

OpenSignal Analyzerand drag the timetable to a display. On theDisplaytab, clickSpectrumto open a spectrum view. On theTimetab, selectShow Markers. Zoom into the missing stretch by setting theTime Limitsto200and250days.

Right-click the signal in the Signal table and selectDuplicate. Rename the copy asPreprocessedby right-clicking the signal in the Signal table and selectingRename. Select the preprocessed signal in the Signal table and, on the分析仪tab, clickPreprocess. In theFunctionsgallery, selectResample. In theFunction Parameterspanel that appears, specify these parameters:

ClickApplyand then clickAccept Allto save the results and exit the preprocessing mode. Overlay the resampled signal on the display by selecting the check box next to its name.

Zoom out to reveal the data for the whole year. On theSpectrumtab, set the leakage to the maximum value. The spectra of the original and resampled signals agree well for most frequencies. The spectrum shows two noticeable peaks, one at around 0.14 cycles/day and the other at very low frequencies. To locate the peaks better, on theDisplaytab, clickData Cursorsand selectTwo. Place the cursors on the peaks. Hover over the frequency field of each cursor to get a more precise value of its location.

Remove the cursors by clickingData Cursors. Remove the original signal from the display. Filter thePreprocessedsignal to remove the effects of the cycles. With the preprocessed signal selected in the Signal Table, on the分析仪tab, clickPreprocess. Inside the preprocessing mode:

Inspect the results and clickAccept All. Plot both signals in the display.

The preprocessed signal shows less fluctuation than the original. The shape of the signal suggests the person's weight varies less in the summer months than in winter, but that may be an artifact of the resampling. Click the icon on theInfocolumn in the Signal table entry for thePreprocessedsignal to see the preprocessing steps performed on it.

To see a full summary of the preprocessing steps, including all the settings you chose, clickGenerate Functionon the分析仪tab. The generated function appears in the MATLAB® Editor.

function[y,ty] = preprocess(x,tx)% Preprocess input x% This function expects an input vector x and a vector of time values% tx. tx is a numeric vector in units of seconds.% Follow the timetable documentation (type 'doc timetable' in% command line) to learn how to index into a table variable and its time% values so that you can pass them into this function.% Generated by MATLAB(R) 9.13 and Signal Processing Toolbox 9.0.% Generated on: 03-Jan-2022 15:47:27targetSampleRate = 1.1574074074074073e-05; [y,ty] = resample(x,tx,targetSampleRate,“pchip”); Fs = 1/mean(diff(ty));% Average sample ratey = highpass(y,5.787e-07,Fs,'Steepnes',0.85,'StopbandAttenuation',60); y = bandstop(y,[1.5625e-06 1.73611111111111e-06],Fs,'Steepness',0.85,'StopbandAttenuation',60);end

See Also

Apps

• Signal Analyzer

Functions

• bandstop|highpass|resample

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More About

• Using Signal Analyzer App
• Edit Sample Rate and Other Time Information
• Data Types Supported by Signal Analyzer
• 在信号分析仪谱计算
• Persistence Spectrum in Signal Analyzer
• Spectrogram Computation in Signal Analyzer
• Scalogram Computation in Signal Analyzer
• Keyboard Shortcuts for Signal Analyzer
• Signal Analyzer Tips and Limitations