Sunspot Periodicity - Maple Help

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Sunspot Periodicity

Introduction

This application will find the periodicity of sunspots with two separate approaches:

• 

A frequency domain transformation of the data

• 

Using autocorrelation

 

Both approaches should yield the same result.

withSignalProcessing: withplots:

International Sunspot Data

The following data table contains mean international sunspot numbers from the year 1700 to present.

Data source: Solar Influences Data Analysis Center (SIDC), RWC Belgium, World Data Center for the Sunspot Index, Royal Observatory of Belgium, 1700-2013. Data available at: http://sidc.oma.be/html/sunspot.html

 

The first column contains the "Year", while the second column represents the "Annual Mean Sunspot Number".

DataReferenceDataSets:-Referencequandl,SIDC/SUNSPOTS_A

DataReferenceData setSunspot Numbers (Annual)Quandl SIDC/SUNSPOTS_Aup to 314 rows (annual), 1 column1700-12-31 - 2013-12-31

(2.1)

dataconvertDataReference, Matrix:

Plot the Data

SunspotNumberdata..,2:

ParseYearxStringTools:-ParseTime%Y-%m-%d,x:-year:

YearParseYear~data..,1:

pointplotseqYeari,SunspotNumberi,i=1..314,labels=Year,Wolf Number,labeldirections=horizontal,vertical,connect=true,title=Sunspot Data, titlefont=Arial,14,thickness=0, gridlines, size=800,golden

Periodicity via Fourier Transformation to the Frequency Domain

Now, calculate the period using a Fast Fourier Transform (FFT) of the first 28 data points:

fSunspots:=FFTSunspotNumber1..28:

Plot the power spectrum:

samplingRate:=1:

psSunspots:=PowerSpectrumfSunspots:

SignalPlotpsSunspots2..numelemspsSunspots2, samplerate=28,labels=Frequency (1/years),Power,title=Power Spectrum,titlefont=Arial,14, size=800,golden

Note the peak at a frequency of 0.09 years-1 . Try zooming in and using the point probe to confirm the value of this peak frequency.

 

The period is the reciprocal of the peak frequency.

period:=10.09

period11.11111111

(4.1)

Hence, the predicted periodicity is approximately 11 years.

 

Periodicity via Autocorrelation

aSunspotNumber:=AutoCorrelationSunspotNumber:

SignalPlotaSunspotNumber1..36,labels=Years,,title=Autocorrelation of Sunspot Data,titlefont=Arial,14,size=800,golden;

Here the first peak is at 11 years, indicating that the periodicity of sunspots is approximately 11 years. This confirms the period predicted by the Fourier Transform approach.


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