Analysis of Sunspot Data: 1749 – 2013
Sunspots are temporary phenomena on the photosphere of the Sun that appear visibly as dark spots compared to surrounding regions, and are closely associated with regions of enhanced solar magnetic activity. The number of sunspots has been routinely counted since 1749 as a measure of solar activity, and has been correlated with a variety of effects on the Earth. More information can be found from Wikipedia:
This task requires you to analyse the monthly mean sunspot number data, identifying the key periodic component and designing, implementing and applying a suitable digital filter to isolate it.
You will need to pre-process the data, removing any linear trend and applying a suitable windowing function.
The monthly mean sunspot data sets that you need to work with are from 1749 - 2014 in the excel sheet called Monthly.
1.
Download and open the above workbook. Plot column C (the date) against column D (the mean sunspot number for that month), using an appropriate plot type.
Choose appropriate scales. Add a suitable title, and labels to each axis. If necessary, resize/rescale the plot so that the sunspot variations are clearly visible. [5 marks] .
2.Using a best-fit straight line, remove the mean and linear trend from the data in column D to create a new data set in column E.
[5 marks]
3. Design and apply a suitable window, tapering the data in column E smoothly to zero at each end. Store the windowed data in column F. [5 marks]
4. (a) Identify the period of the main oscillation visible in the data. State this period, in suitable units.
Using this figure as the filter cutoff period, together with the known sampling interval for the sunspot data, design a suitable low-pass filter that will remove higher frequencies by following these steps:
(b) Estimate a period at which you wish the filter to have -30dB attenuation.
(c) Write down the Nyquist frequency for this data set – the maximum frequency observable. Using this figure, convert the cutoff period from part (a) and the period estimated in (b) into dimensionless frequencies (on the 0 to Pi scale).
(d) Choose a filter type (Butterworth or Chebyshev) and determine the order of the filter necessary to achieve the constraint (a).
(e) Using programs 20 and 21 in dsp.exe, determine the necessary poles and zeros in the filter, and its overall gain factor.
(f) From the information in (e), determine the transfer function H(z) .
(g) Replacing H(z) with Y(z) / X(z) , cross multiply and take inverse z-transforms to find
the corresponding difference equation.
Write out your response to each stage above in your Word document, including
screenshots as necessary.
[60 marks]
5. In the spreadsheet, apply the difference equation to the windowed data in column F,
creating a filtered data set in column G.
[5 marks]
6. Plot this against time and compare it to the plot of the unfiltered data.
[5 marks]
7. Reinstate the mean and linear trend removed in stage 2, and plot this against the
original data set. Comment on the results.
[5 marks]
NB: Remember that dB is defined as follows: 10 20log dB G10G
Presentation
Credit will be awarded for work which is well presented, with each result clearly highlighted
in the Word document and with the Excel spreadsheet providing the detailed results