Assignment: COMPUTATIONAL AND EXPERIMENTAL METHODS
Experimental Methods- Signal Filtering
Several sets of data have been generated which contain ~4000 data points, sampled at 100 Hz and are made up of the superposition of several sine waves at different frequencies and of different magnitude. You can find your specific file and damping ratio to use via the VLE. This should be used in a filter as discussed below. The data files can be downloaded from the assignments section.
After copying to your user area and unzipping the files, the appropriate file can be loaded into a Matlab program by entering
load filename
The data to be analyzed will be contained in a variable y and is of the form y = f(t)
1) Using Matlab, read in the data file and, for the first 100 data points, produce a graph of amplitude against time.
2) Fourier transform this data (noting that there are 4000 data points) and produce a power spectrum, clearly stating the units on each axis. Hence, for each sine wave determine the constants A and W in the equation y = A sin(Wt).
3) Manually design a second order digital filter, with the damping ratio given in the table, to attenuate the highest frequency component found as much as possible while changing the amplitude of the other waves as little as possible. Clearly justify any choice of filter parameters. Manually this filter using bilinear transformation.
4) Compare your filter with that given by the Matlab function ‘bilinear' for the same conditions. The syntax for this filter is
[n,d] =bilinear(num ,[ den1 den2 den3] ,sample _frequency )
Where num is the numerator of the second order filter and den1, den2 and den3 are the three terms in the denominator. The numerator and denominator frequencies should be in rad/sec while the sample frequency should be in Hz, to match the input data.
5) Using the Matlab function ‘filter', use the second order filter to remove the highest frequency component from the original signal. Produce a graph of amplitude against time and a periodogram (power spectrum) for the filtered data and original data.
6) Manually calculate the amplitude ratio of the two highest frequencies, i.e. the frequency that should have been removed and the next highest one that should have been ‘passed' by the filter) and compare the values with those suggested by the periodogram. Suggest reasons for any differences. What would have been the effect of (a) using a first order filter, and (b) changing the damping ratio.
You may find it helpful to work through the file MatlabExercise_FrequencyAnalysis_LowPassFiltering.pdf before attempting the assignment