TSDT14 Signal Theory
Laborations autumn 2017
Hints regarding laborations
You will do several similar calculations, which typically end in graphs. It is therefore a good idea to start writing functions from the beginning, which you call with various arguments to achieve what you want to achieve. Especially, this holds for the power spectral density estimation.
Matlab has a traditional help function that you reach through the menu choice Help/MATLAB Help. There is amount of information that you can find there is overwhelming, and most of the information that is related to these laborations is under MATLAB and Signal Processing Toolbox.
Matlab also has a line-based help. To get help about a command, e.g. filter, type
in the interactive window.
MatLab (actually Signal Processing Toolbox) has its own idea of what is meant by normalized frequencies. The following is in the help text about the command butter:
BUTTER Butterworth digital and analog filter design. [B,A] = BUTTER(N,Wn) designs an Nth order lowpass digital Butterworth filter and returns the filter coefficients in length N+1 vectors B (numerator) and A (denominator). The coefficients are listed in descending powers of z. The cutoff frequency Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to half the sample rate.
There are similar formulations in the help texts of all other filter generating functions. Note that the normalized frequency 1 corresponds to half the sampling frequency, and not the whole sampling frequency as we are used to. Thus, if you want the coefficients of a Butterworth filter of degree 10, and normalized cut-off frequency 0.1 according to our definition, you get that with the command
Don't forget that you can control the appearance of plots by supplying extra arguments to the command plot. As an example, we create two vectors:
Then we plot y against x:
Now, we plot with circles:
Finally, we create a graph that resembles the way time-discrete signals are presented in many Signals & Systems course books, but with green sticks and blue circles:
plot(x,y,'bo') hold on for i=1:length(x) plot([x(i) x(i)],[0 y(i)],'g-') end plot([0 16],[0 0],'k-') hold off
Note that you can essentially achieve the same result with the command stem.
There are more ways to control the appearance of plots. See the help of the command plot.
When you have created a graph in Matlab, you might not be completely satisfied with how it is presented. You might want to adjust the thickness of lines, or correct the grading of the axes, or something else. Matlab has a special tool for that. First choose the graph you want to adjust. Then type
in the interactive window. This gives you a set of editing tools around the graph. When you are done, type
in the interactive window. The editing tools will then dissapear.
Last updated: 2017 08 22 12:08