Filters, Stability, and plots

Notice: for this lecture (as on almost every Wednesday, except during project presentation weeks), we met in computer lab SEL 2249F.

We started this lecture with an example of a linear recursion which models a chemical reaction to purify an uranium hexafluoride concentration. Since the parameters are not specified numerically, Maple is the ideal tool to find the symbolic solution:

• hypertext version of the worksheet
• download the worksheet

Filters

The response from a sinusoidal signal passing through a linear filter is again a sinusoidal signal, but often with different amplitude and frequency. The change in amplitude is called the gain, change in frequency is called phase shift.

Getting the polar plots in Maple is really very easy:

• hypertext version of the worksheet
• download the worksheet

Plots with MATLAB

The MATLAB scripts in the book can all be downloaded at once from the mathworks, selecting "Companion Software for Books".

The MATLAB scripts to make the plots in this chapter are made available below:

• s3fig3.m Figure 3.3: Polar plot of the filter (3.34)
• s3fig4a.m Figure 3.4: Bode plots for averaging filter (3.34)
• s3fig4b.m Figure 3.4: Bode plots for averaging filter (3.34)
• s3fig5.m Figure 3.5: Gain plot in decibels for (3.34)
• s3fig6a.m Figure 3.6: Bode plots for the crude notch filter (3.36)
• s3fig6b.m Figure 3.6: Bode plots for the crude notch filter (3.36)
• s3fig7a.m Figure 3.7: Bode plots for the notch filter (3.37)
• s3fig7b.m Figure 3.7: Bode plots for the notch filter (3.37)
• s3fig7c.m Figure 3.7: Bode plots for the notch filter (3.37)
• s3fig8a.m Figure 3.8: Bode plots of filter (3.34) out to 1KHz
• s3fig8b.m Figure 3.8: Bode plots of filter (3.34) out to 1KHz