NOTE: THIS IS A PHYSIC PROBLEM USING MATHCAB

solve in mathcab only

This mathcab sheet includes examples that you can modifiy to complete the three assigned problems. Solve the problems by modifying various filter and signal parameters, and modify the plots by adding multiple curves, changing plot styles and formats, and if needed changing the plotting ranges. You should treat this problem set as a lab project and so in addition to completing the plots, include discussions of the meaning and significance of your results. One problems asks for you to include a derivation of the filter function used.

Example2. For Problem 2 below on highpass filtering Effect of lowpass filtering a square wave As a reminder, from above: N= 128 T = 64 w = 0.098 N The frequency of the sine wave using the FFT to represent the frequency response corresponds to the number of periods across the N samples T = We = 4wf = 8 1 G(w) = = w. = 1/RC or R/L The lesson writes it as shown on the right, but it is mre compact as written on the left. (Egn. on right is a non executable image.) Gw,w.) = We + jw 1 + jw wc Sfiltz = SGK,8) SfiltBk = Sk Gk,2) stest = IFFT(S) sfilt = IFFT(Sfilt) sfiltB = IFFT (SfiltB) Filtered harmonics of square wave (dB) Time response of square wave after filtering dB SE stesti The small amount of ringing is approximation error due to the FFT data not being calculated up to infinite frequency dB(G(k, 8) 204 sfilt oh dB Sfilt:) w sfilt stest is a test to show that the input square wave is identical to s that the problem started with - 3.01 ...S G - 40F ... Sfilt G(WC) -11 0 11 10 50 100 1 100 i k,k,k, 8 Problem 3. Redo Example 2 for bandpass filtering a square wave Show (as part of your writeup) how the function below can be derived from the voltage divider of the voltage across a capacitor in series with an inductor and resistor Plot and describe how the frequency response and filtered squarewave change as a function of Q and w. Investigate for at least from 0.3 to 5 and and w, from 0.5Wp to 10WF Plot several representative curves on a few plots (like for each value of Q at a specific frequency wo) I R2 jXL & w = 5.We = + VR + VL - + Q = 1.5 |