1. (10 points) (a) Use MATLAB to design a first order Lou pass filter with cutoff frequency- 100. Sketch the magnitude and phase for w€ (-300,300). On the graph show the magnitude at -100 -300 10.1: 300; nun-[ 1: 5 of 7 freqs (num,den,v); subplot(2,1,1),plot (w.abe (H)) subplot(2,1,2), plot(v,angle(H)) Figure 3: Magnitude and phase response of a low pass filter with 100 (b) Use MATLAB to design a second order Low pass filter with cutoff frequency 100. Sketch the magnitude for wE (-300,300) on the same graph as the magnitude for the first order designed in part (1). Which filter is sharper? w-3000.1 deni- [ 300: 14 1: [1]-freqs (num1,den1,v); sun2-[ den2-[ [H2]-freqs (num2, den2,v); plot (w,abs (1),w, abe (H2)) 31 11 (c) Use the second order low pass filter for filtering an input signal z(t)= 2 sin(50)+0.5 cos(250). Sketch the signals at the input (f) and the output (f), what is the frequency of the output signal? nun2- den2- t 0 0.0001 0.5; subplot(2,1,1),plot(t,x) y-lain (num,den,x,t); subplot(2,1,2),plot(t, y) 좋아 01 02 03 04 05 06 07 08 09 " 62 ده 04 05 06 0.7 08 09 Figure 5: The input and output after filtering using second order low pass filter