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+// Example 11.5
+// Design of a Lowpass Filter
+f_co=4000; // In Hertz
+R_L=200;
+R_s=50;
+// Using node equation in figure 11.10
+// (1/R_s+1/R_L+s*C)*V_out=(1/R_s)*V_s;
+// V_out/V_s=H(s)=(K*omega_co)/(s+omega_co)---equation (1)
+// Comparing equation (1) with low pass filter equation we get,
+K=(1/R_s)/(1/R_s+1/R_L);
+omega_co=2*%pi*f_co;
+C=1/(omega_co*(1/R_s+1/R_L));
+R_eq=(R_s*R_L)/(R_s+R_L);
+tau=R_eq*C;
+// design testing
+// Model for voice signal is 3kHz sinusoid with V_m=5V
+// so total input signal will become
+// v_s(t)=5*cos(omega1*t)+0.5*cos(omega2*t)
+omega1=2*%pi*3000;
+omega2=2*%pi*16000;
+// using equation for Low pass filter we get
+H_omega1=(K*omega_co)/(%i*omega1+omega_co);
+H_omega2=(K*omega_co)/(%i*omega2+omega_co);
+a_omega1=abs(H_omega1);
+theta1_r=atan(imag(H_omega1),real(H_omega1));
+a_omega2=abs(H_omega2);
+theta2_r=atan(imag(H_omega2),real(H_omega2));
+t=0:0.0001:0.01;
+v_out=a_omega1*5*cos(omega1*t+theta1_r)+a_omega2*0.5*cos(omega2*t+theta2_r);
+v_s=5*cos(omega1*t)+0.5*cos(omega2*t)
+plot(t,v_out,t,v_s,'-g')
+xlabel('t')
+ylabel('v_out(t)')
+title('Voltage Waveform')
+h1=legend(['v_out';'v_s'])
+disp("waveform Shows that whistle amplitude has been cut down to 3% of the voice signal at the input")