Matlab problems

1. Design 3rd, 4th, and 5thorder Low Pass Filter and High Pass Filter with wc = 200 rad/sec. Check the magnitude response of individual filter with matlab’s bode function. Also, use input signal f(t)=7*cos(2*10*pi*t)+5*cos(2*50*pi*t)+10*cos(2*100*pi*t) to check the effectiveness of your filter. What happens when you increase the order? Use lsim and fft (shiftfft, too) functions in matlab with t (from 0 to 10 sec) and Sampling Frequency Fs = 1000Hz to plot the response in Frequency Domain. (You can use butter command in Matlab)

2. Design 4th and 6th order Band Pass Filter (For the pass range of frequency wn= [10 1000] ) and Band Reject Filter (For the reject range of frequency wn= [10 1000]). Use matlab to draw the magnitude and phase response. (You can use butter command in Matlab)