Poles and Zeros

Given a Butterworth lowpass filter with order n=4. What are the normalized poles of this filter?

• p1=-0.9239-j0.9239, p2=-0.9239+j0.9239, p3=-0.3827-j0.3827,p4=-0.3827+j0.3827
• p1=-0.9239-j0.3827, p2=-0.9239+j0.3827, p3=-0.3827-j0.9239,p4=-0.3827+j0.9239
• p1=0.9239-j0.3827, p2=0.9239+j0.3827, p3=0.3827-j0.9239,p4=0.3827+j0.9239
• p1=0.9239-j0.9239, p2=0.9239+j0.9239, p3=0.3827-j0.3827,p4=0.3827+j0.3827

Given a Chebyshev lowpass filter with n=7 with 0.5 dB of Ripple attenuation and 1rad/s is 3dB cutoff frequency. Which one is a pole of this filter?

• -0.24859
• -0.10570-j0.95497
• -j0.34205
• -0.24869-j0.43481

Given a Bessel lowpass filter with order n=4. Which one is a pole of this filter?

• -1
• 0.9877+j1.2476
• -1.3596-j0.4071
• 0.9877

Given a Cauer lowpass filter with 1 dB of ripple attenuation, 2 rad/s as stopband frequency and at least 30 dB of stopband attenuation. Which one is a pole of this filter?

• -0.1214786+j0.9891762
• -4.922113
• -j0.5400008
• -2.270068

Given an Inverse Chebyshev with order n=5, 3dB bandwidth and 40 dB of stopband attenuation. Which one is a zero of this filter?

• -j2.74925
• -1.27301
• 1.69913
• -0.25195+j0.98715

Which type of filter that is not all-poles filter?

• Bessel
• Butterworth
• Chebyshev-I
• Chebyshev-II

Which frequency at where the magnitude of transfer function has Rp (dB) gap from maximum magnitude?

• pass frequency
• stop frequency
• 3dB cut-off frequency
• none of them

Which type of filter that have poles located on the unit circle?

• Butterworth
• Bessel
• Chebyshev-I
• Chebyshev-II

If we have system function H(s)=(s-1)/(s+2). What is the value of pole?

• 2
• 1
• -2
• -1

To extract the output signal y(t)=1 from x(t)=1+cos(2*pi*1000*t)+sin(2*pi*10000*t). Which filter should be used?

• highpass filter
• bandpass filter
• lowpass filter
• bandstop filter