Assignment

• Objectives: Understand phase response and amplitude response.
• Understand the effect of group delays.
• Understand Linear constant-coefficient difference equations.
• Understand Inverse systems.
• Understand zero and pole plots
• Can use Matlab to create zero and pole plots.

1. Given a complex system transfer function H(w)=Re(H(w))+jlm(H(w)). How can you get its amplitude and phase response?

2. Suppose a system transfer function H(w) has a phase function of p(w), which is unwrapped. Explain how to find it's group delay.

3. What is the formula for group delay if a system has a single pole at p=reis?

4. Suppose a simple delay system is described by the difference equation y[n]=x[n-d]. Find its system transfer function. Find its phase response and group delay.

5. Given an LTI system described by the constant-coefficient difference equation: y[n]-0.6y[n-l]+0.08y[n-2)=x[n)-0.6x[n-1]. Find its system transfer function. Is this system stable? Causal?

6. Given the above LTI system: y[n]-0.6y(n-1]+0.08*-2]=x[n]-0.6x[n-1], what is the transfer function of its inverse system? Is this inverse system stable?

7. Given y[n]-0.6y[n-1j+0.08y[n-2]=x[n]-0.64n-1], list out its zeros and poles. Plot its zero and pole plot.

8. Given a system transfer function with a single pole at p = 0.6ej46, and a zero at the origin, find its system transfer function. Suppose the system sampling frequency is 8000}12, around which frequency the signal is the most amplified?

9. Given an LTI system y[n]-0.6y[n-11+0.08y[n-2)---x[n]-0.6x[n-1], explain how to represent its system transfer function equation in Matlab. Explain how to plot its zero-pole plot based on this representation.

10. In the following Matlab command: 11-freqz(b,a,-3*pi:6*pi/1000:3*pi), explain what are the meaning of the three input parameter? What is the dimension of the output vector H?

11. Explain how can you plot the magnitude and phase response in Matlab given a system transfer function.