数字信号处理代写：EECS152A-Digital-Signal-Processing-Final-Exam

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帮忙做数字信号处理的往届真题，用于复习。

Final Exam Fall 2020

EECS 152A: Digital Signal Processing

110 Minutes

  1. Consider a digital filter with the following difference equation:
    3y(n) = y(n-2) – 2 y(n-3) + 4x(n-1) – 5 x(n-3)
    a) Determine the system function _H_ ( _z_ )
    b) Draw the signal flow graph for the direct form I realization.
  2. a) What is the criteria for system function Ha(s) of an analog filter, for it to be stable?
    b) Assume that you would like to implement a 10th order digital filter and the quantizer that you are using, uses only 4 bits. If you have a choice between a direct form implementation and a cascade form implementation, which one will you pick? Why?
  3. Consider a system with the following input-output relationship
    𝑦𝑦(𝑛𝑛)= −0.5𝑦𝑦(𝑛𝑛− 1 )+𝑥𝑥(𝑛𝑛)
    Assume that we implement the system using 4 bits (one sign bit and three binary bits to represent the magnitude) and rounding up.
    a) Draw the output of the quantizer vs. the input of the quantizer. (You can skip middle parts of the graph if you can show the trend)
    b) Find the response of the system, y(n), for all values of n, to the input x(n) = ¾
    δ(n).
    c) What value does 1010 represent?
    d) What is limit cycle?
  4. a) Draw the impulse response of a type III linear phase filter which has a group delay of 3. You can choose any value for the coefficients that you want.
    b) What is the phase of this filter?
    c) Can we design a lowpass filter that is type III linear phase filter? Explain
  5. We would like to use impulse invariance mapping of an analog 1st order Butterworth
    filter to design a digital lowpass filter with at least 40 dB attenuation at 0.4π ≤ |ω| ≤ π.
    Assume T = 2.
    a) What is the main problem with impulse invariance mapping? How can it be avoided or minimized.
    b) What is the Ha(s) of the analog filter?
    c) What is the H(z) of the digital filter?
  1. We would like to design a 5 tap causal linear-phase FIR filter, approximating an ideal
    high pass filter with cutoff frequency of 𝜋𝜋 3 | using a Hanning window.
    Hanning Window: w(n) =^12 (1 – cos 𝑀𝑀−12𝜋𝜋𝜋𝜋 ) 0 ≤ n ≤ M-
    a) What is the group delay of this filter?
    b) What is H(z) of this filter?
    c) If we wanted to suppress the ripple in the stopband of H(z) further, what would you change in the design of the FIR filter?
    d) Draw the best implementation. Why is this the best implementation?