# Digital electronic（Including extra credits）

1. (TCO 1) How would the pass band and stop band frequency magnitude response of an ideal low pass filter be described? (Points : 10)

Question 2.2. (TCO 3) The cut-off frequency of a filter occurs where the gain is 0.707 of its maximum value. What is another value for this gain? (Points : 10)

Question 3.3. (TCO 6) Why is pre-warping an important process that should be done prior to performing a bilinear transformation on an analog filter? (Points : 10)

Question 4.4. (TCO 2) What is the purpose of an anti-aliasing filter? (Points : 10)

Question 5.5. (TCO 4) What is definition of the transition width of a windowed, impulse response low pass FIR filter? (Points : 10)

Question 6.6. (TCO 4) You are to select a window function to limit the number of samples of an infinite impulse response and the filter specifications are the same, regardless of which window function you select. If you are given the option of using either a Hamming or a Hanning window function, which window function would you select and why if your primary concern was execution speed and the required amount of memory in a real-time? (Points : 20)

Question 7.7. (TCO 5) If N = 75, find the value of the Hamming window coefficient for n = -5. (Points : 20)

Question 8.8. (TCO 5) Given a sampling frequency of 48 kHz and a pass band edge frequency of 10 kHz for a low pass filter design using a windowed impulse response method, what is the value of h1[0]? (Points : 20)

Question 9.9. (TCO 6) For a low pass Butterworth filter, given a prewarped stop band edge frequency of 24621.468 radians/second and a prewarped pass band edge frequency of 2599.358 radians/second, if the gain at the edge of the stop band is -60 dB, calculate the filter order, n, required to meet these specifications. (Points : 20)

Question 10.10. (TCO 2) Given an analog signal with a maximum positive voltage of 3.0 volts and an 10-bit analog to digital converter, what is the resolution of the quantized signal? (Points : 20)

Question 11.11. (TCO 7) For a low pass Chebyshev Type I with a pass band edge gain = -2 dB and a stop band edge gain = -40 dB, find the linear gain at the edge of the stop band. (Points : 20)

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