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(ELEC360)final01f.pdf
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Hong Kong University of Science and Technology Department of Electrical & Electronic Engineering
ELEC 360: Digital Media and Multimedia Applications
Fall 2001 Mansun Chan
Final (December 21, 2001)


Name: ____________________ E-mail: ____________________ I.D. Number: ____________________ Signature: ____________________
Open Books, Open Notes, Open Almost Anything

Treat each sub-part of the problem to be independent on each other
unless otherwise specified.
Use common sense to interpret the questions, or ask if you are not sure


(1) (21%) Audio Sampling and Manipulation
The electrical representation of an audio signal played by a musical instrument is in the frequency and time domain is shown below in Fig. 1:
Fig. 1(a) Fig. 1(b)
a) Answer the following questions based on the above audio signal:
i) What is the overall frequency (pitch) a listener will hear with the above signal?

ii) What is the value of the period (T) of the signal?
iii) A single sine wave is constructed to give a pitch of one octive higher than the give signal. Sketch the frequency and time domain representation of the sine wave.
amplitude

amplitude 2T 3T
timeT



f
500 1000 1500 2000

(Hz)

iv) Suppose a DC offset of 1V is added to the system signal in Fig. 1, sketch the approximate waveform of the resulting signal.
amplitude

amplitude 2T 3T
timeT



f
500 1000 1500 2000

(Hz)

b) The initial signal in problem 1(a) is input to the following system for digitization and 8-bit quantization is performed in the A/D converter. The system is a Nyquist rate system so that all signal in the figure given for part (1a) can be recovered.
TS
Low-pass filter Sample & hold

i) If the entire signal have to be recovered, what is the minimum cutoff frequenct (fC) of the low pass filter?
ii) What is the period (TS) of the Sample and Hold Circuit?
iii) What is the quantization interval of the above system?
iv) What is the range of the qualtization error?
v) What is the signal-to-noise ratio achievable by the system?
c) Suppose a signal is sampled with the system given above with sampling frequency of 400Hz and the following sample sequence is obtained. {124, -82, 123, -55, -29 }. If echo is going to be added to the system, according to the system below, what is the output? If you have to do rounding, round to the low integer (round down). Also note that 8-bit samples only have numerical range from C128 to +127.


d) For the echo system in part 1(c), clipping is actually happening. To avoid clipping, the decay value is reduced. What is the maximum value of the decay possible without clipping.
(2) (19%) Image representation a) Given the CIE color charge with the RGB and White color marked on the diagram
i) On the given diagram, locate the color obtained
by 30% red and 70% green with a x symbol



ii) On the given diagram, locate the color obtained by 20%