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(comp342)[2007](s)midterm~cs_tcxaa^_10202.pdf
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Hong Kong University of Science and Technology
COMP342: Computer Music
Spring 2007
Midterm Examination
Student Name: key
Student ID:
Instructions:
1.
This is a closed-book, closed-notes examination.
2.
Answer all questions in the space provided.
3.
No partial marks will be given on subquestions.
Question
Score
1
/2
2
/8
3
/4
4
/8
5
/4
6
/6
7
/9
8
/4
9
/8
10
/4
11
/4
12
/15
13
/2
14
/10
15
/12
Total
/100
1) Acoustics [2 marks]
What is the relationship between harmonics and their fundamental frequency?
Answer: Harmonics are at integer multiples of the fundamental frequency.
2) Waveforms [8 marks]
What is heard if we use a sampling rate of 22050Hz to sample the following waveforms below?
If there is more than one possible answer, list them all. Give a brief explanation (in 1-2 sentences) for each.
a) A sinewave of 11025Hz (2 marks)
Answer: If all sample points fall on zero-crossings, no sound is heard. [1 mark]
Else there will be no aliasing, so a tone of 11025Hz is heard. [1 mark]
b) A sinewave of 18000Hz (2 marks)
Answer: A music tone of 22050 C 18000 = 4050Hz is heard since aliasing occurs.
c) A sinewave of 22050Hz (2 marks)
Answer: (Give marks for one answer with a reasonable explanation)
- Nothing can be heard, since a waveform of 0Hz is produced.
- If all sample points fall on zero-crossings, no sound is heard. (Else, if the sampler is programmed to produce a sine wave under any situation, then the simplest sine wave it can estimate is 11025Hz, hence a tone of 11025Hz is heard.)
d) A sinewave of 2Hz (2 marks)
Answer: Clicks of 2Hz are heard since waveforms below 20Hz do not sound like a tone.
3) Spectrum Analysis and PVan [4 marks]
a) Why is windowing necessary in time-varying Fourier analysis? (2 marks)
Answer:
[low-level answer:] To smooth samples at the window endpoints. It corrects for an inaccurate user-specified fundamental frequency, and avoids implied discontinuity.
Or:
[high-level answer:] To isolate each moment of the sound. The resulting spectra together form an amplitude envelope to capture the time-varying behavior.
b) Before we open a wave file with PVan, why do we have to estimate the fundamental frequency of the wave file? (2 marks)
Answer:
[low-level answer:] To do Fourier analysis, we first have to estimate its frequency in order to properly window the data.
Or:
[high-level answer:] Because fundamental frequency estimation is an open research problem and cannot be solved accurately automatically. 4) Additive Synthesis [8 marks]
Fix the errors in the code below so that it generates an additive synthesis tone with 5 harmonics. The amplitude of the 1st, 2nd, 3rd, 4th and 5th harmonics are 3400,