Synthesis Theory I: Assignment 2
Do all of the following problems.
1. ||Plot the the function y(t) = A cos(2 pi f t +
phi) using the values A = 0.5, f = 400 Hz, and
phi = 0.
2.|| What are the physical meanings of the symbols
"A", "f", and "phi" in
3.|| How do the physical properties of a sinusoid listed in problem 2 relate
to human hearing?
4.|| What is the minimum sampling frequency (theoretically) necessary
to correctly sample the sinusoid in problem 1? In practice a
filter guard band of at least 5% of the sampling frequency is necessary
to prevent aliasing. What is the minimum sampling frequency (practically)
necessary to sample the 400 Hz sinusoid?
5.|| Sample the sinusoid in problem 1 with a sampling frequency of 1000 Hz.
What is the sampling period in seconds? What is the period of the
400 Hz sinusoid in seconds? Give a table of the first 5 samples.
| time 1: || || sample 1: |
| time 2: || ||sample 2: |
| time 3: || || sample 3: |
| time 4: || ||sample 4: |
| time 5: || || sample 5: |
6.|| What is the mathematical definition of decibels for amplitude? for energy?
7.|| If a sound has twice the amplitude of the reference amplitude, what it
the dB value for the sound?
8.|| Consider the height of a person to be the reference height (amplitude) of
2 meters. What are the sizes of the following items on the dB scale.
- humans (2 meters)
- giraffe (7 meters)
- blue whale (30 meters)
- giant sequoia trees (100 meters)
- distance from Baltimore to Washington (56,000 meters)
- distance from Baltimore to New York (274,000 meters)
- distance from Baltimore to San Francisco (3,965,000 meters)
- diameter of the Earth (12,756,000 meters)
- diameter of the Sun (1,400,000,000 meters)
- distance from the Sun to the Earth (150,000,000,000 meters)
- distance from the Sun to Pluto (5,890,000,000,000 meters)
- diameter of the Milky Way galaxy (946,000,000,000,000,000,000 meters)
- diameter of the universe (230,000,000,000,000,000,000,000,000 meters)
- cat (0.3 meters)
- mouse (0.03 meters)
- bacteria (0.000,001 meters)
- virus (0.000,000,1 meters)
- atom of hydrogen (0.000,000,000,1 meters)
- neutron (0.000,000,000,000,006 meters)
9.|| What are the decimal values of the following hexadecimal numbers:
10.|| Convert the following binary or hexadecimal numbers into hex or binary form:
binary 1111 = hex
hex 80 = binary
binary 0000 = hex
hex ff = binary
hex a7 = binary
binary 1001,1000,0000,1111 = hex
11.|| If the range of hearing is characterized as being from 0 dB(SPL) to 120
dB(SPL), the dynamic range of hearing is 120 dB. (1) How many dB
of dynamic range is gained by each bit of data added to the resolution
of a soundfile? How many bits would each soundfile sample need in order
to match the dynamic range of hearing?
12.|| What is big-endian and little-endian? What is the decimal value of the
following two hexadecimal bytes if they are in (1) little endian form
(2) big endian form:
13.|| Record at least 10 words using your own voice and save them into
a computer soundfile. Make either one soundfile, or 10 separate
files for each word. These will be used for demos in the wavetable
part of class. Place the sounds on mambo.peabody.jhu.edu, e-mail
them to me, or give me a copy of the soundfiles on CDROM.