The purpose of this exercise is to give you some practice with the
variables involved in storing physical-world stimuli as digital
information. These variables include transducers,
analog/digital and digital/analog conversion, quantization, and
encoding.
- Transducer
- A device that converts energy from one form to another. For
example, a microphone is a transducer that converts sound waves in
the air into voltages that are proportional to the sound pressure
level of the sound waves. The voltage that comes from a microphone
is called an analog signal because its level continuously
varies as a direct analog to the intensity of the sound pressure
level strking the microphone.
Similarly, a loudspeaker or earphone is a transducer that converts
analog voltages into sound waves.
- Analog to Digital (A/D) Converter
- An electronic device that converts continuously varying
voltages on a wire (such as the output of a microphone) into binary
numbers.
(This diagram comes from The
Techweb Encyclopedia.)
The exact format of the binary information that comes out of an a/d
converter differs from device to device. For now, think as the a/d
converter as a black box with one wire that brings the analog
voltage into it and with n wires coming out of it, which
continuously carry voltages representing binary ones and zeros.
The converter discriminates among 2n voltage
levels on the input wires, and always outputs the appropriate
n-bit number representing the present input voltage.
For Example: Assume an A/D converter is designed to handle
analog voltages that vary between -1.0 and +1.0 volts and that
it has two wires for the binary outputs. This means that it would
differentiate among four different input voltage levels as
follows:
| Analog voltage in
| Binary number out
|
| -1.0 to -0.5
| 0 0
|
| -0.5 to 0.0
| 0 1
|
| 0.0 to +0.5
| 1 0
|
| +0.5 to +1.0
| 1 1
|
Although both the input and outputs of an A/D converter are
electrical voltages, the input voltage varies continuously in time,
whereas the voltages of the output wires always have just one of
two different values, one of which represents a binary zero and the
other of which represents a binary one.
- D/A Converter
- A digital to analog converter, as its name implies, converts
binary numbers into analog voltages that are proportional to the
magnitude of the binary number at its input. Note that a D/A
converter doesn't generate a continuously varying voltage; it
generates one of 2n voltages, depending on the
value of the n-bit binary number input to it.
In this diagram, the waveform on the right is only a crude
approximation of the original analog signal, on the left. This
exercise deals with the parameters that affect how well the waveform
coming out of the D/A converter approximates the one going into the
A/D converter.
- Quantization
- The term quanization refers to the use of discrete values to
represent continuous variables. In this exercise, the two
variables are the two axes of an analog sound wave. The X axis is
time, and the Y axis is voltage. Both of these axes must be
divided into discrete values in order to store the analog signal in
digital form.
The time axis is divided by a process called sampling: The
output of the A/D converter is recorded at periodic intervals. The
time between samples is called the sampling interval, and its
reciprocal (the number of samples per second) is called the
sampling frequency or rate. The higher the sampling rate, the
finer-grained the quantization, and the more accurately temporal
changes in the input signal can be recorded.
The granularity of the voltage axis depends on the number of bits
that the A/D converter uses to encode voltages. In the example
given above, the A/D converter had two output wires, giving
22 = 4 voltage ranges for the quantization
granularity. The more bits output by the A/D converter, the
smaller the quantization granularity, and the more accurately the
signal's intensity can be approximated.
- Encoding
- In the case we are considering, encoding refers to how binary
numbers are assigned to analog voltage ranges, a process performed
by the A/D converter. Assume that the total possible range of input
voltages is divided into 2n equal-sized intervals,
and assume that the lowest interval maps to a value of zero, the
highest interval maps to the value 2n-1, and
that intermediate intervals map to corresponding intermediate
values. The table above is an example of this type of encoding.
Construct the table for one complete cycle of the sine wave. You can
write a program or a spreadsheet to generate the tables, if you
like.
Draw a diagram showing the encoded waveform (like the right side of the
diagram above) for each row of the table. Be sure to label both the X
and Y axes to show the scale for each graph. You may generate these
diagrams by hand on graph paper, using a spreadsheet, or by writing a
Java program to draw the graphs.