Digitalisation of analogue signals
Before the digitalision of an analogue signal can be done two important choises
must be made:
1. Sample Frequency
According to Nyquist's theorem the Sample Frequency fs must be
higher than twice the highest frequency that exists in the analogue signal
fh.
Nyquist: fs > 2 . fh
Example:
- the highest frequency in audio is supposed to be 20 kHz,
- the Sample Frequency must be higher than 40 kHz.
Practically it is choosen 20% to 10% higher, so in this case 48 kHz or 44,1 kHz.
This gives a stream of 48 000 or 44 100 digital numbers per second.
Caution!
Before these analogue signals are converted into a stream of digital numbers no
frequencies higher than, in this case, 20 kHz are allowed to be present in the
analogue signal. This can be assured by passing it through a Low-Pass Filter.
The smaller the difference between fs and the Nyquist-frequency, the
steeper and more complicated, because more inductors and more capacitors, and
more expensive the low-pass filter will be.
2. Number of bits per digital number (quantisation)
The number of bits per digital number defines the number of different levels
that the digital number can represent. Keep in your mind that 8 bits represent
256 levels or steps. So:
8 bits = 256 steps,
9 bits = 512 steps,
10 bits = 1024 steps,
.......................
16 bits = 65 536 steps.
The number of steps defines the precision of the digitalisation, because each
sample has to be rounded to the nearest available step size. It is depending of
the application how many steps are needed to describe the analogue wave form
precisely enough. For hifi sound 16 bits are needed, 32767 steps positive and
32768 steps negative (and zero of course). For (digital) video 8 bits, 256
steps, are sufficient.
Remind that the rounding to steps introduces rounding errors in the digitised
signal, which is audible (sound) or visible in the analogue final result. This
is called Quantisation-Noise and it is always present after the process of
digitalisation. This is the reason that the number of steps, so the number of
bits, is choosen large enough to make the quantisation noise just unaudible or
unvisible.
The bit-stream
The number of bits per second in the data stream is the result of both choises.
Example:
- For the CD a sample-frequency has been choosen of 44,1 kHz = 44 100 Hz,
- to make the quantisation noise unaudible 16 bits per digital number are needed,
- so there are 44 100 . 16 bits per second in the data stream.
- However a CD is in stereo, there is a stream for left and a stream for right,
- so the total bit-stream is 2 . 44 100 . 16 = 1 411 200 b/s or 1,41 Mb/s.
Storage
The size of digital signals stored onto disc or in memory normally is indicated in
megabytes (MB) or gigabytes (GB).
Way of writing:
When written in full always write lower case: megabit, gigabyte.
Abrieviated: k=kilo, M=mega, G=giga, b=bit, B=byte.
Not everybody is doing this that carefully.
Be aware when counting large numbers of bytes:
A kilobyte most of the time is 1024 bytes, but it could also be 1000 bytes.
To indicate the difference usually KB is written for 1024 and kB for 1000 bytes.
This use can't be continued for:
a megabyte (MB) is 10242 = 1 048 576 bytes, or
a gigabyte (GB) is 10243 = 1 073 741 824 bytes.
So sometimes a MB is simply 106 bytes and a GB 109 bytes.
Expect these things!
CD-sound is using 1 411 200 b/s = 176 400 B/s;
so for a minute (60 sec.) 10 584 000 B or almost 10 MB.