Digital Signal Processing Reference
In-Depth Information
to 96 dB. This only accounts for the effect of quantization noise: in
practice there are other effects which could also degrade SNR in
a system.
There is one last important point on decibels. This is a very
commonly used term in many areas of digital signal processing
subsystems. A decibel is simply a ratio, commonly of amplitude,
power or voltage, similar to percentage. But because of the
extremely high ratios commonly used (a billion is not
uncommon), it is convenient to express this logarithmically. The
logarithmic expression also allow chains of circuits, or signal
processing operations, each with its own ratio (say of output
power to input power), to simply be added up to find the final
ratio.
A common area of confusion is differentiating between signal
levels or amplitude (voltage if an analog circuit) and signal power.
Power measurements are virtual in the digital world, but can be
directly measured in analog circuits with which video systems
interface, such as the RF amplifiers and analog signal levels for
circuits
in head-end cable
systems, or
video satellite
transmission.
There are two definitions of dB commonly used:
dB
voltage
¼
dB
digital value
¼
20
log (voltage signal 1 / voltage
signal 2)
dB
power
¼
log (power signal 1 / power signal 2)
The designation of “signal 1” and “signal 2” depends on the
situation. For example, with an RF power amplifier (analog), the
dB of gain will be the 10 log (output power / input power). For
digital applications, the dB of SNR will be the 20 log (maximum
input signal / quantization noise signal level).
dB can refer tomany different ratios in video systemdesigns and
it is easy toget confusedabout whether touse amultiplicative factor
of 10 or 20, if the reasoning behind these numbers is unclear.
Voltage squared is proportional to power. If a given voltage is
doubled in a circuit, it requires four times as much power. This
goes back to a basic Ohm's law equation:
Power
10
Voltage
2
/ Resistance
In many analog circuits, signal power is used because that is
what the lab instruments work with, and while different systems
may use different resistance levels, power is universal (however,
50 ohm is the most common standard in most analog systems).
When voltage is squared, this needs to be taken into account in
the computation of logarithmic decibel relation. Remember, log
x
y
¼
y log x. Hence, the multiply factor of “2” is required for
voltage ratios, changing the “10” to a “20”.
¼
