The Fine Art of Analog Signal Sampling
Reducing quantization error and aliasing inaccuracy
in analog/digital conversion
The fine art of converting a continuous analog signal into
synthesized discrete digital information (a mouthful for A/D
conversion) involves two important accuracy considerations.
It also reflects the characteristics of the sampled analog
signal. These two considerations involve breaking down the
analog signal’s magnitude into discrete levels or steps
(quantization) and setting the data sampling rate based on
the signal’s maximum change frequency component (aliasing
and the Nyquist Frequency).
Quantization error
The amount of inaccuracy between the analog magnitude and
the converted discrete digital value is known as quantization
error (Fig.1 and Fig. 2). The number of discrete digital values
available to represent the continuous analog signal is set
by the number of bits contained in the digital converter.
The higher the bit level of the converter and the finer the
resolution of the digital values,
the more accurate the digital representation of the analog
signal will be.
Defining the acceptable resolution of your A/D conversion
sets the required bit-level for your digital converter. As
an example, for a 0 to 50V analog signal using an 8-bit A/D
converter, the voltage range will be divided into 256 discrete
levels. Each digital level will be equally spaced by 0.195v
(50v / 256 levels) starting from 0.0 (i.e. 0.000V = Digital
0, 0.195v = Digital 1, 0.390 = Digital 2, . . . 50.00v = Digital
255). Quantization error is 1/2 of the converter’s resolution.
In this example you need to decide if the resolution of
0.195v and quantization error of 0.098v provided by an 8-bit
converter is acceptable. Or, do you need the 0.0122v resolution
and 0.0061v quantization error of a 12-bit converter? Or even
the resolution of 0.00076v and 0.00038v quantization error
of a 16-bit converter?
Aliasing inaccuracy (sampling at too slow
a rate)
Analog signals contain frequency components that make up
the characteristics of the signal’s waveform. If we
sample the signal at too low of a rate, the finer detail of
the signal may be missed as it is converted to a digital equivalent.
Slow sampling tends to miss the high frequency components
while measuring only the signal’s lower frequency components
or inadvertently introducing nonexistent components. This
is called aliasing error (Fig. 3). The Nyquist Theorem helps
us understand the necessary sampling rate to minimize aliasing
error.
The Nyquist Theorem states that the sampling rate must be
at least twice the highest frequency component contained within
the analog signal. So, with a signal that contains 10Hz, 500Hz,
and 5KHz components, the minimum sampling rate is 2 X 5KHz
or 10KHz – 10,000 samples/sec. If the sampling rate
of the A/D converter is capable of it, it is even better to
sample at four to eight times the highest frequency. This
will ensure resolving the signal’s true waveform.
The fine art of Analog/Digital conversion all comes
down to two basic decisions:
What is the needed A/D amplitude resolution
and acceptable data accuracy level? Will 8-bit resolution
suffice, or do I need 16-bits of resolution for my range of
amplitude and accuracy?
The minimum sampling rate to truly capture the essence of
the analog signal is to know the highest
frequency component and sample at a minimum rate of at least
twice the highest frequency.
With these two factors under control, you are ready to go.
|
