The basics of DSP for use in intelligent sensor applications: Part 3
Earlier in this series, we touched on one problem that can arise when sampling an analog signal, namely the problem of aliasing. There are three other issues with signal sampling to which we now turn our attention: digitization effects, finite register length effects, and oversampling.
So far, weve assumed that all of the signals were measuring are continuous analog values; i.e., our measurements are completely accurate. Even in the cases in which we have noise, the underlying assumption is that the measurement itself, for example the noisy sensor output voltage, is known precisely.
In reality, at least for a system that employs digital signal processing, thats not really true because the measured analog signals go through a process known as digitization that converts the analog signal to a corresponding numeric value that can be manipulated mathematically by a processor. Figure 2.16 below shows this process (signal value is sampled at the points shown).
|Figure 2.16. Signal Digitization Process Showing Four Successive Samples|
The issue that we face with digitization is that within any processing unit we have only a finite number of bits with which to represent the measured signal. For instance, lets assume that we want to sample a signal that varies between 0V and 5V.
If we try to represent the measurement with one bit, well have exactly two possible values (0 and 1) that we can use. Designating the measured signal voltage as VS we might choose to map the lower half of the signal range (0 ≥ VS < 2.5V) to 0 and to map the upper half (2.5V ≥ VS < 5V) to 1.
|Figure 2.17. Digitization Error Introduced by Rounding|
Unfortunately, thats pretty poor resolution! While we can obviously improve the resolution significantly by using more bits to represent our numeric values, we will always map a range of input values to a particular output value, which means that almost all measured signal values within that range will be in error (the lone exception being the signal value that corresponds exactly to the numeric value).
This digitization error can be viewed as a noise signal that is superimposed on the true value of the measured signal as shown in Figures 2.17 above and Figures 2.18 below.
|Figure 2.18. Digitization Error Introduced by Truncation|
Note that, depending upon whether we perform the digitization by rounding the measured value (as in Figure 2.17) or by truncating the measured value (as in Figure 2.18), we will essentially have either a triangular noise signal (rounding) or a sawtooth noise signal (truncation).
Although we can never completely eliminate the issue, we can reduce its significance by ensuring that we use a relatively large number of bits (say 16 to 32, depending on the application) to represent the numeric values in our algorithms.
For instance, if we use 16-bit values, we can represent our signals with an accuracy of 0.0015 % (assuming no other sources of digitization noise); using 32-bit values, that resolution improves to 2.3 108% (since there are 232 discrete levels).