A digital filter is only one part of a system composed of a digitizer (A/D), processing device (e.g. microprocessor) and algorithm. The digitizer has a profound effect on the filtering function via three primary characteristics: quantizing error, sample rate and bandwidth limiting. Quantizing error is simply the number of bits the A/D uses for quantization. Determining the required number of bits is usually governed by the system resolution requirements (i.e. a 2.4 mV change in the signal is required to be detectable). With regard to the digital filter, it is difficult to remove quantization noise without undue effort or a priori and fixed frequency characteristics of the signal and noise. Thus quantization size must be chosen to be compatible with the desired filter output SNR.
The sample rate of the A/D is a key parameter for a digital filters. The basis of setting the coefficients for almost all digital filters is an assumption of the sample rate. Changing the sample rate will directly scale the coefficients. A filter you thought filtered at 60Hz will not do so if the sample rate changes. This is a one to one relationship. Thus, you can determine the effects of varying sample rate by the ratio of change from the design specification frequency to the actual rate. The resulting filter frequency is scaled by the same ratio.
Jitter or short term variation of the sample frequency can create very undesirable effects on the filter performance. Simply think of it as the filter breakpoint frequencies shifting around in real time. This can be a significant problem for narrowband or sharp cutoff filters where the signal of interest lies very close if not within these filter bands.
The anti-alias filter is perhaps the most crucial addition to the input of the A/D and to the digital filter. Without an analog filter to perform this function, high frequency interference can show up in the digitized data as a low frequency signal. Those familiar with sampling theory will know this as frequency folding or aliasing. Once aliasing occurs, it is very difficult if not impossible to remove the high frequency components that folded back into the sample bandwidth. By adding an analog filter that limits the A/D input bandwidth to one half the sample rate, aliasing can be reduced or prevented. Most applications use a simple analog RC filter to perform this function. The reader should be aware that this filter does not roll off very quickly and thus large amplitude interference above the cutoff frequency can and will still enter the system and be folded back into the sampling bandwidth. Higher order analog filters are still required where this situation is possible to occur.
The processor chosen for the task plays an important role in a number of ways. The most obvious is the processor's math function capabilities. digital filters inherently are composed of repetitive multiplication and additional operations. More over, roundoff errors can accumulate quickly. Hence, most software applications utilize floating point variables to reduce roundoff error accumulation (some require double precision for high accuracy applications). Floating point multiplications generally consume large quantities of processor time unless a math coprocessor is present. This can prevent the processor from performing real-time processing if it interferes with maintaining a uniform sample rate. Thus processor speed and capability are important parameters in the implementation of a digital filter.
