Analog Filters, Software-Based FILTERS

Analog Filters, Software-Based and
Owing to the way that analog and digital filters are physicallyimplemented, an analog filter is inherently more size-andpower-efficient, although more component-sensitive, than itsdigital counterpart - if it can be implemented in astraightforward manner. In general, as signal frequencyincreases, the disparity in efficiency increases.Characteristics of applications where digital filters are moresize and power efficient than analog filters are: linear phase,very high stop band attenuation, very low pass band ripple;the filter’s response must be programmable or adaptive; thefilter must manipulate phase and, very low shape factors (adigital filter’s shape factor is the ratio of the filter’s pass bandwidth plus the filter’s transition band width to the filter’s passband width).
General-purpose digital signal microprocessors, nowcommodity devices, are used in a broad range ofapplications and can implement moderately complex digitalfilters in the audio frequency range. Many standard signalprocessing algorithms, including digital filters, are availablein software packages from digital signal processor and thirdparty vendors. As a result, software development costs aretrivial when amortized over production quantities.The architectures of digital signal microprocessors areusually optimized to perform a sum-of-products calculationwith data from RAM or ROM. They are not optimized for anyspecific DSP function.
However, to get extended samplingrate performance from a digital filter requires hardwaredesigned to perform the intended filter function at thedesired sampling frequencies.For example, Intersil Corporation offers a family of standarddigital filter products with several others in development.Some hardware-specific digital filters can now sample atrates approaching 75 Megasamples Per Second (MSPS).Higher performance is possible for high volume applicationsby limiting the range of parameters. Standard filter productsstrike a balance between optimized filter architectures andprogrammability by offering a line of configurable filters. Thatis, these products are function-specific, with optimizedarchitectures and programmable parameters.

Frequency-Domain Versus Time Domain Thinking

Thinking about analog filters, most engineers arecomfortable in the time domain. For example, the operationof an RC lowpass filter can easily be envisioned as acapacitor charging and discharging through a resistor.
Likewise, it is easy to envision how a negative-feedbackactive filter uses phase shift as a function of frequency,which is a time domain operation.A digital filter is better conceptualized in the frequencydomain. The filter implementation simply performs aconvolution of the time domain impulse response and thesampled signal.
A filter is designed with a frequency domainimpulse response which is as close to the desired idealresponse as can be generated given the constraints of theimplementation. The frequency domain impulse response isthen transformed into a time domain impulse responsewhich is converted to the coefficients of the filter.

STRENGTH AND WEAKNESSES

Because an IIR filter uses both a feed-forward polynomialzeros as the roots) and a feedback polynomial (poles as theroots), it has a much sharper transition characteristic for agiven filter order. Like analog filters with poles, an IIR filterusually has nonlinear phase characteristics. Also, thefeedback loop makes IIR filters difficult to use in adaptivefilter applications.Due to its all zero structure, the FIR filter has a linear phaseresponse when the filter’s coefficients are symmetric, as isthe case in most standard filtering applications.
A FIR’simplementation noise characteristics are easy to model,especially if no intermediate truncation is used. In thiscommon implementation, the noise floor is at - 6.02 B + 6.02log2NdB where B is the number of actual bits used in thefilter’s coefficient quantization and N is again the filter order.This is why most Intersil filter ICs have more coefficient bitsthan data bits.An IIR filter’s poles may be close to or outside the unit circlein the Z plane.
This means an IIR filter may have stabilityproblems, especially after quantization is applied. An FIRfilter is always stable. FIR filters also allow development ofcomputationally efficient architectures in decimating orinterpolating applications, which will be described in moredetail later.

FILTER RESPONSE DESIGN METHODS

The total specification of the ideal filter includes the locationof passbands and stopbands, the minimum stopbandattenuation, the maximum passband ripple, the filter order,and perhaps the shape of the response in some of thespecified bands.Typically, there are three stages to the design of digital filterresponses for passband filters. First, the ideal filter responseis specified. Next, a floating point response is designed.Finally, the floating point coefficients are quantized to yield afixed point response.Creating a floating-point IIR filter response starts with aprototype analog filter. Then an s-domain to z-domaintransformation is used to generate a set of digital filtercoefficients.
Common methods of designing floating-pointFIR filter responses are windowing, frequency sampling, andoptimal. All are described in general digital signal processingtexts and are standard in most commercially available digitalfilter design software packages.Converting floating-point coefficients into fixed-pointcoefficients requires quantizing the coefficients andcalculating the frequency domain impulse response of thefilter or filter model to verify that the filter meets the requiredspecification.
If it does not, either the number of coefficientbits can be increased, the filter response can be redefinedand step two repeated, or the filter arithmetic can beredesigned, or a combination of these procedures can beperformed. When filter hardware is at a premium,sophisticated simulated annealing techniques can be usedfor both fixed-point FIR and IIR filters to produce the best setof filter coefficients, given a fixed filter order and coefficientwidth.