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Distributed Arithmetic (DA) architecture yields better area, power and speed trade off balance. [1]. A 7th order band pass filter is designed, simulated and synthesized. Modified DA architecture for the implementation of higher order filter is also discussed. | Chapter 16 Practical Considerations All of the digital filter designs presented up until now have been based on infinite-precision mathematics. That is we have assumed that all of the signal samples filter coefficients and results of mathematical computations are represented exactly or with infinite precision. In most cases we have used the double data type in c to approximate such precision. In Think c for the Apple Macintosh the double data type has a 64-bit mantissa that provides approximately 19 decimal digits of precision. In Turbo c for the PC the double data type has a 52-bit mantissa that provides approximately 15 decimal digits of precision. For most practical situations either 15 or 19 digits of precision is a reasonable approximation to infinite precision. Furthermore the double type is a floating-point format and thus provides good dynamic range in addition to high precision. Although floating-point formats are used in some digital filters cost and speed considerations will often dictate the use of fixed-point formats having a relatively short word length. Such formats will force some precision to be lost in representations of the signal samples filter coefficients and computation results. A digital filter designed under the infinite-precision assumption will not perform up to design expectations if implemented with short-word-length fixed-point arithmetic. In many cases the degradations can be so severe as to make the filter unuseable. This chapter examines the various types of degradations caused by finite-precision implementations and explores what can be done to achieve acceptable filter performance in spite of the degradations. 16.1 Binary Representation of Numeric Values Fixed-point formats Binary fixed-point representation of numbers enjoys widespread use in digital signal processing applications where there is usually some control over the 299 300 Chapter Sixteen range of values that must be represented. Typically all of the coefficients h n for
