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# Sign to Noise and Numeric Range issues for Direct Form I II IIR Filters on Modern Analog Devices and TI Digital Signa .

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Signal to Noise and Numeric Range issues for Direct Form I & II IIR Filters on Modern Analog Devices and TI Digital Signal Processors. Presented at the 2004 comp.dsp conference Mark Allie Consulting LLC. Main Topics.
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﻿Flag to Noise and Numeric Range issues for Direct Form I & II IIR Filters on Modern Analog Devices and TI Digital Signal Processors Presented at the 2004 comp.dsp meeting Mark Allie Consulting LLC. Check Allie comp.dsp 2004

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Main Topics Filter setups Direct Form I and II and the transposes are researched. This presentation contains a synopsis of the issues of flag to clamor and numeric scope of Direct Form IIR sifting. Outline criteria joined with sensible dsp decisions are introduced. Stamp Allie comp.dsp 2004

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Direct Form I, II and Transposes Filter Assumptions. Solidarity increase second request channel areas (biquads) are utilized. The exchange capacity of the biquad is given in conditions 1 & 2. The recursive coefficients are scaled to yield a 0 = 1. The channels are executed with all terms being included. 1 2 Mark Allie comp.dsp 2004

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Filter Forms Mark Allie comp.dsp 2004

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Matlab Design Example Because all items are summed the Matlab created recursive coefficients a 1 and a 2 must be discredited for use in the channel. For instance a Butterworth second request low pass channel with a cutoff recurrence of 0.01 * Fs has the coefficients: b 0 = 0.00094469184384 b 1 = 0.00188938368768 b 2 = 0.00094469184384 a 0 = 1.00000000000000 a 1 = - 1.91119706742607 utilize - a1 or 1.91119706742607 a 2 = 0.91497583480143 utilize - a2 or - 0.91497583480143 Mark Allie comp.dsp 2004

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Topics of Interest Overflow in perfect and genuine channels. Clamor issues. Clamor Compensation issues. Stamp Allie comp.dsp 2004

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Two Types of Overflow The last result floods. Halfway results flood. Flood of the outcome. Solidarity pick up channels can have yields that are more noteworthy than ±1 with a limited info. Stamp Allie comp.dsp 2004

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Ideal Frequency Response Mark Allie comp.dsp 2004

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Ideal Time Response Mark Allie comp.dsp 2004

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Internal Overflow with Fixed Point Math Modulo math is your companion. Modulo math is the default when not in immersion mode. Jackson\'s Rule: Any number of increases and additionally subtractions may happen. Moderate results and operands may fall into any modulo. For whatever length of time that the last result is made to fall into the main modulo by outline, it will be representable in two\'s supplement at the picked wordlength, and a substantial result. When flood recognition is connected to the outcome the right sign will be reflected in the soaked esteem. Check Allie comp.dsp 2004

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Noise Issues Noise is created by truncating high determination comes about. The clamor produced by truncation frequently takes after the range of the flag being separated. The produced commotion is most destructive when it re-courses through the recursive coefficients. Constrain corresponded truncation commotion to be arbitrary (white) by utilizing dither. In the event that the truncation procedure is deterministic then amendment can be connected to the channel. Settled point truncation is deterministic. Skimming point truncation is not deterministic. Stamp Allie comp.dsp 2004

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Fixed Point Truncation Mark Allie comp.dsp 2004

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Floating Point Truncation The information word in a gliding point processor is made out of a type and a mantissa. The quantity of bits used to speak to a mantissa is not straightforwardly diminished. The quantity of bits used to speak to one mantissa is generally in a roundabout way decreased when two numbers are included. This happens in light of the fact that the types of drifting point numbers must be equivalent to include them. There is no backhanded truncation when the types are as of now equivalent. The quantity of bits lost is dependant on the proportion of the 2 numbers being included. Check Allie comp.dsp 2004

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Floating Point Truncation For instance: When adding 1 to 1/256, 7 bits are truncated on account of moving when the types are coordinated. The truncation connected with skimming point expansion is not deterministic on account of Direct Form IIR channels. The quantity of bits truncated can be diverse for every expansion. The quantity of bits truncated relies on upon the coefficients and info flag measurements. Truncation mistakes can not be redressed. They typically should be acknowledged! In the event that the recursive items can be kept bigger than the immediate items then the recursive information way won\'t be truncated in particular. Check Allie comp.dsp 2004

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Noise pay Fixed point remuneration is expert through a blunder criticism flag. What is the mistake signal? e(n) = y(n) – y t (n). Skimming point remuneration can not be performed. So how terrible is this issue? Stamp Allie comp.dsp 2004

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How is the mistake term created? Stamp Allie comp.dsp 2004

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Direct Form Implementation Analysis Overload contemplations. Input scaling. Modulo math. Commotion era contemplations. Truncation commotion. Terms influenced. Stamp Allie comp.dsp 2004

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Mark Allie comp.dsp 2004

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Floating Point Truncation Analysis Mark Allie comp.dsp 2004

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Floating Point Truncation Analysis Example Mark Allie comp.dsp 2004

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Floating Point Truncation Analysis Example Mark Allie comp.dsp 2004

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Mark Allie comp.dsp 2004

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Mark Allie comp.dsp 2004

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Tabulated Results + Good Attribute + Qualified Good Attribute - Poor Attribute Mark Allie comp.dsp 2004

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Error Compensation Fixed Point Only. Coordinate Forms with 1 mistake term. Endeavor to right commotion by bolstering back the mistake flag. Assess DFI in view of Dottorro and Wilson. Stamp Allie comp.dsp 2004

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Error Compensation Mark Allie comp.dsp 2004

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Trivial Noise Shaping with the Error Term Mark Allie comp.dsp 2004

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Optimal Noise Shaping with the Error Term Mark Allie comp.dsp 2004

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2N Word Equivalent to 2 nd Order Error Compensated Filter. Stamp Allie comp.dsp 2004

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Is This Good News? Yes DFI and DFIIT both work. A processor with 32 bit whole number local word measure abilities needn\'t bother with truncation blunder pay. Some cutting edge coasting point processors can do this reasonably and quick. Some present day altered point processors can do this reasonably and all the more gradually. Check Allie comp.dsp 2004

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Floating Point? All DF IIR channels can work. Convoluted investigation and numbers to be added assessment. Gliding point processors with augmented exactness results may function admirably. Simple gadgets has processors with 32 bit mantissa capacities. Altered point handling at 32 bits a beyond any doubt wager. Stamp Allie comp.dsp 2004

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References J. Dattorro, "The Implementation of Recursive Digital Filters for High Fidelity Audio," J. Sound Eng. Soc., vol 36, pp 851-878 (1988 Nov) R. Wilson, "Channel Topologies," J. Sound Eng. Soc., vol 41, pp 667-678 (1993 Sept) S.P. Lipshitz, R.A. Wannamaker and J. Vanderkooy, "Quantization and Dither: A Theoretical Study," J. Sound Eng. Soc., vol 40, pp355-375 (1992 May) Mark Allie comp.dsp 2004

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