Optimal synthesis of second-order state-space structures for digital filters

Jackson, Leland B.; Lindgren, Allen G.; Kim, Young

doi:10.1109/tcs.1979.1084623

Cited by 157 publications

(48 citation statements)

References 13 publications

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“…The noise gain of the second-order state-space structure of [3] is approximately a constant function of the pole angle, having the value 17 dB when and 8 dB when It is concluded that when the pole angle is small, the transposed DFII delta realization outperforms the nine-coefficient statespace structure with respect to output roundoff noise.…”

Section: Comparison Of Structuresmentioning

confidence: 96%

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Delta operator realizations of direct-form IIR filters

Kauraniemi¹,

Laakso²,

Hartimo³

et al. 1998

IEEE Trans. Circuits Syst. II

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Abstract-The use of the delta operator in the realizations of digital filters has recently gained interest due to its good finite-word-length performance under fast sampling. We studied efficient direct form structures, and show that only some of them can be used in delta configurations, while others are evidently unstable. In this paper, we focus on the roundoff noise analysis. Of all the direct-form structures, the direct form II transposed (DFIIt) delta structure has the lowest quantization noise level at its output. This structure outperforms both the conventional direct-form (delay) structures, as well as the state-space structures for narrow-band low-pass filters with respect to output roundoff noise. Excellent roundoff noise performance is achieved at the cost of only a minor additional implementation complexity when compared with the corresponding delay realization. Complexity of a signal processor implementation of the DFIIt delta structure, which was found to be the most suitable delta structure for signal processors, is compared with those of the direct form and state-space delay structures. In addition, some hardware implementation aspects are discussed, including the minimization of the internal word length.Index Terms-Delta operator, direct-form structures, roundoff noise.

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Section: Comparison Of Structuresmentioning

confidence: 96%

“…State-space structures which minimize the output roundoff noise were studied in [1]- [3], and coefficient sensitivity minimizing networks were analyzed in [4] and [5]. An efficient method to reduce the effects due to signal quantizations is the concept of error feedback, sometimes called residue feedback, error spectrum shaping, or noise shaping [6]- [8].…”

mentioning

confidence: 99%

Delta operator realizations of direct-form IIR filters

Kauraniemi¹,

Laakso²,

Hartimo³

et al. 1998

IEEE Trans. Circuits Syst. II

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“…This condition, together with , is sufficient for (unscaled) optimality [3]. Note that the state matrix is equal to , so equality of its diagonal entries is met.…”

Section: Optimal Form Structurementioning

confidence: 98%

“…The elements on its principal diagonal are the power gains from the input to the states, and should be unity for a correctly scaled section. The scaled noise gain is then (3) where its makes no difference for the result if we calculate from the matrices and of the unscaled structure.…”

mentioning

confidence: 99%

Noise gain expressions for low noise second-order digital filter structures

Ritzerfeld

2005

IEEE Trans. Circuits Syst. II

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Abstract-The quantization noise of a fixed-point digital filter is commonly expressed in terms of its noise gain, i.e., the factor by which the noise power 2 12 of a single quantizer is amplified to the output of the filter. In this brief, first a closed-form expression for the optimal second-order noise gain in terms of the coefficients of the numerator and denominator polynomials of the transfer function is derived. It is then shown, by deriving a similar expression for its noise gain, that the second-order direct form structure has an arbitrarily larger noise gain the closer the filter poles are to the unit circle. The main result, however, is that the wave digital form and the normal form structures have noise gains which are only marginally larger than the minimum gain. For these forms, the expressions for their noise gain in terms of the transfer function are given as well. The importance of these forms lies in the fact that they use less multipliers than the optimal structure and that they are much easier to design: properly scaled forms are given requiring no design tools.Index Terms-Filter structures, quantization noise, noise gain, second-order modes, wave digital filters.

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“…Thus, by carefully choosing the final realization, it is possible to minimize the impact of finite word-length on the performance of the system. For example, structures particularly suitable to operate with poles close to the unit circle can be found in [13], [14], optimal state-space realizations of second-order filters having minimum roundoff noise are described in [15], [16], and procedures to get low sensitivity are presented in [17], etc. It is also possible to apply techniques based on genetic algorithms, to obtain robust second-order structures under finite word-length conditions [18], [19].…”

Section: Implementation Structuresmentioning

confidence: 99%

Polyphase FIR Networks Based on Frequency Sampling for Multirate DSP Applications

Cruz–Roldán

Campo

Godino-Llorente

et al. 2010

Circuits Syst Signal Process

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It is well known that the frequency sampling approach to the design of Finite Impulse Response digital filters allows recursive implementations which are computationally efficient when most of the frequency samples are integers, powers of 2 or nulls. The design and implementation of decimation (or interpolation) filters using this approach is studied herein. Firstly, a procedure is described which optimizes the tradeoff between the stopband energy and the deviation of the passband from the ideal filter.The search space is limited to a small number of samples (in the transition band), imposing the condition that the resulting filter have a large number of zeroes in the stopband. Secondly, three different structures to implement the decimation (or interpolation) filter are proposed. The implementation complexity, i.e. the number of multiplications and additions per input sample, are derived for each structure. The results shown that, without taking into account finite word-length effects, the most efficient implementation depends on the filter length to decimation (or interpolation) ratio.

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Optimal synthesis of second-order state-space structures for digital filters

Cited by 157 publications

References 13 publications

Delta operator realizations of direct-form IIR filters

Delta operator realizations of direct-form IIR filters

Noise gain expressions for low noise second-order digital filter structures

Polyphase FIR Networks Based on Frequency Sampling for Multirate DSP Applications

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