Delta operator realizations of IIR filters have received a lot of interest due to their good finite-wordlength properties. We present a detailed analysis of the computationally efficient transposed direct form II delta structure, which is also known to have excellent roundoff noise performance under fast sampling. The focus is on the roundoff noise minimization in fixed-point implementations. The free /spl Delta/ parameter in the delta operator is optimized with respect to the output roundoff noise within the scaling constraints. Moreover, the required internal wordlength to obtain a prespecified noise performance is derived.

A criterion for the absence of zero-input limit cycles in recursive digital filter structures that can be implemented with a single quantizer in the recursive loop is presented. The criterion can be applied with a rounding or with a magnitude truncation quantizer and accounts for the use of error feedback as well. Additionally, a criterion for the elimination of constant-input limit cycles is formulated. The criteria are applied to several well-known filter structures. Since most of the structures have previously been analyzed in a multiquantizer implementation only, new results on their stability properties in the single-quantizer configuration are obtained.>

The authors propose the use of error feedback for roundoff noise reduction in cascade-form recursive digital filters employing floating-point arithmetic. The floating-point error feedback has a similar mechanism to the fixed-point error feedback. However, the optimal error feedback solution (in the sense of minimum mean-square error) for the floating-point case is different from the corresponding fixed-point case. The formulated optimal feedback coefficients are shown to be independent of the section of ordering and zero-pole pairing, which does not hold in the fixed-point case. Finally, a suboptimal error feedback is proposed and shown to provide a constant output SNR (signal-to-noise ratio) independent of the specific characteristics of the filter except the filter's order. Several examples are given to verify these results.>

The concept of data flow computing is applied to digital signal processing (DSP). A data flow signal processor (DFSP) architecture is presented. The principles of data flow computing are carefully considered in order to conform with the special properties of DSP. The bus oriented architecture is easily configured to meet various performance requirements. The DFSP architecture is most suitable for nonrecursive algorithms. Typical tasks of this nature are transforms and FIR filters. A simulation model of the DFSP architecture has been developed. Simulation results of two application examples are given.

Recursive computation can be used to generate sine waveforms. The waveforms are degraded by the round-off noise caused by rounding the results of multiplications. The variance of the round-off noise will increase during the computation if white noise model is assumed. However, in certain cases this will not happen. In this paper the so called 'locking' phenomenon is described. A measure is given to the locking sensitivity of a certain algorithm. Some results of computer simulations and hardware measurements are also given.

A new architecture based on the data flow principle has been developed for signal processing purposes. The Data Flow Signal Processor (DFSP) is capable of highly parallel computation of block realizations of nonrecursive algorithms. The flexibility and modularity of the DFSP architecture are illustrated by two examples. The three-sensor problem shows the high performance of the DFSP in handling three 100 kHz input streams and performing correlation computations on them. The second example shows that 256 × 256 images can be processed with spatially restricted operations at video rate.

Recently, Silverston1has given an algorithm to produce sinusoids with only two multiplications per cycle. With a simple substitution the algorithm can be further changed to have only one multiplication per cycle. The stability of these recursive algorithms depends on the roundoff errors and it cannot be stated straightforward.