In this work we consider optimized twiddle factor multipliers based on shift-and-add-multiplication. We propose a low-complexity structure for twiddle factors with a resolution of 32 points. Furthermore, we propose a slightly modified version of a previously reported multiplier for a resolution of 16 points with lower round-off noise. For completeness we also include results on optimal coefficients for eight-points resolution. We perform finite word length analysis for both coefficients and round-off errors and derive optimized coefficients with minimum complexity for varying requirements.

Hypercomplex coefficient digital filters provide several attractive advantages such as compact realization with reduced system order, inherent parallelism. However, they also possess a drawback in that a multiplier requires a large amount of computations. This paper proposes a computationally efficient implementation of digital filters whose coefficient is a type of hypercomplex number; a bicomplex number. By decomposing a bicomplex multiplier into two parallel complex multipliers, we show that hypercomplex digital filters can be implemented as two parallel complex digital filters. The proposed implementation offers more than a 60% reduction in the count of real multipliers.

Digital Signal Processors with complex arithmetic capability (DSP-C) are useful for various applications. In this paper, we propose a method for the effective implementation of specific circuits with real coefficients on DSP-C. DSP-C has special hardware such as a complex multiplier so that a complex calculation can be performed with only one instruction. First, we show that nodes with two real coefficient input branches can be implemented by complex multiplications. We apply this implementation to 2D circuits and transversal circuits with real coefficients. Next, we introduce a new computational mode (Advanced mode) and a new multiplier into PSI, a kind of DSP-C which has been proposed already, in order to process the circuits effectively. The effectiveness of the proposed method is shown by simulation in the last part.

This correspondence reports novel computationally efficient algorithms for multiplication of bicomplex numbers, which belong to hypercomplex numbers. The proposed algorithms require less number of real multiplications than existing methods. Furthermore, they give more effective implementation when applied to constant coefficient digital filters.