Modular Computation for Digital Signal Processing: Precision Without Penalty

Digital Signal Processing (DSP) plays a critical role in modern electronics, powering everything from audio systems and medical imaging to radar, sonar, and high-definition video. Many DSP applications demand high numeric precision to preserve signal fidelity, minimize quantization error, and ensure algorithmic stability—especially in systems involving long filters, spectral analysis, or fine-grained feature extraction.

Traditional approaches often rely on floating-point arithmetic, particularly FP32 or extended formats, to meet these demands. However, as highlighted in both academic literature and industry design reports, the use of high-precision binary arithmetic introduces performance and resource bottlenecks, especially on programmable DSPs or FPGA-based platforms. The need for multiple-word accumulation, normalization steps, and carry handling leads to increased complexity and power usage—factors that become limiting in real-time or embedded systems.

Modular computation, based on the Residue Number System (RNS), offers a powerful solution for this class of problems. By decomposing values into a set of independent residues, RNS arithmetic eliminates carry propagation and allows high-precision fixed-point formats—such as 64.64 or 128.128—to be processed with linear hardware scaling and inherently parallel architectures. In contrast to binary multipliers, which grow quadratically in size and power with precision, RNS-based multipliers scale linearly, enabling deeper data paths without compromising speed or efficiency.

This is especially valuable for DSP workloads such as FIR filters, FFTs, and convolution engines, where accuracy over long accumulations is paramount. Modular computation enables extended precision accumulation across multiple taps or frequency bins with just a single normalization step at the end—preserving accuracy while avoiding repeated rounding or error propagation. Moreover, because RNS operations are digit-separated, modular DSP engines can be highly pipelined and mapped efficiently onto FPGAs or ASICs.

Applications such as audio mastering, real-time radar and sonar detection, biomedical signal analysis, and scientific instrumentation all benefit from this approach, especially in environments where both precision and throughput must coexist. As signal processing continues to evolve toward more sophisticated algorithms and high-dynamic-range systems, modular computation provides a scalable and energy-efficient path forward—enabling DSP platforms to break free from the constraints of conventional binary math.