Design and Analysis of Direct and Post-Truncated Adder Tree Architectures for FFT and FIR Filter Implementations

Digital Signal Processing (DSP) systems require high-speed arithmetic units for efficient implementation of algorithms such as Fast Fourier Transform (FFT) and Finite Impulse Response (FIR) filters [1], [2]. The performance of these systems heavily depends on multiplier-accumulator (MAC) architectures and adder tree structures. Conventional adder trees introduce higher power consumption, propagation delay, and silicon area overhead, especially when implemented in deep submicron CMOS technology [3], [4]. To address these limitations, this paper presents the design and analysis of Direct Truncated and PostTruncated Adder Tree architectures optimized for FFT and FIR filter implementations. The proposed design utilizes truncation techniques to eliminate unnecessary computation of less significant bits (LSBs) that minimally affect final output quality [5]. In Direct Truncation, LSB bits are discarded before or during addition stages, reducing adder width and switching activity from the beginning of computation. In Post-Truncation, full-precision addition is performed first, and truncation is applied only at the final output stage, offering a balanced trade-off between accuracy and hardware efficiency [6]. The architectures are described using Verilog HDL and synthesized using a standard CMOS technology library (180nm/90nm technology node). Performance evaluation demonstrates that the proposed truncated adder trees achieve 15-30% reduction in silicon area, 1025% reduction in dynamic power consumption, and improved maximum operating frequency compared to conventional fullprecision adder tree implementations [7], [8]. The quantization error introduced by truncation remains within acceptable limits for most DSP applications including wireless communication, audio processing, biomedical signal analysis, and image processing. The proposed architectures are particularly suitable for ASIC and FPGA-based DSP accelerators where power efficiency and area optimization are critical design parameters [9], [10].