Recursive Digital Sinusoid Correction for Quantization Drift
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Solution Overview
Problem
Existing digital sinusoid generators face limitations in frequency resolution and throughput due to on-chip RAM constraints and suffer from accumulation of quantization errors in recursive methods, leading to degraded output quality over time.
Innovation Solution
A digital sinusoid generator that incorporates a high precision sine value generator to periodically replace recursive values with pre-calculated, high precision replacement values at a lower frequency, using a control circuit to manage this process without interrupting the sinusoid output, and employs a CORDIC for precise calculations, optimizing hardware reuse and reducing errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If on-chip RAM is used to store sinusoid values for generation, then frequency resolution can be improved, but chip area becomes excessively large and throughput speed is limited
Solution Approach 1:
The patent replaces the mechanical/RAM-based storage system with a mathematical recursive system. Instead of storing sinusoid values in memory, the system uses a second-order IIR filter that recursively calculates sinusoid values through the difference equation y[n] = 2cos(θ)y[n-1] - y[n-2], eliminating the need for large on-chip RAM while maintaining frequency resolution through proper coefficient selection.
Solution Approach 2:
The patent changes the approach from static memory storage to dynamic recursive calculation by transforming the sinusoid generation problem into a parameter-driven difference equation solution. By using the relationship between consecutive sinusoid samples and the cosine of the frequency angle, the system generates values on-the-fly without storage requirements.
2Area of stationary object
If recursive method is used for digital sinusoid generation, then chip area is reduced, but quantization errors accumulate over time degrading output quality
Solution Approach 1:
The patent applies periodic correction to the recursive sinusoid generation process. A correction mechanism periodically resets the recursive filter state by reloading initial conditions or correcting accumulated quantization errors at specific intervals, preventing error accumulation while maintaining the area-efficient recursive structure.
Solution Approach 2:
The patent introduces feedback mechanisms to monitor and correct quantization error accumulation in the recursive system. By detecting when error thresholds are exceeded and applying corrective actions such as state resetting or parameter adjustment, the system maintains output quality over extended operation periods.
3Reliability
If high precision replacement values are periodically inserted, then quantization error accumulation is reduced, but system complexity increases
Solution Approach 1:
The patent implements a self-correcting recursive system where the generation process itself provides the correction mechanism. The same recursive structure that generates sinusoid values also generates the correction values, and the system automatically detects when correction is needed based on error accumulation thresholds, eliminating the need for separate complex correction hardware.
Data Source
AI summary
A recursive digital sinusoid generator generates recursive values used in the production of a digital sinusoid output. The recursive values are generated at a first frequency. A sinusoid value generator generates replacement values at a second frequency, wherein the second frequency is less than the first frequency. The generated recursive values are periodically replaced with the generated replacement values without interrupting production of the digital sinusoid output at the first frequency. This periodic replacement effectively corrects for a finite precision error which accumulates in the recursive values over time.