Digital Oscilloscope Fractional Calculus Lookup Table
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Solution Overview
Problem
The existing digital oscilloscopes face limitations in storage resource and computing ability, which restrict the application of digital implementation of fractional calculus operations, especially when processing input signals.
Innovation Solution
A digital oscilloscope with a fractional calculus module that includes a fixed coefficient memory, D flip-flop delay units, fractional operation units, and a control module to perform fractional differentiation or integration, improving real-time calculation performance and dynamic configuration of operation parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If digital implementation of fractional calculus operation is adopted, then computing precision is improved, but storage resource consumption increases
Solution Approach 1:
The fractional calculus operation is divided into multiple sub-operations with different orders (e.g., 0.1, 0.2, ..., 0.9). Each sub-operation uses pre-calculated binomial coefficients stored in separate lookup tables, allowing the system to achieve high precision through composition of simpler operations rather than storing all coefficients at once.
Solution Approach 2:
Binomial coefficients for fractional calculus operations are pre-calculated and stored in lookup tables during system initialization or offline preparation. This preliminary action eliminates the need for real-time computation of coefficients, reducing both storage requirements during operation and computing time.
2Measurement precision
If digital implementation of fractional calculus operation is adopted, then computing precision is improved, but computing time increases
Solution Approach 1:
Binomial coefficients are pre-calculated and stored in lookup tables before actual signal processing begins. This eliminates the need for complex real-time computations during fractional calculus operations, significantly reducing computing time while maintaining precision.
Solution Approach 2:
The system uses lookup tables that store pre-computed binomial coefficients as copies of mathematical data. Instead of computing coefficients during signal processing, the system retrieves them from stored copies, dramatically speeding up the fractional calculus operation.
3Manufacturing precision
If hardware architecture with lookup tables is used for fractional calculus, then operation accuracy is improved, but device complexity increases
Solution Approach 1:
The hardware architecture uses a universal lookup table structure that can store binomial coefficients for multiple different fractional orders (0.1, 0.2, ..., 0.9) in a single system. This multi-functional design allows the same hardware to perform various fractional calculus operations without requiring separate dedicated circuits for each order, reducing overall device complexity.
Solution Approach 2:
Lookup tables serve as intermediary structures between the input signal and the fractional calculus operation. Instead of directly implementing complex fractional differentiation/integration circuits, the system uses these intermediate lookup tables to store pre-computed coefficients that mediate the calculation process, simplifying the overall hardware architecture.
Data Source
AI summary
The present invention provides a system for data mapping and storing in digital three-dimensional oscilloscope, wherein the fixed coefficients, which are calculated according the parameters and settings of a digital oscilloscope, are stored into a fixed coefficient memory CO RAM, the fixed coefficients are outputted to N fractional operation units through N−1 D flip-flop delay units to multiply with the acquired data x(n) and then be accumulated, thus N fractional calculus results are obtained. In this way, N fractional calculus results can be obtained by performing L/N fractional calculus operations. N fractional calculus results are sent to a signal processing and display module, in which they are converted into a display data through a drawing thread, and the display data are sent to LCD for displaying, thus the fractional calculus operation and display of a input signal in a digital oscilloscope is realized.