Trigonometric Function Calculating Device Using Bit Segmentation
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Solution Overview
Problem
Existing trigonometric function calculating devices require increased circuit sizes to achieve high accuracy in sine wave generation, as longer data lengths are needed for precise calculations, leading to larger and more complex calculation circuits.
Innovation Solution
A trigonometric function calculating device that uses a combination of a storage section with separate tables for upper and lower bit phases, along with a correction mechanism to ensure accurate calculations without increasing circuit sizes, by storing first and second sines and cosines at 8 decimal places and using a correction value table to refine results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If longer data lengths are used in trigonometric function tables to improve calculation accuracy, then measurement precision is improved, but device complexity increases due to larger circuit sizes
Solution Approach 1:
The phase angle is segmented into upper bits and lower bits, with separate trigonometric function tables storing values for each segment. This allows the use of shorter data lengths in each table while maintaining overall calculation accuracy through the addition theorem: sin(α+β) = sinαcosβ + cosαsinβ
Solution Approach 2:
The invention changes the parameter representation by storing trigonometric values at 8 decimal places rather than longer precision, and compensates for the reduced precision through the correction mechanism using the addition theorem, thus achieving high accuracy without requiring long data lengths
2Measurement precision
If longer data lengths are stored in tables to ensure high accuracy, then measurement precision is improved, but loss of substance increases due to larger storage requirements
Solution Approach 1:
By segmenting the phase angle into upper and lower bits and using separate tables for each segment, the invention reduces the storage capacity required in each individual table while maintaining overall calculation accuracy through combination of the segmented results
Solution Approach 2:
The invention changes the data length parameter to 8 decimal places in the stored tables, which reduces storage requirements compared to longer precision values, and compensates for this reduction through the correction mechanism applied during calculation
Data Source
AI summary
A trigonometric function calculating device includes: an address generator that generates an address signal that is formed from plural bit strings and corresponds to a phase; a trigonometric function table that stores first sines and first cosines that respectively correspond to phases expressed by upper bits of the address signals, and second sines and a second cosines that respectively correspond to phases expressed by lower bits of the address signals; a calculation circuit that outputs, as a calculated value, a sine that corresponds to the address signal by calculating processing using the first sine, the first cosine, the second sine and the second cosine that correspond to the address signal and have been extracted by referring to the trigonometric function table; and a correcting section that corrects the calculated value on the basis of a correction value corresponding to the address signal.