MDCT Signal Processing with N/4 DFT Rotation Table Reuse
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Solution Overview
Problem
The high computational complexity of the modified discrete cosine transform (MDCT) for large datasets in real-time digital audio coding leads to inefficiencies, particularly due to the need for significant storage and computational resources in existing fast MDCT methods based on FFT, which affects transform efficiency.
Innovation Solution
A signal processing method that includes pre-rotating and post-rotating data using specific rotation factors, followed by discrete Fourier transforms of N/4 points, reducing the storage requirements and computational complexity by utilizing symmetrical properties of the rotation factors WNn+0.5 and WNk+0.5, thereby minimizing storage consumption and enhancing transform efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If fast MDCT algorithm based on N/4-point FFT is used, then computational speed is improved, but storage resources are consumed due to needing to store N/2 values for pre- and post-rotation
Solution Approach 1:
The patent merges the pre-rotation and post-rotation operations into a unified processing framework where the same N/4-point cosine table is reused for both operations. By combining these rotation steps and exploiting their mathematical relationship, the patent eliminates the need to store separate pre-rotation and post-rotation tables, reducing total storage from N/2 values to N/4 values while maintaining the computational speed benefits of the N/4-point FFT approach.
Solution Approach 2:
The patent changes the parameter representation by expressing both pre-rotation and post-rotation factors in terms of the same N/4-point cosine table with different indexing schemes. Instead of storing N/2 distinct values, the patent transforms the rotation factors into a form that can be generated from N/4 stored values through parameter transformation, thereby reducing storage requirements while preserving computational accuracy.
2Device complexity
If fast MDCT algorithm based on N/2-point FFT is used, then computational complexity is reduced, but storage requirements increase due to needing to store N values for asymmetric pre- and post-rotation
Solution Approach 1:
The patent addresses the asymmetric nature of pre- and post-rotation by introducing a symmetric indexing approach. By redefining the rotation factors to use symmetric indexing patterns, the patent creates a unified treatment of otherwise asymmetric operations, allowing both to be derived from the same N/4-point table rather than requiring N separate storage locations.
3Speed
If FFT-based fast MDCT is used for large N, then real-time processing becomes difficult, but existing methods consume large storage resources
Solution Approach 1:
The patent segments the rotation operation into two phases: an N/4-point FFT that processes data in smaller chunks, followed by a post-rotation that uses the same compact N/4-point table. This segmentation allows real-time processing of large N datasets while maintaining minimal storage requirements, as neither phase requires storing N or N/2 values - only N/4 values are stored and reused.
Data Source
AI summary
The present invention discloses a signal processing method and a data processing method and apparatus. A time-domain to frequency-domain signal processing method includes: pre-processing time-domain data; pre-rotating the pre-processed data by using a rotation factor a·WNn+0.5; performing a discrete Fourier transform (DFT) of N/4 points on the pre-rotated data; and post-rotating the data transformed by the DFT by using a rotation factor b·WNk+0.5 to obtain frequency-domain data. A frequency-domain to time-domain signal processing method includes: twiddling frequency-domain data; pre-rotating the twiddled data by using a rotation factor c·WNk+0.5; performing a DFT of N/4 points on the pre-rotated data; and post-rotating the data transformed by the DFT by using a rotation factor d·WNn+0.5; and post-processing the post-rotated data to obtain time-domain data. The present invention increases the efficiency of signal processing.