Chroma Vector Extraction Using Sinusoidal Matrix Correlation
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Solution Overview
Problem
Conventional methods for extracting chroma from audio signals, such as using Discrete Fourier Transform (DFT), suffer from inaccuracies due to frequency mismatch and the need for windowing, leading to 'smearing' and reduced accuracy, especially for lower frequencies and short signal portions.
Innovation Solution
A computer-implemented method that segments audio signals into time-ordered segments and uses a matrix of sinusoidal functions to derive chroma vectors, allowing direct computation of frequency magnitudes without requiring frequency conversion or smoothing, thereby improving accuracy and resolution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Discrete Fourier Transform (DFT) is used to extract chroma from audio signal, then frequency analysis can be performed, but frequency mismatch causes smearing and reduces accuracy especially for lower frequencies
Solution Approach 1:
The patent changes the fundamental parameter of frequency analysis by replacing DFT with a direct sinusoidal matching approach. Instead of transforming to frequency domain with fixed bin centers, the invention directly computes correlation between the audio signal and sinusoids at the exact chroma frequencies of interest, eliminating frequency mismatch and smearing effects
Solution Approach 2:
The patent substitutes the mechanical DFT computation process with a direct sinusoidal correlation method. Rather than using the standard DFT algorithm with its inherent frequency binning, the invention directly computes the real and imaginary parts by correlating the signal with sinusoids at the precise chroma frequencies, replacing the mechanical transformation process with a more accurate direct computation
2Reliability
If windowing is applied to short audio segments for DFT, then artifacts from non-periodicity are reduced, but the quality and accuracy of extracted chroma is further reduced
Solution Approach 1:
The patent extracts only the essential frequency information needed for chroma representation by directly computing sinusoidal correlations at the specific chroma frequencies. This extraction approach avoids the need for windowing entirely, as the method does not rely on transforming the entire signal spectrum through DFT, thereby eliminating the trade-off between artifact reduction and quality loss
Solution Approach 2:
The patent performs preliminary computation of sinusoidal functions at the exact chroma frequencies before processing the audio signal. By pre-computing the real and imaginary sinusoidal components and storing them in lookup tables, the method prepares the exact frequency templates needed, eliminating the need for subsequent windowing operations that would degrade chroma quality
3Productivity
If DFT is used for chroma extraction, then frequency spectrum can be obtained, but smearing and smoothing operations cause values in chroma to lose accuracy
Solution Approach 1:
The patent substitutes the DFT mechanical transformation process with direct sinusoidal correlation computation. By replacing the DFT algorithm with direct correlation at specific chroma frequencies, the invention eliminates the smearing and smoothing operations inherent in DFT, thereby maintaining both productivity through efficient computation and high measurement precision in chroma values
Solution Approach 2:
The patent changes the computational parameter from general-purpose DFT frequency binning to specific chroma frequency targeting. By computing correlations only at the precise chroma frequencies of interest rather than across the entire DFT spectrum, the method maintains computational efficiency while eliminating the smearing effect that degrades chroma value accuracy
Data Source
AI summary
A matrix is generated that stores sinusoidal components evaluated for a given sample rate corresponding to the matrix. The matrix is then used to convert an audio signal to chroma vectors representing of a set of “chromae” (frequencies of interest). The conversion of an audio signal portion into its chromae enables more meaningful analysis of the audio signal than would be possible using the signal data alone. The chroma vectors of the audio signal can be used to perform analyzes such as comparisons with the chroma vectors obtained from other audio signals in order to identify audio matches.