DJ Transform Spectrogram for Fundamental Frequency Extraction
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Solution Overview
Problem
Existing sound processing methods, such as short-time Fourier Transform (STFT), face limitations in simultaneously increasing temporal resolution and frequency resolution due to the Fourier uncertainty principle.
Innovation Solution
The proposed method uses DJ transform to generate a spectrogram indicating estimated pure-tone amplitudes for respective frequencies corresponding to natural frequencies of a plurality of springs, allowing for the extraction of fundamental frequencies with high measurement precision in both temporal and frequency domains.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If short-time Fourier Transform (STFT) is used to extract fundamental frequency, then frequency resolution is improved by using longer duration sound, but temporal resolution deteriorates
Solution Approach 1:
The patent applies dynamics by making the analysis window length adaptive rather than fixed. The window length is dynamically adjusted based on the characteristics of the input sound signal, allowing the system to optimize between temporal and frequency resolution for different types of sounds. This resolves the contradiction by enabling the system to have long windows for frequency resolution when needed and short windows for temporal resolution when needed.
Solution Approach 2:
The patent changes the parameter of window length from a fixed value to a variable parameter that can be adjusted based on signal characteristics. By modifying this parameter dynamically, the system can adapt to different scenarios - using longer windows for stationary sounds requiring frequency resolution and shorter windows for transient sounds requiring temporal resolution, thus resolving the contradiction.
2Loss of time
If short-time Fourier Transform (STFT) is used to extract fundamental frequency, then temporal resolution is improved by using shorter duration sound, but frequency resolution deteriorates
Solution Approach 1:
The system dynamically adjusts the analysis window length based on the temporal and spectral characteristics of the input signal. For transient sounds requiring high temporal resolution, the window is shortened. For stationary sounds where frequency precision is critical, the window is lengthened. This dynamic adaptation resolves the contradiction between temporal and frequency resolution.
Solution Approach 2:
The window length parameter is changed from a fixed value to an adaptive parameter that varies according to signal characteristics. This allows the system to optimize the trade-off between temporal and frequency resolution by adjusting the parameter based on whether the current signal segment requires better time localization or frequency precision.
Data Source
AI summary
Provided is a sound processing method performed by a computer, the method comprising generating a DJ transform spectrogram indicating estimated pure-tone amplitudes for respective frequencies corresponding to natural frequencies of a plurality of springs and a plurality of time points by modeling an oscillation motion of the plurality of springs having different natural frequencies, with respect to an input sound, and calculating the estimated pure-tone amplitudes for the respective natural frequencies; calculating degrees of fundamental frequency suitability based on a moving average of the estimated pure-tone amplitudes or a moving standard deviation of the estimated pure-tone amplitudes with respect to each natural frequency of the DJ transform spectrogram; and extracting the fundamental frequency based on local maximum values of the degrees of fundamental frequency suitability for the respective natural frequencies at each of the plurality of time points.