CN111613241B - High-precision high-stability stringed instrument fundamental wave frequency detection method - Google Patents
High-precision high-stability stringed instrument fundamental wave frequency detection method Download PDFInfo
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- CN111613241B CN111613241B CN202010443971.9A CN202010443971A CN111613241B CN 111613241 B CN111613241 B CN 111613241B CN 202010443971 A CN202010443971 A CN 202010443971A CN 111613241 B CN111613241 B CN 111613241B
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS OR SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/03—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the type of extracted parameters
- G10L25/18—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the type of extracted parameters the extracted parameters being spectral information of each sub-band
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS OR SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/45—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 characterised by the type of analysis window
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10L—SPEECH ANALYSIS OR SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING; SPEECH OR AUDIO CODING OR DECODING
- G10L25/00—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00
- G10L25/48—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 specially adapted for particular use
- G10L25/51—Speech or voice analysis techniques not restricted to a single one of groups G10L15/00 - G10L21/00 specially adapted for particular use for comparison or discrimination
Abstract
The invention discloses a high-precision high-stability stringed instrument fundamental wave frequency detection method, provides an objective basis for sound correction of a stringed instrument, and relates to the technical field of sound correction of stringed instruments. The method integrates the technologies of frequency domain spectrum analysis, time domain circular correlation, circular residual error and the like. Performing Fourier transform and spectrum thinning algorithm on the audio, determining candidate maximum fundamental frequency, determining candidate minimum fundamental frequency by using circular correlation operation in a time domain, determining maximum harmonic times according to the candidate maximum and minimum fundamental frequencies, calculating all submultiples of the maximum harmonic times, calculating a circular residual error according to the number of periods or sampling points corresponding to the submultiples, and taking the ratio of the circular correlation to the circular residual error as a confidence coefficient, wherein the larger the confidence coefficient is, the higher the possibility that the frequency corresponding to the submultiples is taken as the fundamental frequency of the audio is. The method has the advantages of high precision, good robustness and wide application range.
Description
Technical Field
The invention relates to the technical field of sound correction of stringed instruments, in particular to a high-precision and high-stability method for detecting fundamental wave frequency of stringed instruments, and provides an intuitive and objective standard for sound correction of the stringed instruments.
Background
Nowadays, musical instruments are entering more and more families, and pianos, which are representative of the stringed musical instruments, are known as the king of the musical instruments and are more popular. However, the key pitch misalignment causes a serious deterioration in sound quality, and therefore, it is often necessary to correct the pitch. At present, the sound correction of the stringed instrument is mostly corrected by repeatedly debugging according to the feeling of people, and the sound correction depends heavily on the hearing and experience of professional toning technicians. Due to individual difference between people and the influence of a plurality of factors such as physiology, psychology and environment, the sound correction work of the musical instrument is often lack of objective standards. Therefore, it is urgently required to establish an objective standard capable of excluding subjective factors.
The vision tone correction is to detect the fundamental frequency of the musical tones through a software algorithm by utilizing the modern digital signal processing technology and display the result in a visual form. Compared with auditory tuning, visual tuning is more objective and stable, and the operation is easy. The current software sound correction algorithm mainly comprises a time domain method and a transform domain method, wherein the time domain method mainly comprises a zero-crossing method, an autocorrelation function and an average amplitude difference function, and the transform domain method mainly comprises a frequency spectrum compression method, a cepstrum method, a wavelet transform and the like. Since musical tone signals are complicated and varied, it is often difficult to realize high-precision and high-stability fundamental frequency detection with a single method, and a simple combination of multiple methods multiplies the amount of calculation and does not necessarily achieve the desired effect.
Disclosure of Invention
The invention aims to provide a method for detecting the fundamental wave frequency of a stringed instrument, which can realize the detection of the fundamental wave frequency of the stringed instrument with high precision and high stability.
Therefore, the invention provides a method for combining time domain and frequency domain, which comprises the following steps: the frequency domain spectrum thinning algorithm provides high-precision frequency estimation; the frequency spectrum analysis is combined with the circular correlation to limit the possible values of the fundamental frequency to a few numerical values, thereby greatly reducing the algorithm complexity; finally, the cyclic correlation, combined with the cyclic residual, can determine the fundamental frequency with maximum probability. The technical scheme of the invention is detailed as follows.
The invention provides a high-precision and high-stability stringed instrument fundamental wave frequency detection method, which comprises the following steps of:
Step 2, for a frame of audio signal x [ n ]]Windowing to obtain a windowed audio frame signal x w [n]Then to x w [n]Performing fast Fourier transform to obtainTo the Fourier spectrum X w [k]；
Step 3, from X w [k]Determining the range of the peak frequency, performing spectrum refinement analysis on the frequency spectrum in the range of the peak frequency, and determining the peak frequency F max Peak frequency F max Is the candidate maximum fundamental frequency;
step 4, calculating x [ n ]]Cyclic correlation function R of cx [m]Wherein m is more than or equal to 0 and less than or equal to N-1,
wherein x is c [n-m]Represents x [ n ]]Cyclic shift of m bits, take R cx [m]In the interval [ (N-1)/10, N-1]Calculating the candidate maximum fundamental wave period to obtain the candidate minimum fundamental wave frequency F min ；
Step 5, from F max And F min Determining the maximum harmonic degree H max ，H max ＝round(F max /F min ) Where round () is the operator rounded to the nearest integer;
step 6, calculating H max All submultiples of (1, H) 1 ,…,H i ,…,H max In which H is i E N is H max Divisor of (H) i Corresponding frequency F i ＝F max /H i Corresponding period T i ＝1/F i ，T i The corresponding number of samples is
Step 7, calculating each candidate period T i Confidence coefficient of (2)
E cx [m]Is x [ n ]]The cyclic residual sequence of (1), wherein
Step 8, defining lambda opt ＝max{λ i }，λ opt Corresponding factor H i For an optimum factor, λ opt Corresponding T i Is a fundamental period, λ opt Corresponding frequency F i ＝1/T i Is x [ n ]]The fundamental frequency of (2).
In a preferred embodiment, step 2 is specifically:
for a frame of audio signal x [ n ]]Adding Hamming Window, window function w [ n ]]∈R N Obtaining a windowed audio frame signal x w [n]，x w [n]＝x[n]w[n]For windowed audio frame signal x w [n]Performing fast Fourier transform to obtain Fourier spectrum X w [k]Is marked as
X w [k]＝FFT{x w [n]}。
In a preferred embodiment, step 3 is specifically:
according to X w [k]Calculating the peak frequency index I fpeak To further determine [ I fpeak -1,I fpeak +1]Corresponding peak frequency range f L ,f H ]Determining frequency spectrum thinning parameters omega and a according to the peak frequency range and the frame length N, wherein omega is the step length of thinning angular frequency, a is the starting point of thinning frequency, and obtaining the frequency spectrum in the local frequency range of the amplitude spectrum by a frequency spectrum thinning algorithm CZT
X czt [k]＝CZT{x w [n],N,ω,a}，
According to X czt [k]Calculating the peak frequency F peak Is taken as a candidate maximum fundamental frequency and is denoted as F max 。
In a preferred embodiment, in step 4: from R cx [m]In the interval [ (N-1)/10, N-1]The index corresponding to the maximum value in the index is calculated to be x [ n ]]To obtain a candidate minimum fundamental frequency F min 。
The invention has the beneficial effects that: the frequency spectrum thinning technology ensures that the fundamental frequency estimation has high enough precision, the combination of cyclic correlation and cyclic residual can ensure the robustness of the fundamental frequency estimation, the factorization of the highest harmonic frequency can definitely limit the possible values of the fundamental frequency to a few numerical values, and the combination of the technologies ensures that the string instrument fundamental frequency detection method has the advantages of high detection precision, good stability, wide application range and the like.
Drawings
In order to more clearly illustrate the technical solution of the embodiments of the present invention, the drawings used in the embodiments will be briefly described below. It is understood that the following drawings only show some embodiments of the invention and are therefore not to be considered limiting of its scope, for a person skilled in the art to which it pertains, from which further related drawings can be derived without inventive effort.
Fig. 1 is a flow chart of a method for detecting the fundamental frequency of a stringed instrument according to embodiment 1.
Fig. 2 is a time domain waveform diagram of an audio signal provided in embodiment 1.
Fig. 3 is a FFT spectrum diagram of an audio signal provided in embodiment 1.
Fig. 4 is a diagram of local refinement of the spectrum of an audio signal provided in embodiment 1.
Fig. 5 is a diagram of a cyclic correlation function of an audio signal provided in embodiment 1.
Fig. 6 is a sequence diagram of the cyclic residual of the audio signal provided in embodiment 1.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
The present embodiment provides a method for detecting fundamental frequency of stringed instrument with high precision and high stability, the flow chart of which is shown in fig. 1, the method comprises the following steps:
Step 2, for a frame of audio signal x [ n ]]The time domain waveform is shown in fig. 2; for x [ n ]]Adding Hamming Window, window function w [ n ]]∈R N Obtaining a windowed audio frame signal x w [n]，x w [n]＝x[n]w[n](ii) a For x w [n]Fast Fourier Transform (FFT) is carried out to obtain Fourier spectrum X w [k]Is marked as X w [k]＝FFT{x w [n]}，X w [k]The amplitude-frequency spectrum of (a) is shown in fig. 3, and is referred to as an amplitude spectrum for short.
Step 3, according to X w [k]Calculating the peak frequency index I fpeak To further determine [ I fpeak -1,I fpeak +1]Corresponding peak frequency range f L ,f H ]Determining frequency spectrum thinning parameters omega and a according to a peak frequency range and a frame length N, wherein omega is a thinning angular frequency step length, a is a thinning frequency starting point, and obtaining a thinned frequency spectrum X in a local frequency range of a magnitude spectrum through a frequency spectrum thinning algorithm (CZT, chirp Z-transform) czt [k]，
X czt [k]＝CZT{x w [n],N,ω,a}，
X czt [k]The spectrum is shown in FIG. 4 according to X czt [k]Calculating the peak frequency F peak In the present embodiment, F peak =249.0197Hz, which is the candidate maximum fundamental frequency and is denoted as F max . The frequency spectrum thinning technology provides a basis for providing a high-precision fundamental frequency detection result.
Step 4, calculating the audio signal x [ n ]]Cyclic correlation function R of cx [m]，
R cx [m]The waveform of (b) is shown in FIG. 5, where 0. Ltoreq. M.ltoreq.N-1, x c [n-m]Represents x [ n ]]Cyclic shift m bits of (1); because R is cx [0]The nearby partial points cannot participate in the comparison, so R is taken cx [m]In the interval [ (N-1)/10, N-1]Maximum value pair inCorresponding index I Rmax According to I Rmax Calculating x [ n ]]The frequency corresponding to the candidate maximum fundamental period of (2) is the candidate minimum fundamental frequency F min 。
Step 5, from F max And F min Determining the maximum harmonic degree H max ，H max ＝round(F max /F min ) Where round () is the operator rounded to the nearest integer.
Step 6, calculating H max All divisors of (a). According to the theory of harmonic analysis, the fundamental frequency F of the audio is F min Integer multiples of (i.e. F/F) min ＝k∈N，F max Is an integer multiple of F, i.e. F max /F = j ∈ N, thus there is H max = kj, means H max Can be written as the product of two integers, based on which the maximum harmonic number H is max Decomposition prime factor, denoted as Div { H max }＝{1,H 1 ,…,H i ,…,H max And (c) wherein Div { } is a divisor operator. H max All submultiples of (1, H) 1 ,…,H i ,…,H max In which H is i E N is H max Divisor of (H) i Corresponding frequency F i ＝F max /H i Corresponding period T i ＝1/F i . The number of integers within 50, 48 having a maximum divisor, is 10 in total. General stringed musical instruments H max Less than or equal to 50. Will T i Conversion to number of samples
Each->
All are values in the array {0,1, \8230; N-1 }.
Step 7, calculating each candidate period T i Confidence coefficient of (a) i ，
Wherein E is cx [m]For audio signals x [ n ]]The cyclic residual sequence of (a) is determined,
all of the ÷ or ÷ determined in step 6>
Is a value in an array {0,1, \8230; N-1}, will->
Value of (a) instead of formula
M in (1), E obtained by calculation cx [m]Is the corresponding value>
The value of (c). E cx [m]The spectrum is shown in FIG. 6.
Will be provided with
In place of the formula->
M in (1), R is calculated cx [m]Is the corresponding value>
The value of (c). From this it can be derived for each lambda i The value of (c).
Step 8, defining lambda opt ＝max{λ i }，λ opt Corresponding factor H i For an optimum factor, λ opt Corresponding period T i Is a fundamental period, λ opt Corresponding frequency F i ＝1/T i I.e. the audio signal x n]The fundamental frequency of (2). And comparing the detected fundamental wave frequency of the stringed instrument with the standard sound to perform sound calibration.
The string instrument fundamental wave frequency detection method provided by the invention integrates multiple technologies of signal frequency domain analysis, time domain correlation, time domain residual error and the like, wherein the frequency spectrum thinning technology can provide a high-precision fundamental wave frequency detection result, the frequency spectrum peak value and the harmonic frequency determined by the correlation peak value limit the possible fundamental wave frequency to a few possible values by solving the divisor of the highest harmonic frequency, and finally the best fundamental wave frequency is determined with high confidence degree by combining the ratio of cyclic correlation and cyclic residual error, so that the popularization value is high.
Claims (4)
1. A high-precision high-stability stringed instrument fundamental wave frequency detection method is characterized by comprising the following steps:
step 1, performing framing processing on audio stream signals, wherein the frame length is N, and one frame of audio signal is marked as x [ N ]]，x[n]∈R N ；
Step 2, for a frame of audio signal x [ n ]]Windowing to obtain windowed audio frame signal x w [n]Then to x w [n]Performing fast Fourier transform to obtain Fourier spectrum X w [k]；
Step 3, from X w [k]Determining the range of the peak frequency, performing spectrum refinement analysis on the frequency spectrum in the range of the peak frequency, and determining the peak frequency F max Peak frequency F max Is the candidate maximum fundamental frequency;
step 4, calculating x [ n ]]Cyclic correlation function R of cx [m]Wherein m is not less than 0 and not more than N-1, wherein
Wherein x c [n-m]Represents x [ n ]]Cyclic shift of m bits of R cx [m]In the interval [ (N-1)/10, N-1]Calculating the candidate maximum fundamental wave period to obtain the candidate minimum fundamental wave frequency F min ；
Step 5, from F max And F min Determining the maximum harmonic degree H max ，H max ＝round(F max /F min ) In which round () is the operator rounded to the nearest integer;
step 6, calculating H max All submultiples of (1, H) 1 ,…,H i ,…,H max In which H is i E N is H max Divisor of (H) i Corresponding frequency F i ＝F max /H i Corresponding period T i ＝1/F i ，T i The number of corresponding samples is
Step 7, calculating each candidate period T i Is a confidence coefficient of
E cx [m]Is x [ n ]]The cyclic residual sequence of (1), wherein
Step 8, defining lambda opt ＝max{λ i }，λ opt Corresponding factor H i For an optimum factor, λ opt Corresponding T i Is a fundamental period, λ opt Corresponding frequency F i ＝1/T i Is x [ n ]]The fundamental frequency of (2).
2. A method for detecting fundamental wave frequency of stringed musical instrument with high precision and high stability as claimed in claim 1, wherein step 2 is specifically:
for a frame of audio signal x [ n ]]Adding Hamming Window, window function w [ n ]]∈R N Obtaining a windowed audio frame signal x w [n]，x w [n]＝x[n]w[n]For windowed audio frame signal x w [n]Performing fast Fourier transform to obtain Fourier spectrum X w [k]Is marked as
X w [k]＝FFT{x w [n]}。
3. A method for detecting fundamental wave frequency of stringed musical instrument with high precision and high stability as claimed in claim 1, wherein step 3 is specifically:
according to X w [k]Calculating the peak frequency index I fpeak To further determine [ I fpeak -1,I fpeak +1]Corresponding peak frequency range f L ,f H ]Determining frequency spectrum thinning parameters omega and a according to the peak frequency range and the frame length N, wherein omega is a thinning angular frequency step length, a is a thinning frequency starting point, and obtaining the frequency spectrum in the local frequency range of the amplitude spectrum through a frequency spectrum thinning algorithm CZT
X czt [k]＝CZT{x w [n],N,ω,a}，
According to X czt [k]Calculating the peak frequency F peak Is taken as a candidate maximum fundamental frequency and is denoted as F max 。
4. A high-precision high-stability stringed instrument fundamental wave frequency detecting method according to claim 1, wherein in step 4:
from R cx [m]In the interval [ (N-1)/10, N-1]The index corresponding to the maximum value in the table is calculated as x [ n ]]To obtain a candidate minimum fundamental frequency F min 。
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| CN112885374A (en) * | 2021-01-27 | 2021-06-01 | 吴怡然 | Sound accuracy judgment method and system based on spectrum analysis |
| CN113129853B (en) * | 2021-04-22 | 2023-11-14 | 深圳市左轮音乐科技有限公司 | Sound diagnosis device and use method thereof |
| US11545143B2 (en) * | 2021-05-18 | 2023-01-03 | Boris Fridman-Mintz | Recognition or synthesis of human-uttered harmonic sounds |
| CN114371342B (en) * | 2022-03-21 | 2022-05-27 | 国仪量子(合肥)技术有限公司 | FPGA (field programmable Gate array), real-time signal frequency measurement method based on FPGA and lock-in amplifier |
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