CN112545528A - Electrocardio T wave feature extraction method based on fractional Fourier transform and tensor decomposition - Google Patents
Electrocardio T wave feature extraction method based on fractional Fourier transform and tensor decomposition Download PDFInfo
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- A61B5/7267—Classification of physiological signals or data, e.g. using neural networks, statistical classifiers, expert systems or fuzzy systems involving training the classification device
Abstract
The invention discloses an electrocardio T wave feature extraction method based on fractional Fourier transform and tensor decomposition, and belongs to the field of electrocardio signal processing. The electrocardio signals of a plurality of heart beats are continuously processed, the T wave data of each heart beat are subjected to dimension expansion by adopting fractional Fourier transform to obtain a T wave matrix, the T wave matrix of the continuous heart beats is constructed into a third-order tensor, a projection component in a third direction is obtained by Tucker decomposition, and an entropy value of the projection component is taken as the characteristic of the section of the electrocardio T wave, so that the T wave matrix can be combined with machine learning to classify the electrocardio signals, particularly detect the TWA phenomenon.
Description
Technical Field
The invention provides an electrocardiosignal feature extraction method, which is suitable for establishing a classification model by combining a proper classifier and detecting electrocardio abnormity, particularly T wave abnormity, and belongs to the field of electrocardiosignal processing.
Background
Body surface Electrocardiogram (ECG) is the most common noninvasive detection method for cardiac states, and cardiac anomalies are closely related to the occurrence of malignant arrhythmia. The T-wave alternans (TWA) phenomenon based on the electrocardiogram has a corresponding relation with malignant arrhythmia in clinic due to a basic generation mechanism, and is considered to be a noninvasive electrophysiological detection index with an important prediction effect on the malignant arrhythmia at present.
Twa (T-wave alternating) refers to an electrocardiographic variation phenomenon that the amplitude or polarity of T waves or ST segments in an electrocardiographic signal changes alternately with heartbeat to form ABABAB … when the heart rate is regulated. Since many T-wave alternans are in the microvolt range, few T-wave alternans are distinguishable to the naked eye. Therefore, it is very important to find a high-precision automatic TWA detection method. The existing T-wave alternation detection methods include a spectrum analysis method, a nonlinear method, a symbol conversion method, and the like. Noise exists in electrocardiosignals generally, and the noise is removed in the TWA detection process. However, since the T wave is very weak, a small amount of noise may completely mask the T wave, so that part of the T wave may be removed in the process of removing the noise.
Tensor analysis is one of multi-factor analysis methods, and is widely applied to the fields of data mining, image analysis, machine learning, chemical analysis and the like by analyzing and processing high-order data through a tensor space. Tensor analysis can fully reflect structural features, internal correlation and cooperativity of signals, and therefore the tensor analysis can be used as a basis and means for feature extraction and recognition and classification. Therefore, the T wave feature extraction method based on fractional Fourier and tensor decomposition is provided, and aims to detect T wave abnormity, especially existing micro-volt TWA phenomenon, from single-lead electrocardiosignals.
The invention content is as follows:
in view of the time-varying and non-linear characteristics of the cardiac electrical signal. The invention provides an electrocardiosignal feature extraction method based on Fractional Fourier Transform and tensor decomposition by combining the FRFT (Fractional Fourier Transform) time frequency analysis capability, the tensor decomposition principal component analysis capability and the information entropy measurement capability on the signal chaos degree.
Step S1: continuously acquiring electrocardiosignals containing P cardiac cycles and preprocessing the electrocardiosignals to obtain a signal d; the number P of cardiac cycles contained in the section of electrocardio is more than or equal to 8;
the preprocessing comprises the removal of power frequency interference, myoelectric interference and baseline drift in the electrocardiosignals. The pre-processing also includes up-sampling the signal to a uniform sampling rate.
Step S2: performing QRS complex positioning on the signal d preprocessed in the step S1 to obtain a starting point and a stopping point of each QRS complex and position information of an R wave peak of the QRS complex;
step S3: constructing T-wave matrices
S3-1: positioning the starting point and the ending point of the T wave between every two adjacent QRS complexes, namely between the ending point of the first QRS complex and the starting point of the second QRS complex, and calculating the number X of sampling points between the starting point and the ending point of the T wave; then searching a maximum value between the starting point and the end point of the T wave, and taking the maximum value as a peak value of the T wave;
the number of the detected T waves is N, and N is less than or equal to P; the minimum value of X corresponding to each detected T wave is set as the minimum sampling point number Xmin；
For each detected T wave peak, taking the position of the T wave peak as a central sampling point, respectively taking n sampling points to the left side and the right side of the T wave peak, adding 2n +1 sampling points of the T wave peak, and arranging according to the time sequence to form a T wave vector of the T wave with the length of 2n +1 points;
the point number 2n +1 is less than or equal to the minimum sampling point number X between the starting point and the end point of the T wavemin；
S3-2: respectively performing M fractional order Fourier transform on T wave vectors with the length of 2n +1 points of each T wave, and performing i-order fractional order Fourier transform on the jth T wave vector to obtain a signal D with the length of 2n +1 pointsji(ii) a Wherein j is less than or equal to N, i is less than or equal to 1 and the M fractional Fourier transforms are combined in the same order for all T waves;
s3-3: calculating each signal Dji(iv) fractional Fourier magnitude spectral signal Fvji；
Further onPreferably, the following components: calculating each signal Dji(iv) fractional Fourier magnitude spectral signal FvjiThereafter, for each T wave, for each fractional Fourier magnitude spectral signal FvjiNormalization is performed with respect to the maximum and minimum values at the order i to make each FvjiEach point of (1) is in the interval of 0 to 1; and obtaining a normalized fractional Fourier magnitude spectrum signal with the length of 2n +1 points.
S3-4: for each T wave, taking M fractional Fourier magnitude spectrum signals of different orders as row vectors, and arranging the row vectors from top to bottom in sequence according to the order of fractional Fourier transform from small to large to form a T wave matrix of M rows X (2n + 1); step S3-1 detects N T-waves in total and thus N such matrices; preferably, M is less than or equal to 20;
step S4: constructing a T-wave tensor space
Sequentially arranging N T wave matrixes according to the occurrence sequence of T waves to obtain a third-order tensor of Mx (2N +1) xN;
step S5: tensor resolution
Carrying out tensor decomposition on the third-order tensor by adopting a Tucker decomposition method to obtain a core tensor G and projection matrixes in three projection directions, wherein the projection matrixes U correspond to fractional Fourier transform order directions1Projection matrix U of corresponding order of T wave vector direction2Projection matrix U corresponding to the direction of the heartbeat3；
Step S6:
projection matrix U corresponding to central shooting direction3And calculating an entropy value which is taken as the T wave characteristic of the section of electrocardio.
Preferably, in step S6, the entropy value is an entropy vector, and the calculation method is as follows:
to projection matrix U3And calculating entropy values of each row, and sequentially arranging the obtained entropy values according to the row number to obtain the entropy vector of the projection matrix.
Or, in step S6, the entropy calculation method includes:
to projection matrix U3And solving the mean value of each column to obtain a one-dimensional row vector, and solving the entropy value of the row vector to obtain the entropy value of the projection matrix.
Projection matrix U3The entropy calculation method for each row is as follows:
will project the matrix U3Normalizing each point value, namely enabling the value range of each point value to be in an interval of 0 to 1; then dividing the space between 0 and 1 into m partitions equally; calculating the probability of each partition falling on the numerical value of each point in the row, and making the probability of each point in the x-th row falling on the q-th partition be pxqThe value is the point number of the line falling in the q-th subarea divided by the total point number of the line, q is more than or equal to 1 and less than or equal to m, and the entropy E of the x-th line is calculated according to the following formulax
The logarithm takes 2 as the base, or takes other logarithm bases, and the logarithm bases can be converted by a base-changing formula.
Further, when the extracted T wave features of the section of electrocardio are used for electrocardio signal classification, the T wave features are used as feature vectors, a classifier is trained, and then classification is carried out.
In particular, when the extracted features are used for detecting whether the T wave alternative TWA phenomenon appears in the section of electrocardiosignals: firstly, establishing data sets of two types of samples of electrocardio with TWA and electrocardio without TWA, wherein the number of T waves contained in each section of electrocardio is more than or equal to 8, and then extracting the T wave characteristics from the electrocardio in the data sets for training a classifier;
the number of T waves contained in the electrocardiosignal to be detected is consistent with the number of T waves contained in the training sample;
and after the classifier finishes training, extracting the T wave characteristics of the electrocardiosignals to be detected, inputting the T wave characteristics into the classifier, and judging whether the T wave alternate TWA phenomenon occurs or not by the classifier.
Compared with the prior art, the invention has the beneficial effects that: the electrocardio of a plurality of heart beats is continuously processed, the T wave data of each heart beat is subjected to dimension expansion by adopting fractional Fourier transform to obtain a T wave matrix, the T wave matrix of the continuous heart beats is constructed into a third-order tensor, a projection component in a third direction is obtained by Tucker decomposition, and the entropy value of the projection component is taken as the characteristic of the section of the electrocardio T wave, so that the fluctuation information of the T wave is carried, and the T wave can be combined with machine learning to classify electrocardio signals, particularly detect TWA phenomenon.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a schematic diagram of performing tensor quantization on N T waves.
Detailed Description
The present invention will be described in detail below while describing the technical problems and advantages solved by the technical solutions of the present invention, and it should be noted that the described examples are only intended to facilitate the understanding of the present invention, but do not limit the present invention in any way.
The following describes an embodiment of the present invention with reference to the drawings, taking TWA phenomenon detection as an example. The algorithm flow chart is shown in figure 1. The database used included PhysioNet: the T-Wave Alternans Challenge Database and the MIT-BIH Normal Sinus Rhythm Database.
From PhysioNet: 29 electrocardiosignal data containing TWA with the serial numbers of 01,06,09,13,15,17,21,25,28,29,30,33,34,35,50,51,64,67,69,70,72,73,76,79,82,88,91,97 and 98 are taken out from a T-Wave alternating Challenge Database, the electrocardiosignal contains 12 channels for about 2 minutes, the sampling frequency of each data is 500Hz, about 60000 points, and the signals in the 12 channels in each data are taken out separately, so that 29 electrocardiosignal data containing TWA phenomenon are obtained in total, 29 electrocardiosignal data are obtained, 12 are obtained, and 348 electrocardiosignal data contain TWA phenomenon.
18 data with the number of 16265,16272,16273,16420,16483,16539,16773,16786,16795,17052,17453,18177,18184,19088,19090,19093,19140,19830 are taken out from an MIT-BIH Normal Sinus Rhythm Database, each data comprises 2 channels, the sampling frequency of each data is 128Hz, 2 channel signals in each data are taken out independently, and each data is intercepted to obtain 10 data with 60000 points. A total of 18 × 2 × 10 ═ 360 normal cardiac signal data are then obtained. Because the sampling frequency of the electrocardiosignals containing the TWA phenomenon is 500Hz, the normal electrocardiosignals are up-sampled to 500Hz in order to ensure that the sampling frequency of the normal electrocardiosignals is the same as the sampling frequency of the electrocardiosignals containing the TWA phenomenon. In the embodiment, the electrocardio sample is further segmented according to requirements.
Step S1: continuously acquiring electrocardiosignals containing P cardiac cycles and preprocessing the electrocardiosignals to obtain a signal d; the number P of cardiac cycles contained in the section of electrocardio is more than or equal to 8;
the preprocessing comprises the removal of power frequency interference, myoelectric interference and baseline drift in the electrocardiosignals. The preprocessing further includes upsampling the cardiac signal to a uniform sampling rate.
Preferably, the 50Hz power frequency interference, the myoelectric interference and the baseline shift in the ECG signal are removed by an FIR band-pass filter, and the filter cut-off frequency is set to be 5Hz and 15 Hz.
Step S2: and (4) carrying out QRS complex positioning on the signal d preprocessed in the step (S1) to obtain the start point and the stop point of each QRS complex and the position information of the R wave peak of the QRS complex. Algorithms for positioning the QRS complex are many, and for example, the classical Pam-Tompkins algorithm can be adopted to realize the detection and positioning of the QRS complex and the R wave peak position.
Step S3: constructing T-wave matrices
S3-1: positioning the starting point and the ending point of the T wave between every two adjacent QRS complexes, namely between the ending point of the first QRS complex and the starting point of the second QRS complex, and calculating the number X of sampling points between the starting point and the ending point of the T wave; then searching a maximum value between the starting point and the end point of the T wave, and taking the maximum value as a peak value of the T wave;
there are several methods for locating the start and end points of T-waves, such as CN201810187726.9, CN201910437430.2, pari-magnifiance, key technical research on T-wave electric alternative detection in electrocardiogram [ D ].2015.
The number of the detected T waves is N, and N is less than or equal to P; the minimum value of X corresponding to each detected T wave is set as the minimum sampling point number Xmin；
For each detected T wave peak, taking the position of the T wave peak as a central sampling point, respectively taking n sampling points to the left side and the right side of the T wave peak, adding 2n +1 sampling points of the T wave peak, and arranging according to the time sequence to form a T wave vector of the T wave with the length of 2n +1 points; in the embodiment, n is 30, i.e. the T-wave vector includes 61 sampling points.
The point number 2n +1 is less than or equal to the minimum sampling point number X between the starting point and the end point of the T wavemin；
In the embodiment, after 348 electrocardiosignal data containing TWA phenomenon and 360 normal electrocardiosignal data are preprocessed and T-wave positioned, 31T-wave sampling points and 61T-wave sampling points are respectively taken.
S3-2: respectively performing M fractional order Fourier transform on T wave vectors with the length of 2n +1 points of each T wave, and performing i-order fractional order Fourier transform on the jth T wave vector to obtain a signal D with the length of 2n +1 pointsji(ii) a Wherein j is less than or equal to N, i is less than or equal to 1 and the M fractional Fourier transforms are combined in the same order for all T waves;
the formula for the fractional fourier transform is as follows:
wherein
Where α ═ p π/2, p is the order of fractional Fourier transform (range 0-1), FpRepresenting a fractional fourier transform operator.
S3-3: calculating each signal Dji(iv) fractional Fourier magnitude spectral signal Fvji(ii) a Further, as preferable: calculating each signal Dji(iv) fractional Fourier magnitude spectral signal FvjiThereafter, for each T wave, for each fractional Fourier magnitude spectral signal FvjiNormalization is performed with respect to the maximum and minimum values at the order i to make each FvjiEach point of (1) is in the interval of 0 to 1; and obtaining a normalized fractional Fourier magnitude spectrum signal with the length of 2n +1 points.
S3-4: for each T wave, taking M fractional Fourier magnitude spectrum signals of different orders as row vectors, and arranging the row vectors from top to bottom in sequence according to the order of fractional Fourier transform from small to large to form a T wave matrix of M rows X (2n + 1); step S3-1 detects N T-waves in total and thus N such matrices; see figure 2.
In the embodiment, a fractional Fourier transform at 20 orders is used for constructing a T wave matrix.
Step S4: constructing a T-wave tensor space
Sequentially arranging N T wave matrixes according to the occurrence sequence of T waves to obtain a third-order tensor of Mx (2N +1) xN; see figure 2.
Step S5: tensor resolution
Carrying out tensor decomposition on the third-order tensor by adopting a Tucker decomposition method to obtain a core tensor G and projection matrixes in three projection directions, wherein the projection matrixes U correspond to fractional Fourier transform order directions1Projection matrix U of corresponding order of T wave vector direction2Projection matrix U corresponding to the direction of the heartbeat3；
Step S6:
projection matrix U corresponding to central shooting direction3And calculating an entropy value which is taken as the T wave characteristic of the section of electrocardio. To projection matrix U3And solving the mean value of each column to obtain a one-dimensional row vector, and solving the entropy value of the row vector to obtain the entropy value of the projection matrix. The entropy may be some of shannon entropy, renyi entropy, approximate entropy, sample entropy, and the like. The present embodiment uses shannon entropy.
Or, in step S6, the entropy value is an entropy vector, and the calculation method is as follows:
to projection matrix U3And calculating entropy values of each row, and sequentially arranging the obtained entropy values according to the row number to obtain the entropy vector of the projection matrix. Projection matrix U3The entropy calculation method for each row is as follows:
will project the matrix U3Normalizing each point value, namely enabling the value range of each point value to be in an interval of 0 to 1; then dividing the space between 0 and 1 into m partitions equally; calculate the probability that the value of each point in the row falls in each partition, let line xThe probability that each point falls in the q-th subarea is pxqThe value is the point number of the line falling in the q-th subarea divided by the total point number of the line, q is more than or equal to 1 and less than or equal to m, and the entropy E of the x-th line is calculated according to the following formulax
The logarithm takes 2 as the base, or takes other logarithm bases, and the logarithm bases can be converted by a base-changing formula. The projection matrix U can also be aligned according to the above-mentioned idea3And calculating entropy values of each column, and arranging the obtained entropy values once according to the column number to obtain the entropy vector of the projection matrix.
When the extracted features are used for detecting whether a T wave alternate TWA phenomenon appears in the section of electrocardiosignals: firstly, establishing data sets of two types of samples of electrocardio with TWA and electrocardio without TWA, wherein the number of T waves contained in each section of electrocardio is more than or equal to 8, and then extracting the T wave characteristics from the electrocardio in the data sets for training a classifier; the number of T waves contained in the electrocardiosignal to be detected is consistent with the number of T waves contained in the training sample; and after the classifier finishes training, extracting the T wave characteristics of the electrocardiosignals to be detected, inputting the T wave characteristics into the classifier, and judging whether the T wave alternate TWA phenomenon occurs or not by the classifier.
In this example, it is desirable to detect whether there is a TWA phenomenon in a section of electrocardiogram, and what needs to be solved is a two-classification problem, so the embodiment adopts a simple, general and efficient SVM algorithm (when the sample size of a data set increases, the classification effect can be further improved by modeling with other machine learning algorithms), and the results are as follows:
when the 20 fractional Fourier transform orders are in different ranges, the electrocardio length of each sample is 2 minutes, and the detection effect of TWA is as follows:
when the number of T waves used for constructing the third-order tensor is 8, 30 and 60 respectively, the TWA detection effect when the 20 fractional order Fourier transform order ranges are 0.5-1 is as follows:
the method can further improve the performance after the combination of the optimized parameters by combining with a machine learning algorithm, and can also be used for the identification and classification of other types of electrocardio.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can understand that the modifications and substitutions within the technical scope of the present invention disclosed by the present invention should be covered within the scope of the present invention, and therefore, the scope of the present invention should be subject to the protection scope of the claims.
Claims (9)
1. An electrocardio T wave feature extraction method based on fractional Fourier transform and tensor decomposition is characterized by comprising the following steps:
step S1: continuously acquiring electrocardiosignals containing P cardiac cycles and preprocessing the electrocardiosignals to obtain a signal d; the number P of cardiac cycles contained in the section of electrocardio is more than or equal to 8;
step S2: performing QRS complex positioning on the signal d preprocessed in the step S1 to obtain a starting point and a stopping point of each QRS complex and position information of an R wave peak of the QRS complex;
step S3: constructing T-wave matrices
S3-1: positioning the starting point and the ending point of the T wave between every two adjacent QRS complexes, namely between the ending point of the first QRS complex and the starting point of the second QRS complex, and calculating the number X of sampling points between the starting point and the ending point of the T wave; then searching a maximum value between the starting point and the end point of the T wave, and taking the maximum value as a peak value of the T wave;
the number of the detected T waves is N, and N is less than or equal to P; the minimum value of X corresponding to each detected T wave is set as the minimum sampling point number Xmin；
For each detected T wave peak, taking the position of the T wave peak as a central sampling point, respectively taking n sampling points to the left side and the right side of the T wave peak, adding 2n +1 sampling points of the T wave peak, and arranging according to the time sequence to form a T wave vector of the T wave with the length of 2n +1 points;
the point number 2n +1 is less than or equal to the minimum sampling point number X between the starting point and the end point of the T wavemin；
S3-2: respectively performing M fractional order Fourier transform on T wave vectors with the length of 2n +1 points of each T wave, and performing i-order fractional order Fourier transform on the jth T wave vector to obtain a signal D with the length of 2n +1 pointsji(ii) a Wherein j is less than or equal to N, i is less than or equal to 1 and the M fractional Fourier transforms are combined in the same order for all T waves;
s3-3: calculating each signal Dji(iv) fractional Fourier magnitude spectral signal Fvji；
S3-4: for each T wave, taking M fractional Fourier magnitude spectrum signals of different orders as row vectors, and arranging the row vectors from top to bottom in sequence according to the order of fractional Fourier transform from small to large to form a T wave matrix of M rows X (2n + 1); step S3-1 detects N T-waves in total and thus N such matrices;
step S4: constructing a T-wave tensor space
Sequentially arranging N T wave matrixes according to the occurrence sequence of T waves to obtain a third-order tensor of Mx (2N +1) xN;
step S5: tensor resolution
Carrying out tensor decomposition on the third-order tensor by adopting a Tucker decomposition method to obtain a core tensor G and projection matrixes in three projection directions, wherein the projection matrixes U correspond to fractional Fourier transform order directions1Projection matrix U of corresponding order of T wave vector direction2Projection matrix U corresponding to the direction of the heartbeat3；
Step S6:
projection matrix U corresponding to central shooting direction3And calculating an entropy value which is taken as the T wave characteristic of the section of electrocardio.
2. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claim 1, wherein the method comprises the following steps: in step S6, the entropy value is an entropy vector, and the calculation method is as follows:
to projection matrix U3And calculating entropy values of each row, and sequentially arranging the obtained entropy values according to the row number to obtain the entropy vector of the projection matrix.
3. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claim 1, wherein the method comprises the following steps: the entropy calculation method in step S6 includes:
to projection matrix U3And solving the mean value of each column to obtain a one-dimensional row vector, and solving the entropy value of the row vector to obtain the entropy value of the projection matrix.
4. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claim 1, wherein the method comprises the following steps:
the preprocessing in the step S1 includes removing power frequency interference, myoelectric interference, and baseline wander from the electrocardiographic signal.
5. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claim 2, wherein the method comprises the following steps: step S6, projecting matrix U3The entropy calculation method for each row is as follows:
will project the matrix U3Normalizing each point value, namely enabling the value range of each point value to be in an interval of 0 to 1; then dividing the space between 0 and 1 into m partitions equally; calculating the probability of each partition falling on the numerical value of each point in the row, and making the probability of each point in the x-th row falling on the q-th partition be pxqThe value is the point number of the line falling in the q-th subarea divided by the total point number of the line, q is more than or equal to 1 and less than or equal to m, and the entropy E of the x-th line is calculated according to the following formulax
The logarithm takes 2 as the base, or takes other logarithm bases, and the logarithm bases can be converted by a base-changing formula.
6. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claim 1, wherein the method comprises the following steps:
and when the extracted T wave features of the section of electrocardio are used for electrocardio signal classification, training a classifier as a feature vector, and then classifying.
7. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claims 1 and 6, wherein: when the extracted features are used for detecting whether a T wave alternate TWA phenomenon appears in the section of electrocardiosignals: firstly, establishing data sets of two types of samples of electrocardio with TWA and electrocardio without TWA, wherein the number of T waves contained in each section of electrocardio is more than or equal to 8, and then extracting the T wave characteristics from the electrocardio in the data sets for training a classifier;
the number of T waves contained in the electrocardiosignal to be detected is consistent with the number of T waves contained in the training sample;
and after the classifier finishes training, extracting the T wave characteristics of the electrocardiosignals to be detected, inputting the T wave characteristics into the classifier, and judging whether the T wave alternate TWA phenomenon occurs or not by the classifier.
8. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claim 1, wherein the method comprises the following steps: in step S3-4, M is less than or equal to 20.
9. The method for extracting electrocardiograph T wave characteristics based on fractional Fourier transform and tensor decomposition as claimed in claims 1-8, wherein: in step S3-3: calculating each signal Dji(iv) fractional Fourier magnitude spectral signal FvjiThereafter, for each T wave, for each fractional Fourier magnitude spectral signal FvjiNormalizing by using the minimum value of the maximum value under the order i as a referenceLet each FvjiEach point of (1) is in the interval of 0 to 1; and obtaining a normalized fractional Fourier magnitude spectrum signal with the length of 2n +1 points.
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| CN116570295A (en) * | 2023-07-14 | 2023-08-11 | 浙江好络维医疗技术有限公司 | Electrocardiogram low-voltage T-wave end point positioning method |
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