A Precise Frequency Recognition Method of Short-Time SSVEP Signals Based on Signal Extension

Objective: Improving the Information Transfer Rate (ITR) is a popular research topic in steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs). The higher recognition accuracy of short-time SSVEP signal is critical to improving ITR and achieving high-speed SSVEP-BCIs. However, the existing algorithms have unsatisfactory performance on recognizing short-time SSVEP signals, especially for calibration-free methods. Method: This study for the first time proposed improving the recognition accuracy of short-time SSVEP signals based on the calibration-free method by extending the SSVEP signal length. A signal extension model based on Multi-channel adaptive Fourier decomposition with different Phase (DP-MAFD) is proposed to achieve signal extension. Then the Canonical Correlation Analysis based on signal extension (SE-CCA) is proposed to complete the recognition and classification of SSVEP signals after extension. Result: The similarity study and SNR comparison analysis on public SSVEP datasets demonstrate that the proposed signal extension model has the ability to extend SSVEP signals. The classification results show that the proposed method outperforms Canonical Correlation Analysis (CCA) and Filter Bank Canonical Correlation Analysis (FBCCA) significantly in the measure of classification accuracy and information transmission rate (ITR), especially for short-time signals. The highest ITR of SE-CCA is improved to 175.61 bits/min at around 1s, while CCA is 100.55 bits/min at 1.75s and FBCCA is 141.76 bits/min at 1.25s. Conclusion: The signal extension method can improve the recognition accuracy of short-time SSVEP signals and further improve the ITR of SSVEP-BCIs.


A Precise Frequency Recognition Method of Short-Time SSVEP Signals Based on Signal Extension I. INTRODUCTION
B RAIN-COMPUTER interface (BCI) is a direct information pathway established between the brain and external devices without depending on the normal human neural pathways, which allows patients who suffer from severe motor disabilities or communication difficulties to control and interact with external devices with brain activity [1]. When human eyes are stimulated by external signals, the electrical activity in the brain, called visual evoked potential (VEP), will be triggered in the visual cortex. As for the external visual stimulus that is continuous (generally >3 Hz), the EEG in the visual cortex will be modulated to form the steady-state visual evoked potential (SSVEP) [2]. Over the past decades, SSVEP has become the most widely used BCI paradigm and demonstrated its great potential for real-life applications [3], [4], [5], [6].
Improving the Information Transfer Rate (ITR) is a popular research topic in SSVEP-BCIs. In the past decades, many advanced encoding techniques and powerful stimulus presentation methods have effectively solved the problem of the limited number of stimuli that can be encoded in a small frequency-band range and presented by computer displays, such as Chen et al. used the joint frequency-phase modulation (JFPM) method to achieve high-speed speller with 40 stimulus targets in a limited frequency band [4]. Han et al. used motion checkerboard stimulation to design BCI speller with 80 stimulus targets [6]. In addition, Chen et al. used multi-frequency sequence coding (MFSC) to encode and present 160 stimulus targets [7].
The key to improving ITR is the SSVEP recognition algorithm performance, especially achieving high recognition accuracy using shorter-time SSVEP signals. With the advances in decoding schemes, it is obvious to witness significant progress in the accuracy and ITR improvements of the SSVEP-BCIs in the past years [8], [9], [10], [11]. In 2007, Canonical Correlation Analysis (CCA) [11] was used for SSVEP decoding, and CCA had become the benchmark of SSVEP decoding because it applies the spatial information between multi-channel signals and has better decoding performance compared with Fourier Transform (FT) and other methods. In recent years, researchers have extended CCA from different perspectives to further improve the decoding performance for SSVEP. Some researchers improve the recognition accuracy by optimizing the standard reference template to include more EEG information, such as Multiway Canonical Correlation Analysis (MwayCCA) [12], [13], Multiset Canonical Correlation Analysis (MsetCCA) [14], Individual Template Canonical Correlation Analysis-Based Methods (IT-CCA) [15] et al. Phase Constrained Canonical Correlation Analysis (P-CCA) [16] is optimized from the perspective of phase by recognizing the phase of SSVEP responses based on the apparent latency, which can identify different phases of the same frequency, but abundant computation limits its practical application. Filter Bank Canonical Correlation Analysis (FBCCA) [8] from the perspective of harmonic enhancement makes full use of SSVEP harmonic components and becomes the state-of-the-art method among calibration-free methods. Extended Canonical Correlation Analysis (eCCA) [4], [17], in where incorporates the averaged superimposed EEG signals with the standard reference signal template to construct three spatial filters for enhancing the target classification performance. CCA requires the spatial filters to be orthogonal, which is difficult to do for complex SSVEP signals [18], therefore, Correlated Component Analysis (CORRCA) [19] was introduced into the SSVEP-BCI system to compute the same spatial filter for two multichannel signals by learning the calibration data and maximizing the linear components of the two multichannel signals. Task-Related Component Analysis (TRCA) [9] improves signal SNR and classification accuracy by training spatial filters from calibration data to extract task-relevant components and maximize the similarity of the same task across trials. The SSVEP introduced by different stimulus frequency have the same spatial pattern, hence Ensemble Task-Related Component Analysis (eTRCA) [9] use ensemble spatial filters strategy to decoding SSVEP within a very short data length, and thus achieving an extremely high ITR.
However, the performance of calibration-free (or trainingfree) methods such as CCA and FBCCA et al. is poor for short-time SSVEP signals. Compared with calibration-free methods, calibration-based (training-based) methods such as MwayCCA, MsetCCA, IT-CCA, eCCA, CORRCA, TRCA and eTRCA et al. have better performance. But these calibration-based methods require a large amount of the subject's SSVEP data (or labeled data, calibration data) to obtain recognition model parameters (spatial filters, EEG templates et al.), which is time-consuming, the long-time calibration progress easily leads to fatigue, resulting in a poor experience for the subject in using SSVEP-BCIs, and further limits the development and practical application of high-speed SSVEP-BCIs.
To tackle the calibration issue, many researchers have developed ways to reduce calibration data, such as cross-subject spatial filter transfer methods in [10] and [20], cross-subject EEG template transfer methods in [21], cross-target spatial filter transfer methods in [21], [22], [23], and [24], crosstarget EEG template transfer methods in [23], [25], and [26]. Besides, using online unlabeled data from previous trials to update spatial filter trail by trail based on calibration-free methods in [22]. In [25], the time-frequency-joint representation and the multi-channel adaptive Fourier decomposition with different Phase (DP-MAFD) were proposed to transfer common components and reconstruct SSVEP signal across stimuli. Although these methods enhance the recognition performance for short-time SSVEP signals, which is still poor, the performance of these methods is seriously limited by the amount of calibration data [23], [24] or the prediction accuracy of historical trail data labels [22].
Some researchers adjust data length (or time-window length) adaptively for the tradeoff between detection speed and detection accuracy through an adaptive scheme [27], [28], [29], [30]. Although they got higher ITR, they didn't explore ways to improve the recognition accuracy of short-time SSVEP signals.
A user-friendly SSVEP-BCI prefers no calibration and uses short-time SSVEP signals for its target recognition methods. However, thus far, there is no effective solution for precise target recognition of short-time SSVEP signals based on calibration-free methods. Previous studies have demonstrated that the recognition accuracy can be improved as the longer SSVEP signal length is used [8], [9], [10], [31], [32]. The main reason for this is that CCA and its extended methods, which are based on covariance matrix estimation, could become unreliable in the case of short-time signals, and the obtained spatial filter may be inaccurate. If the SSVEP signal contains the sufficient period number of interest features, CCA et al. based on statistics will achieve reliable recognition. In conclusion, the longer the signal length, the more beneficial to improve the recognition accuracy. Inspired by the above, this study from a new perspective proposes improving the poor recognition performance of short-time SSVEP signals based on the calibration-free method by signal extension method to further improve the ITR. The main contributions of this study lie in the following aspects: 1. This study proposes improving the recognition performance of short-time SSVEP signals based on the calibration-free method using the signal extension strategy for the first time, which provides a novel way for SSVEP recognition. 2. A SSVEP signal extension method based on DP-MAFD (DP-MAFD-SEM) is proposed. 3. A recognition method CCA based on signal extension (SE-CCA) is proposed to accomplish the recognition and classification of SSVEP signals after extension. 4. The experimental results on public SSVEP datasets demonstrate that our proposed method has higher recognition accuracy and ITR than the state-of-the-art calibration-free method FBCCA, especially for shorttime signals.
The later section is organized as follows: section II provides the proposed method, and section III verifies the feasibility of the DP-MAFD-SEM for SSVEP signal extension and evaluates the classification performance of the proposed method SE-CCA. The paper discusses covered in section IV and Conclusion in section V.

A. SSVEP Dataset
This study used the widely-used and reliable Benchmark dataset collected by the Tsinghua group [33]. The dataset includes SSVEP-BCI recordings of 35 healthy subjects focused on 40 stimulus targets flickering at different frequencies (from 8-15.8 Hz with an interval of 0.2 Hz). For each subject, the experiment is made up of 6 blocks, each containing 40 trials corresponding to all 40 stimulus targets presented in random order. Each trial began with a 0.5s target cue. Then, all stimuli were flashed on the screen for 5s. Finally, the screen was blanked for 0.5s before the next trial. 64 channels of EEG signals were recorded and sampled down to 250 Hz. A notch filter at 50 Hz was used to remove power-line noise. The channel selected for SSVEP signal analysis in this study were O1, O2, Oz, PO3, PO4, POz, PO5, PO6, and Pz. The first 0.14s SSVEP data after stimulus onset is removed due to the visual delay in the human eye under SSVEP stimulation [4]. In addition, the EEG data from each 6s-trial were filtered using band-pass filters with low and high cutoff frequencies of 6 Hz and 90 Hz, respectively, according to the range of stimulation frequencies.

B. Basis of SSVEP Signal Extension
With the pursuit of higher ITR and the application of SSVEP-BCIs in real life, shorter SSVEP signal lengths are being used, but shorter SSVEP signal lengths lead to lower classification accuracy, as shown in Fig. 1, which demonstrates the impact of signal length in different spatial filters obtained by CCA. The result is the statistic of all blocks of all subjects from the Benchmark dataset. The blue curve shows the result of standard CCA for target recognition with different SSVEP signal lengths. The green curve indicates using the spatial filters obtained by 5s-SSVEP signals for target recognition with different SSVEP signal lengths. The purple curve indicates using the spatial filters obtained by 1s-SSVEP signals for target recognition with different SSVEP signal lengths. The result reveals that: i) As the signal length increases, the classification accuracy higher.
The spatial filter is considered as one of the most important parameters in EEG-BCIs because it directly affects the signal-to-noise ratio (SNR) of multi-channel EEG data [15], [25], [34]. Many researchers study by obtaining better spatial filters to realize higher recognition accuracy. The spatial filter represents the subject's spatial pattern, each subject has his/her own spatial pattern [23]. Therefore, the spatial filter obtained by SSVEP signals can be considered as the observed value of the real spatial pattern.
ii) As the signal length increases, the obtained spatial filter becomes more and more precise.
In other words, with the increase of SSVEP signal length, the obtained spatial filter gradually approximates the real spatial pattern. And the spatial filter obtained by the 5s-SSVEP signal is preferable to 1s.
As above discussed, the purple curve in Fig. 1 can be regarded as the impact of SSVEP signal length for target recognition accuracy using a poor spatial filter, while a better spatial filter was utilized in the green curve. The blue curve is the normal CCA recognition result, which can be regarded as the impact of the combination of SSVEP signal length increases and the spatial filter gets better for target recognition accuracy. Assuming that the effect of the spatial filter and signal length on SSVEP recognition performance is linearly superimposed, the difference between the blue and purple curves can be considered as being caused by the difference in spatial filter performance, while the difference between the blue curves and red dotted line can be considered as being caused by the signal length. And the difference between green and purple curves can be considered as being caused by the difference of spatial filter. The difference between the blue and purple curves is smaller than the difference between the purple curve and the red dotted line, and the difference between green and purple curves decreases with signal length increase. If the above hypothesis is true, then it reveals that the impact of SSVEP signal length on target recognition accuracy is more significant than the impact of spatial filter, and the difference caused by the difference of spatial filter can be compensated by the SSVEP signal length. In other words, once the signal length is long enough, even a poor spatial filter can achieve high recognition accuracy. In conclusion: iii) signal length also plays an important role in SSEVP decoding, and may be more critical than the spatial filter.
Based on the above three observations, it's a good idea to realize higher recognition accuracy with a longer signal. However, the longer signal cannot be obtained due to the pursuit of high ITR and fast response speed required in practical applications. To address the above problems, this study proposes extending the SSVEP signal length by signal extension to improve the target recognition accuracy based on the calibration-free method for short-time SSVEP signals. Furthermore, SSVEPs are time-locked and phase-locked and have the same rhythm as visual stimuli, so they have a certain periodicity and regularity to be easily extended. In this study, the following three principles are established for SSVEP signal extension: (1) The SSVEP signal after extension should maintain the rhythm of the main components and have a high correlation with the real SSVEP signal.
(2) The SSVEP signal after extension has the same spectral distribution as the real SSVEP signal with the same signal length.
(3) Compared with the SSVEP signal before extension, the SSVEP signal after extension has a higher signal-to-noise ratio (SNR).

C. SSVEP Signal Extension Model
It's difficult to realize signal extension accurately without training data. Wang et al. proposed Multi-channel adaptive Fourier decomposition with different Phase (DP-MAFD) for extracting the common components of SSVEP signals evoked by different stimulus frequencies to reconstruct cross-target SSVEP signals [25]. Furthermore, DP-MAFD decomposes signals with explicit mathematical explanations. Therefore, it's possible to realize signal extension by time shift when reconstructing the signal after utilizing DP-MAFD decompose SSVEP signal. Inspired by the above, this study proposes a signal extension model based on DP-MAFD (DP-MAFD-SED) to realize the extension of short-time SSVEP signal length.
DP-MAFD-SED uses DP-MAFD to decompose one or more stimulus-frequency SSVEP signals simultaneously for extracting common features, then the common features are used to reconstruct SSVEEP signals, and the signals are extended by time shift during reconstruction. The details are shown in Fig. 2.
If the SSVEP signals with J stimulus frequencies (source stimuli) are used to construct the extended model, all the SSVEP signals of the c-th channel are chosen to construct a new signal set S c (S c ∈ R J ×L where L is the signal length), S c represents averaged SSVEP signals across trails of all source stimulus for the c-th channel and can be described as: where x c,J (t)(x c,J (t) ∈ R 1×L ) denotes averaged SSVEP signal across trails of the j-th stimulus with stimulus phase θ j for the c-th channel, Fs is the sample frequency. Then DP-MAFD is used to decompose S c . The SSVEP signals induced by different stimulation frequencies are synchronized by time-frequency-joint representation to emphasize common components. The transformations between signals in the time domain and time-frequency-joint representation are defined as follows: where s(θ ) denotes the time-frequency-joint representation.
x(t) denotes the SSVEP signal in the time domain, T stim denotes the period of stimulus, θ stim denotes the stimulus phase.
In new SSVEP signal model, which can be described as: s stim (θ ) denotes common periodic component in the timefrequency-joint representation, which is periodic with the period of 2π and is the same for different stimuli. w stim (θ ) denotes uncommon periodic component in the time-frequencyjoint representation, which is also periodic with the same period as s stim (θ ). n stim is noise. s stim (θ ) can be shared between different stimuli, while w stim (θ ) can't. s stim (θ ) can be regarded as the SSVEP-task signal, w stim and n stim can be regarded as signals unrelated to the SSVEP task [25]. The aim of DP-MAFD decomposes SSVEP signals is extracting s stim (θ ).
The DP-MAFD generates adaptive bases B c,n (θ ) based on the matching pursuit process [25], [35], [36] to realize adaptive signal decomposition, where a c,n ∈ D, D = {z ∈ C : |z| < 1}, C is the complex plane, and n denotes the decomposition level [25], [35], [36], c is the c-th channel. The basic components in B c,n ∞ n=1 is periodic with period 2π . B c,n determined by a c,n .
The signal x c, j (t) must be transferred to DP-MAFD analytic signals g c, j (t), which can be denoted as: where H {·} represents the Hilbert transform. To guarantee a fast signal decomposition in terms of energy convergence and thus make the decomposition components A c, j,n B c,n (θ ) match well with the processed signal and so that the decomposed components match all single-period signals (SPSs), the basis parameter a c,n can be obtained by the following equation: whereθ is limited to one period from θ j to θ j + 2π and repeatedly applied to all periods of the c-th channel of the j-th source frequency for focusing on analyzing SPSs. Thus, θ = 2π f j t − 2π d + θ j , d = t/T j , ⌊·⌋ denotes obtaining the largest integer less than or equal to the input, T j is the period of the j-th stimulus. And t 1 is defined in dT j , (d + 1)T j for each value of d, D j = T w /T j , and T w is the total signal length of the processed signal. e a θ is the evaluator of searching a c,n and is defined as: G c, j,n (t 1 ) is called the reduced remainder and can be obtained through the following recursive procedure: where A c, j,n denotes the decomposition coefficient of the n-th decomposition level of the c-th channel of the j-th source frequency, which can be calculated by A c, j,n = G c, j,n (t 1 ) , e {ac,n} θ .
The total number of decomposition level N 0 is set as 50 in this study. After the decomposition is completed by DP-MAFD, the common components of the SSVEP signal are obtained by selecting the decomposed components. The energy of the task-related components in the SSVEP signal should be much higher than that of the non-task-related components, so the levels of decomposition according to common component should be in the first N c decomposition levels and satisfy the following relation: where ϵ denotes a small positive number, and the selection parameter α can be set according to the noise level of the processed signals, in this study α is equal to 0.9. After decomposing signal channel by channel through the above operation, the corresponding decomposition coefficients A c, j,n , the basis B c,n (θ ) and N c are obtained, therefore signal can be reconstructed by: where t 2 = [ 1 Fs , . . . , L+L 1 Fs ],X c,i denotes the reconstructed signal of the c-th channel of the i-th stimulus,θ = 2π f i t 2 − 2π d + θ i , d = ⌊t 2 f i ⌋ , f i denotes the i-th stimulus frequency, θ i denotes the i-th stimulus phase. Since SSVEP signals with closed stimulus frequencies are more similar, choosing the decomposition coefficient A c, j,n of the source stimulus frequency f j closest to f i as A c,i,n , when the number of source frequencies is greater than 1 and f i is not the same as the source stimulus frequencies.
Finally, the signal after extension can be obtained by: whereX ext denotes the signal after extension, X(X ∈ R C×L ) denotes the tested signals.X f i (X f i ∈ R C×L 1 ) denotes the segment of the extended signal, L 1 is the length ofX f i .X f i can be obtained by: . . .

D. Recognition Method of SSVEP Based on Signal Extension
After establishing the extension model, a recognition method Canonical Correlation Analysis based on signal extension (SE-CCA) is proposed to accomplish the recognition and classification of SSVEP signals, the details are shown in Fig. 3.
For two sets of multidimensional variable signals X and Y , the goal of CCA is to find two sets of linear projection vectors w X and w Y to maximize the correlation coefficients of the linear combinations w T X X and w T Y Y . The maximum correlation coefficient of X and Y can be obtained by: Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
where X denotes multi-channel EEG, the reference signal Y at the stimulus frequency f i can be constructed by: (15) where k represents the number of EEG harmonics, in this study k = 5.
The signal extension is applied to the tested signal at each frequency, which can be expressed as: then, the correlation coefficient is calculated with the corresponding reference signal Y f i by CCA, the correlation coefficient is calculated by: The frequency corresponding to the maximum correlation coefficient is regarded as the final recognition result:

E. Analysis Method
Firstly, the feasibility of the proposed signal extension model for SSVEP signal extension is verified to lay the foundation of SE-CCA. The feasibility was verified by similarity analysis in the time and frequency domain between the SSVEP signal after extension and the real SSVEP signal and SNR comparison between the SSVEP signal after extension and the SSVEP signal before extension. The similarity is evaluated by the Pearson correlation coefficient. In this study, for SNR comparison, the noise is defined as the average of the squared amplitudes of the spectrum of all frequencies except the target frequency, the frequency range is from 8Hz to 15.8Hz with an interval of 0.1Hz. And the SNR can be calculated by: where A denotes the amplitude of the spectrum according to frequency f . Then, the classification accuracy and ITR were used to estimate the performance of the proposed method. The accuracy and ITR of each subject are expressed as mean values by superimposing and averaging the accuracies of all blocks of all subjects. And the ITR was calculated as: where P is the classification accuracy, and N is the number of stimuli, in the Benchmark dataset N = 40. T det is the sum of the time window length of the real EEG signal length used for recognition and time offset or visual delay (0.14s is taken in this study). This study focuses on the effectiveness of signal extension methods for the frequency recognition of short-time SSVEP signals. Since signal extension methods are mainly applied to calibration-free methods, so it is compared with CCA and FBCCA, where FBCCA and CCA use the same harmonic as the proposed method with 5, and FBCCA uses the number of sub-bands with 5, and the parameters are set to a = 1.25 and b = 0.25 in FBCCA, as recommended in [8]. And Paired-test was used to determine significant differences in accuracy and ITR for different methods.

III. RESULT A. Feasibility of SSVEP Signal Extensional Model
The feasibility of the proposed SSVEP signal extension model for SSVEP signal extension was verified by similarity analysis and SNR comparison in the time and frequency domains. Firstly, the SSVEP signals were averaged across all 6 trials for each stimulus. Then one source stimulus is randomly selected and the first 1s-SSVEP signal was used to construct the DP-MAFD-SEM. Finally, the SSVEP signal lengths are extended from 1s to 2s for each stimulus, obtaining the SSVEP signal after extension. The averaging Pearson correlation coefficient is 0.7493 ± 0.0813 for all stimuli of 35 subjects on the Oz channel between the SSVEP signal after extension and the real SSVEP signal with 2s length in the time domain, while the averaging Pearson correlation coefficient is 0.7973 ± 0.1111 in the frequency domain. The averaging SNR is 10.5628 ± 4.6764 for all stimuli of 35 subjects on the Oz channel on the SSVEP signal after extension, while 4.7549 ± 2.0320 on the SSVEP signal before extension. Fig. 4  shows the comparison of the signals in the time and frequency before and after signal extension, red is the SSVEP signal after extension, black is before extension, and only the Oz channel is used as an example. The signals are all from subject 3, and the stimulus frequencies of (a) (b) (c) (d) are 8.4 Hz, 9.6 Hz, 11.8 Hz, and 14.2 Hz, respectively. The spectrograms of the SSVEP signals after extension had the same distribution as the SSVEP signals before extension, and the energy of the signals is enhanced at the main components. Fig. 5 shows the comparison of the real SSVEP signal with the SSVEP signal after extension in the time and frequency domains, with the real SSVEP signal in black and the SSVEP signal after extension in red, and only the Oz channel is chosen as an example. The signals are all from subject 3, and the stimulus frequencies of (a) (b) (c) (d) are 8.4 Hz, 9.6 Hz, 11.8 Hz, and 14.2 Hz, respectively. This comparison shows the main components of the SSVEP signals after extension according to stimulus frequency are the same as the real SSVEP signals.
In summary, the extended signals are highly correlated with the real signals in time and frequency domains, and the extended signal maintains the rhythm of the main components of the original signal and enhances the energy of the main components of the SSVEP. The results above all verified the feasibility of the proposed signal extension model for the SSVEP signal extension.

B. Classification Performance of SSVEP Based on Signal Extension
All data from the Benchmark dataset (35 subjects, 40 stimuli, 6 blocks) were used to test the classification performance of the proposed method. The performance of the classification was evaluated by the classification accuracy and the ITR. For each subject, one source stimulus was randomly chosen to construct DP-MAFD-SEM, with averaging across all 6 trials. To avoid the stochastic effects, the source stimulus is selected five times without repetition, and the classification results were averaged as the final results. The length of the SSVEP signal after extension is twice the length of the SSVEP signal before extension (original signal). Fig. 6(a) and (b) show the classification performance of three methods. The proposed method in this study significantly outperforms the other two methods, especially for short-time SSVEP signals within 2s. The proposed method achieves higher accuracy with shorter signals, and the recognition accuracy reaches more than 80% at 1.25s signal length. The recognition accuracy within 2s is substantially improved compared to FBCCA and CCA. The proposed method achieves higher ITR with shorter signals and reaches the highest ITR of 175.61 bits/min at around 1s signal length, which is much higher than the highest ITR of 141.76 bits/min at around 1.25s for FBCCA and 100.55 bits/min at around 1.75s for CCA.
For the differences in classification performance due to individual differences for different subjects, Fig. 7 shows the maximum ITR of 35 subjects, with each point represents the maximum ITR of each subject. All the points in Figure 7  region and far away from the red diagonal line, which indicates that the proposed method outperforms CCA and FBCCA.

C. Effects of Source Stimulus Number on Classification Performance
The SSVEP signal extension method proposed in this study requires at least one source-stimulus SSVEP signals to construct the DP-MAFD-SEM. And Fig. 8 shows the impact of the number of source stimuli on the classification performance. For each number of source stimuli, the source stimuli were randomly selected and averaged across all 6 trials to construct the DP-MAFD-SEM. The length of the SSVEP signal after extension is twice the length of the SSVEP signal before extension. To avoid the stochastic effects, the source stimulus is selected five times without repetition and the classification results are averaged. The result shows that when the signal length is below 1.75s, the performance of classification is improved as the number of source stimuli increases but no significant effect on the signal length above 1.75s. When the signal length is above 1.75s, the DP-MAFD-SEM constructed with 1 source stimulus has the best performance, and the DP-MAFD-SEM constructed with 2 source stimuli always has the worst performance.
The possible reason for this is that realizing classification is determined by the common periodic components (s stim ) and the non-common periodic component (w stim ) with frequency specificity. But the DP-MAFD-SEM extends the signal length only by extracting the common components of the SSVEP signals. As the number of source stimuli increases, the extracted feature contains more common periodic components and fewer non-common periodic components. Therefore, the common features in the extended signal are enhanced and the non-common periodic features are weakened, which is consistent with the result that the recognition performance becomes better with the increase of the number of source stimuli when the number is larger than 1. When the number of source stimuli is equal to 1, the non-common periodic components have the largest percentage, leading to better classification than the number of stimulus source is 2. But the long-time signals have sufficient periods of interest signals and also lack non-common periodic features to distinguish targets from different stimuli, resulting in more effective recognition performance for long-time signals using one source stimulus. Although increasing the number of source stimuli to construct the signal extension model can improve the classification performance, especially for the short-time signal length, which will lead to a large amount of calibration data required and a tedious process of collecting data. Overall, the DP-MAFD-SEM constructed by one source stimulus has better performance, so one source stimulus is recommended to construct the SSVEP signal extension model in this study. Fig. 9 shows the impact of different SSVEP signal extension lengths on classification performance. The DP-MAFD-SEM is constructed by the SSVEP signals averaged according to one source stimulus selected randomly and non-repeatedly, and the length of the SSVEP signal is extended 0.5 times (0.5×), 1 time (1×), 1.5 times (1.5×) and 2 times (2×). To avoid the stochastic effects, the source stimulus is selected five times and the results of classification are averaged. The results show that the classification performance is best at about 1× for short-time SSVEP signals before the 2s-SSVEP signal, and at about 0.5× after the 2s-SSVEP signal. Within 2.5s, the classification performance rises and then falls as the signal length becomes longer, which is in line with our expectation, because there are some differences between the extended signal and the real signal, and it is impossible to achieve the same classification accuracy as the real signal that keeps rising as the signal length gets longer. Above 2.5s, the longer the length of the extension, the worse the classification performance is because the long-time signal already has sufficient common periodic components and lacks non-common periodic features. The part of the extension signal is mainly extended by the SSVEP signal extension model according to the common periodic features of SSVEP, therefore, when the length of the extended signal is longer, the non-common periodic features in the original signal will be weakened. But the performance after the extension is still better than that are not extended. The 1× always have high classification performance, therefore, the length of the SSVEP signal is extended 1× is recommended in this study.

E. Effects of Distribution of Source Stimuli on Classification Performance
Since SSVEP signals with closed frequencies shared more similarity, the different distribution of source stimuli frequency leads to different classification performances. Fig. 10 shows the impact of the distribution of source stimuli on the classification performance. The SSVEP signal extension models are constructed by three source stimuli, 9.6 Hz, 12 Hz, and 14.4 Hz, respectively. 12 Hz is the stimulus frequency in the middle of the range from 8 to 15.8Hz, which corresponds to the uniform distribution, while 9.6 Hz and 14.4 Hz correspond to the non-uniform distribution. Within 2.5s, the signal extension model constructed with uniform distribution source stimuli has better classification performance. From an overall view, the signal extension model constructed with uniform distribution source stimuli has high classification performance. It is recommended to choose uniform distribution when selecting the source stimuli for constructing the signal extension model.

IV. DISCUSSION
In this study, the method of signal extension is proposed for the first time to achieve higher recognition accuracy by using shorter signal lengths. It provides a novel way to improve the recognition accuracy of short-time SSVEP signals, further improving ITR. At present, the main ways to improve the recognition accuracy of short-time SSVEP signals are to train high-performance spatial filters and construct reference templates with real EEG signals (or EEG templates). However, these require a large amount of calibration data, which severely limits the development and practical application of SSVEP-BCIs. A user-friendly SSVEP-BCI prefers no calibration and uses short-time SSVEP signals for its target recognition methods. However, there is no effective target recognition scheme based on calibration-free for short-time SSVEP signals. Signal extension from the point of view of data, a more reliable spatial filter can be obtained by extending the signal length, and the SSVEP signals after extension have more periods of interest signals, resulting in reliable evaluation, such as CCA. Besides, based on the assumption in session III.B, we can know that compared with the spatial filter, the SSVEP signal length has a more significant impact on recognition accuracy. Therefore, signal extension is a good strategy to improve the recognition accuracy of short-time SSVEP signals. The results from IV.B also show that compared with CCA and FBCCA, the method based on signal extension strategy achieves higher recognition accuracy at shorter signals. The signal extension can effectively shorten the induction time of SSVEP-BCIS, and it will have a broader application prospect for BCI speller, BCI UAV, BCI wheelchair and other high-speed BCIs, BCI rehabilitation systems with short-term sequence requirements, and rapid visual acuity assessment based on SSVEP.
In [25], Wang et al. proposed a new SSVEP signal model, and pointed out that SSVEPs induced by different stimulus frequencies have high similarity in the time-frequency-joint representation, in other words, SSVEP-task signals are similar in SSVEPs induced by different frequencies, only the real EEG signals with signal states rotating at different speeds for different stimuli and being disturbed by non-SSVEP-related components. Therefore, SSVEP of the new target frequency can be constructed by extracting the common components for the SSVEP of other stimulus frequencies, which can be realized by DP-MAFD. The adaptive decomposition process of DP-MAFD has explicit mathematical explanations. Meanwhile, SSVEPs are synchronized by time-frequency-joint representation, and the signal is decomposed into a period of 0-2π for decomposition, which is beneficial to realize signal extension by extracting and using the characteristic of SSVEP, lays the groundwork for DP-MAFD-SED signal extension model proposed in this study. DP-MAFD-SED constructs the extension model with one or more stimulus-frequency SSVEP signals, using extracted SSVEP-task components and the time shift of adaptive bases generated by DP-MAFD to realize the extension of SSVEP signals of different frequencies. Based on current technology, it is very difficult to implement the extension of new signals without training data (or calibration data) based train-free methods, because we do not know the label and data distribution characteristics of the new signal. Although DP-MAFD-SED requires one or more stimulus-frequency SSVEP signals to construct the extension model, it is a better solution to achieve the highest recognition performance at the lowest cost.
Although the proposed method has a good classification performance, there are some limitations. First of all, the proposed signal extension model requires at least one stimulus-frequency SSVEP signal to construct the model, which cannot be achieved completely without calibration data. Therefore, the extension methods with zero-calibration data and can extend signal cross-subject are yet to be explored. Secondly, the study regards all SSVEP signals as in the steady state, and the extension method is linear, but the short-time signal, especially in the first 1s, the SSVEP signal undergoes a process from nothing to the steady state, and SSVEP is nonlinear and nonstationary, so more advanced extension techniques such as nonlinear extension techniques and extension methods of artificial neural networks are to be explored. Finally, the focus of this paper is to explore the feasibility of improving the classification accuracy of short-time SSVEP signals by signal extension method, without using more state-of-theart recognition methods, such as combining signal extension method with filter bank strategy [8], training spatial filter methods [4], [9], [24], recontributing EEG templates methods [23], [25], [26], chaotic detection [37]. And perhaps these techniques can further improve the classification performance of the proposed method for short-time SSVEP signals.

V. CONCLUSION
This study for the first time proposed a method to improve the recognition accuracy of short-time SSVEP signals by extending the SSVEP signal length. A signal extension model based on DP-MAFD (DP-MAFD-SEM) is proposed utilizing one or more stimulus-frequency SSVEP signals to achieve signal extension. A frequency recognition method based on signal extension (SE-CCA) is proposed to complete the recognition and classification of SSVEP signals after extension. The similarity study between the SSVEP signal after extension and the real SSVEP signal in the time and frequency domain demonstrates high similarity and the SSVEP signal after extension maintains the rhythm of the main components of the original signal. The SNR comparison between the SSVEP signal after and before extension shows the SSVEP signal after extension enhances the energy of the main components. These verify the feasibility of DP-MAFD-SEM for the SSVEP signal extension. Comparing classification performance, SE-CCA outperforms CCA and FBCCA significantly, and SE-CCA has higher classification accuracy and ITR, especially for shorttime signals. The highest ITR of SE-CCA is improved to 175.61 bits/min at around 1s, while CCA is 100.55 bits/min at 1.75s and FBCCA is 141.76 bits/min at 1.25s. The signal extension method realizes that utilizing shorter-time SSVEP signals achieves higher recognition accuracy. It provides a new idea and approach for the precise recognition of short-time SSVEP signals, which helps to further improve the accuracy and ITR of SSVEP-BCIs, promotes the development of high-speed BCIs, and facilitates the real-world application of SSVEP-BCI.