###### Abstract
The JFFT method capitalized on the sparsity inherent in time series data within the frequency domain, skillfully employing a limited number of learnable frequencies to adeptly capture temporal dependencies. Through extensive experimentation, the authors demonstrated that this method significantly enhanced prediction performance while concurrently reducing computational overheads, rendering it a promising and efficient approach for time series forecasting. Recently, the integration of the attention mechanism [15] within the domain of deep learning has garnered substantial traction, yielding promising and impactful outcomes. [PERSON] et al. [16] put forth an alternative prediction method for air pollutant concentrations, leveraging the Kalman filter, attention, and long and short-term memory (Kalman-attention-LSTM) model. The augmentation of the attention mechanism into the conventional LSTM architecture empowered the model with enhanced capabilities to effectively capture temporal information features. Through extensive experimentation, the researchers unveiled that the second prediction approach, employing the Kalman-attention-LSTM model, exhibited superior fitting results in comparison with six other competing models. This underscored the potential efficacy of the proposed method in advancing air pollutant concentration predictions. [PERSON] et al. [17] introduced a novel air quality prediction model called CNN-BiNLSTM-attention. This model comprised three essential components: CNN, BiNLSTM, and attention. The incorporation of attention was instrumental in effectively capturing the impacts of distinct temporal feature conditions on Air Quality Index (AQI) prediction, thereby facilitating more precise AQI predictions for the subsequent hour. The empirical findings demonstrated that the proposed CNN-BiNLSTM-attention model outperformed the other five models, rendering it a more suitable choice for air quality prediction tasks. In order to take full advantage of the frequency information of the PM2.5 concentration data as well as to enable the BiLSTM model to aggregate the attention to key positions, this paper establishes a TF-BiLSTM-attention model for PM2.5 concentration prediction among 12 monitoring sites in Beijing, China. This paper contributes to existing knowledge in the following ways:  
1. First, it uses DCT to transform the input data from the time domain to the frequency domain. Next, the amalgamation of the time domain dataset with the frequency domain dataset is executed to generate an integrated dataset. This unified dataset is designated as the model's input, enabling optimal utilization of frequency information while encompassing essential time domain information. 2. Adding the attention mechanism after the BiLSTM layer can improve the role of important time steps in BiLSTM, which can in turn improve the prediction effect of the model. Finally, using time frequency domain information, BiLSTM, and attention, it develops the TF-BiLSTM-attention model to predict PM2.5 concentration. 3. For the multivariate model, the input variables consist solely of the PM2.5 concentration at the site itself and at the remaining 11 sites within the study area, without considering the effects of other pollutant factors and meteorological factors. Empirical findings demonstrate that the multivariate model with these variables added has a good prediction effect.