Accurately estimating the state of charge (SOC) and state of health (SOH) of lithium-ion batteries remains a significant challenge due to complex electrochemical dynamics and varying operational conditions. This research aims to overcome these challenges by proposing a novel hybrid neural network that combines octave convolution (OctConv) and long short-term memory (LSTM). The methodology begins with preprocessing battery voltage, current, temperature, internal impedance, and capacity data through outlier removal and min-max normalization, followed by partitioning into training, validation, and test sets. The OctConv module then decomposes the input into high- and low-frequency feature maps, enhancing extraction efficiency by reducing spatial redundancy. These multi-scale features are subsequently processed by LSTM layers to model both short-term fluctuations and long-term degradation trends across battery cycles. The model was trained using the Adam optimizer with MSE loss and ReLU activations and evaluated against established deep learning approaches, including OCT, LSTM, and CNN-LSTM, on the NASA dataset. Experimental results demonstrate the superior performance of the proposed OCT-LSTM model. It achieved significant improvements in SOC and SOH estimation, reducing the mean squared error (MSE) by 84.53% and 82.44%, respectively, compared to the CNN-LSTM benchmark. Furthermore, the model attained a 6.21% reduction in simulation parameters, highlighting greater parameter efficiency. The proposed method outperforms state-of-the-art approaches across multiple metrics, including the number of parameters, MSE, RMSE, MAE, prediction accuracy, and computational speed, demonstrating its potential as a significant advancement in this domain.