Fiber specklegram sensors are widely studied for their high sensitivity and compact design. However, as the number of modes in the fiber increased, the speckle sensitivity heightened along with the correlation diminished, lowering the sensing performance. This paper introduces an innovative method based on digital aperture filtering (DAF) that adopts physical principle analysis, which reduces the collection aperture by computationally screening out the energy of higher-order modes within the speckle, therefore enhancing the correlation among speckles. Subsequently, a multi-layer convolutional neural network is designed to accurately and efficiently identify the measurands represented from the filtered speckles. By comparing the experimental results of speckle demodulation method on different multimode fibers in light field direction sensing, the DAF method has shown outstanding performance in sensing accuracy, sensing range, stability, resolution, and generalizability, fully demonstrating its tremendous potential in the advancement of fiber sensing technology.