Blind source separation (BSS), also known as audio signal separation, is the process of extracting individual sound sources from an audio mixture. This technique has widespread applications in audio signal processing, speech enhancement, and other related fields. The present study investigates the separation of sound signals contaminated by additive white Gaussian noise (AWGN). Due to the presence of such noise, accurately retrieving individual signals becomes a significant challenge. This work employs independent component analysis (ICA) to address the separation problem. A mixing matrix, incorporating down-sampled signals, is dynamically generated using AWGN prior to signal mixing. To further suppress noise in the combined signal, a Fast Fourier Transform (FFT)-based de-noising method is applied. Subsequently, the Inverse Fast Fourier Transform (IFFT) is used to reconstruct the separated signals. Compared with conventional approaches, the proposed framework enhances noise removal and improves the auditory quality of the recovered signals, rendering them perceptually close to the originals.