This thesis is concerned with noise reduction in hearing aids. Hearing - impaired listeners and hearing - impaired users have great difficulty understanding speech in a noisy background. This problem has motivated the development and the use of noise reduction algorithms to improve the speech intelligibility in hearing aids. In this thesis, two noise reduction algorithms for single channel hearing instruments are presented, evaluated using objective and subjective tests. The first noise reduction algorithm, conventional Spectral Subtraction, is simulated using MATLAB 6.5, R13.The second noise reduction algorithm, Spectral Subtraction in wavelet domanin is introduced as well. This algorithm is implemented off line, and is compared with conventional Spectral Subtraction. A subjective evaluation demonstrates that the second algorithm has additional advantages in speech intelligibility, in poor listening conditions relative to conventional Spectral Subtraction. The subjective testing was performed with normal hearing listeners, at Ryerson University. The objective evaluation shows that the Spectral Subtraction in wavelet domain has improved Signal to Noise Ratio compared to conventional Spectral Subtraction.