This paper presents a method for least squares design of nonuniform filter banks for application in subband signal processing. Design objectives aim to optimize the filter bank frequency response while minimizing subband and output aliasing. Aliasing is minimized although magnitude and phase changes affect the aliasing terms. Filter banks with increasing bandwidth are designed with the proposed method and evaluated in speech enhancement using a spectral subtraction algorithm. When using a nonuniform frequency resolution approximating that of the human auditory system it is shown that an increased noise reduction and SNR improvement is achieved while maintaining the speech quality for a fixed number of frequency-bands.