Efficient formation of filter banks with frequency dependent resolution

Filter banks with frequency dependent resolution are sometimes required in digital signal processing applications involving spectrum analysis over a wide frequency band. For example, exponentially spaced filters can be useful in applications to geological exploration, audio systems, sonar, and radar. This paper presents two efficient techniques, the channel FFT and Frequency Domain Interpolation, for achieving arbitrary resolution. Efficiency is measured by comparison with the computational complexity required when the filter bank is implemented by brute force means. Emphasis is placed on the design of exponentially spaced filter banks. Details of the resulting filters are exhibited, and a least squares optimal approach to the design problem is discussed. It is demonstrated that filters with near optimal magnitude response may be implemented very efficiently as compared to the brute force case. Processor loading estimates are presented for exponentially spaced filter banks, using both techniques proposed in this paper, for various numbers of filters and frequency bandwidths to be spectrally analyzed.