The paper provides a technique to design and approximate computationally efficient digital filter banks whose centre frequencies are spaced logarithmically. The design procedure consists of two steps: The design of ‘mother’ filter banks and the frequency windowing processing for the final filter banks. The resonator with the purely imaginary transfer function on the unit circle is treated as the basic element of the mother bank and the frequency interpolating filter bank structure is applied. Different pole-zero structures are studied and an infinite filter bank is explored from the theoretical point of view. The outputs of the mother filter banks are weighted and summed to produce the final banks with significantly improved responses. Linear programming is applied to find the optimal weighting coefficients, and the experiments for a variety of windows are made with a discussion of the results and some tradeoffs for window selection. The results show that these filter banks have good frequency response and allow control of crossover gain, and they are useful for voice and music analysis and tone receivers.