This paper proposes a multistage filterbank-based channelizer for software radio base stations. The proposed channelizer is capable of receiving channels with potentially different bandwidths as required in a multi-standard cellular based station. It consists of multiple stages of DFT filter banks and efficient sample rate changers. The front-end DFT filter bank of the channelizer has a fixed number of channels but the passband supports overlap with each other. The received signals selected by a given output of this filter bank are fed into sample rate changers so that they can fit into the fixed channel spacing of the DFT filter banks in the following stages. Due to the lowered sample rate, these back-end DFT filter banks can have either fixed or variable number of channels. Repeatedly using this multistage architecture, channels with different bandwidths can be isolated. The design and implementation of the proposed channelizer are discussed in detail. An example of dual-mode GSM/W-CDMA channelizer is also discussed to illustrate the proposed design methodology.