Abstract: The digital-backend technique has become the main-stream signal-processing technology of radio astronomy and has been applied in China and abroad.In this paper we review the principles of signal filtering and application of polyphase filter banks (PFBs) in multi-channel signal filtering.We particularly discuss approaches to optimize the bandpass performance using a PFB.Using the backend-developing platform provided by the CASPER of the UC Berkeley, we have designed and constructed a digital backend with a bandwidth of 400MHz divided into 16k channels (corresponding to a frequency resolution of 25kHz).We have also carried out a frequency-sweep test of the backend.The processing of the digital backend has been designed to be as follows.Input analog signals are converted into digital signals by an ADC.The digital signals are filtered by a PFB in multiple frequency channels, and the filtered signals in each channel are transformed by the FFT block to yield a power spectrum.The power spectra in multiple channels are summed and sent to other devices through a 10GbE interface for further processing or storage.The backend as designed can be applied in extragalactic HI surveys using the FAST radio telescope.