On the Compensation of Delay in the Discrete Frequency Domain

The ability of a DFT filterbank frequency domain filter to effect time domain delay is examined. This is achieved by comparing the quality of equalisation using a DFT filterbank frequency domain filter with that possible using an FIR implementation. The actual performance of each filter architecture depends on the particular signal and transmission channel, so an exact general analysis is not practical. However, as a benchmark, we derive expressions for the performance for the particular case of an allpass channel response with a delay that is a linear function of frequency. It is shown that a DFT filterbank frequency domain filter requires considerably more degrees of freedom than an FIR filter to effect such a pure delay function. However, it is asserted that for the more general problem that additionally involves frequency response magnitude modifications, the frequency domain filter and FIR filters require a more similar number of degrees of freedom. This assertion is supported by simulation results for a physical example channel.