This paper introduces a method of designing an M-channel, causal, stable and perfect reconstruction (PR), infinite impulse response (IIR), parallel uniform discrete Fourier transform (DFT) filter banks. The basic idea behind this is based on an efficient technique of designing and implementing narrowband lowpass finite impulse response (FIR) filters, called the interpolated FIR (IFIR) technique. In this paper, we have extended the IFIR concept to the IIR filter, known as Interpolated IIR (IIIR), and applied the concept to IIR DFT filter banks. It has been shown that this technique is good for IIR DFT filter banks in polyphase oversampled case and also has a modular structure which is therefore very useful for very large scale integration (VLSI) implementation.