Is sub-sampling delay estimation possible without interpolation? I want to estimate time delay between two complex narrow band signals. I can use any correlation method. There are several methods in the literature about sub-sample time delay estimation. Generally this subs-sample delay estimation is done through phase estimation. My question is: are these sub-sampling methods using phase requires interpolation or not? I was expecting that we are interpolating in Fourier domain and using phase information to estimate time delay. Any comment would be appreciated.
For finite length signals, interpolation (both for frequency and phase) in the frequency domain is helpful if the frequency is not at a DFT/FFT bin center.  Relative phase estimation is required for delay estimation in the frequency domain.  This relative phase estimation can produce a sub-time-domain-sample delay estimation result.  This delay estimation can have an uncertainty related to an unknown integer multiple of the signal's period due to phase unwrapping errors, unless there is some other time domain envelope information available.