# 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.

• Frequency domain interpolation is directly meaningful if your signals are sinusoidal (or complex exponential), as you need the phase of the sinusoid at its true frequency, not at that of the nearest bin. For general signals phase is not so helpful as it would need to be unwrapped for comparison between the two signals, and that is difficult. Sep 15, 2015 at 6:25
• yes, our interest is narrow band. The question is about interpolation. Is it interpolation, any comment please. Sep 15, 2015 at 6:54
• If the signal is sinusoidal and you know the frequency in advance (or somehow track it) then you can use something like the Goertzel algorithm to directly calculate the Fourier transform at the frequency. There's no frequency domain interpolation there. Sep 15, 2015 at 18:44
• @OlliNiemitalo I am interested in the sub-sample time delay estimation not frequency.According to wikipedia Goertzel algorithm is related to frequency estimation. Sep 15, 2015 at 19:35
• There are forms of the (complex) Goertzel algorithm that can be used for phase estimation as well. Sep 15, 2015 at 23:08