The estimation of the time delay of arrival (TDOA) or the direction of arrival (DOA) has been an important research topic within the last few decades. In several applications, e.g., acoustic source localization or source separation, the estimation of the delay or the direction is a significant processing block. Most of the available algorithms estimate the delay in the time domain. Therefore, the estimate is an integral multiple of the sampling period. Depending on the sampling rate and other parameters, the resolution is restricted and possibly not adequate for specific applications. To overcome the resolution problem, a new method based on the phase delay between two sensors and a line detection approach commonly used in image processing is proposed. Experimental results demonstrate the advantage of the introduced approach.