To read a digital watermark from printed images requires that the watermarking system read correctly after affine distortions. One way to recover from affine distortions is to add a synchronization signal in the Fourier frequency domain and use this synchronization signal to estimate the applied affine distortion. If the synchronization signal contains a collection of frequency impulses, then a least squares match of frequency impulse locations results in a reasonably accurate linear transform estimation. Nearest neighbor frequency impulse peak location estimation provides a good rough estimate for the linear transform, but a more accurate refinement of the least squares estimate is accomplished with partial pixel peak location estimates. In this paper we will show how to estimate peak locations to any desired accuracy using only the complex frequencies computed by the standard DFT. We will show that these improved peak location estimates result in a more accurate linear transform estimate. We conclude with an assessment of detector robustness that results from this improved linear transformation accuracy.