In this paper, we introduce a new approach to two-dimensional (2-D) processing of the one-dimensional (1-D) speech signal in the time-frequency plane. Specifically, we obtain the shortspace 2-D Fourier transform magnitude of a narrowband spectrogram of the signal and show that this 2-D transformation maps harmonically-related signal components to a concentrated entity in the new 2-D plane. We refer to this series of operations as the "grating compression transform" (GCT), consistent with sine-wave grating patterns in the spectrogram reduced to smeared impulses. The GCT forms the basis of a speech pitch estimator that uses the radial distance to the largest peak in the GCT plane. Using an average magnitude difference between pitch-contour estimates, the GCT-based pitch estimator is shown to compare favorably to a sine-wave-based pitch estimator for all-voiced speech in additive white noise. An extension to a basis for two-speaker pitch estimation is also proposed.