Conventional ptychography translates an object through a localized probe beam to widen the field of view in real space. Fourier ptychography translates the object spectrum through a pupil aperture to expand the Fourier bandwidth in reciprocal space. Here we report an imaging modality, termed synthetic aperture ptychography (SAP), to get the best of both techniques. In SAP, we illuminate a stationary object using an extended plane wave and translate a coded image sensor at the far field for data acquisition. The coded layer attached on the sensor modulates the object exit waves and serves as an effective ptychographic probe for phase retrieval. The sensor translation process in SAP synthesizes a large complex-valued wavefront at the intermediate aperture plane. By propagating this wavefront back to the object plane, we can widen the field of view in real space and expand the Fourier bandwidth in reciprocal space simultaneously. We validate the SAP approach with transmission targets and reflection silicon microchips. A 20-mm aperture was synthesized using a 5-mm sensor, achieving a fourfold gain in resolution and 16-fold gain in field of view for object recovery. In addition, the thin sample requirement in ptychography is no longer required in SAP. One can digitally propagate the recovered exit wave to any axial position for post-acquisition refocusing. The SAP scheme offers a solution for far-field sub-diffraction imaging without using lenses. It can be adopted in coherent diffraction imaging setups with radiation sources from visible light, extreme ultraviolet, and X-ray, to electron.