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For pt.II, see ibid., vol.52, no.2, p.192-207 (2005). This paper, the last from a series of three papers on the application of coded excitation signals in medical ultrasound, investigates the possibility of increasing the frame rate in ultrasound imaging by using modulated excitation signals. Linear array-coded imaging and sparse synthetic transmit aperture imaging are considered, and the trade-offs between frame rate, image quality, and SNR are discussed. It is shown that FM codes can be used to increase the frame rate by a factor of two without a degradation in image quality and by a factor of 5, if a slight decrease in image quality can be accepted. The use of synthetic transmit aperture imaging is also considered, and it is here shown that Hadamard spatial encoding in transmit with FM emission signals can be used to increase the frame rate by 12 to 25 times with either a slight or no reduction in signal-to-noise ratio and image quality. By using these techniques, a complete ultrasound-phased array image can be created using only two emissions.