In short: an SDR is a radio with no IF, Modulator, or Demodulator stages as we generally understand those terms: a receiving RF preamp feeds directly into a (very fast) A-to-D converter, which is connected to a computer DSP/CPU to tune a signal and extract the modulated audio or data; on the transmit side, the CPU and DSP generate the modulation directly, and feed it to an RF power amp.
In the HF and ham world, it has appeared in 2 distinct phases; in use in high end amateur transceivers and receivers, and utilizing a PC as a controller, letting external software define how the SDR is addressed and utilized.
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An additional review of the Perseus can be found in the September 2009 MT article by Larry Van Horn, 'Perseus Software Defined Radio - A Whole Universe of Listening Possibilities' pp.66-68