Thanks Frank -- I remember using transistor-based analog computers at collage in the late 1970s -- I wish I coudl go back and show myself things like MP3 players (and tell myself to buy stock in Apple and SanDisk and... (grin)
The first single-chip DSP processor came from Bell Labs in 1979, but building block compenents came earlier -- Fairchild had a 2x4 multiplier IC in 1970.
It's difficult to discover the first usage of the phrase "digital signal processing," but it is worth noting that the first A/D and D/A converters were developed using vacuum tubes in the late 1930s.
I tell you, I wish I had learned more about digital signal processing when I was younger ... but now I come to think about it I don't even know if there was such a beast when I was at college in the late 1970s. Does anyone know when the term DSP first appeared on the scene?