Digital Signal Processing. This course discusses the analysis and representation of discrete-time signal systems, digital filters, and computation of the discrete Fourier transform. Digital Signal Processing begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform.
The motivation for computing a fast Discrete Fourier Transform was the concern about verifying a nuclear arms treaty with the Soviet Union. A very much faster Fourier Transform was needed to plant sensors in the ground in countries surrounding the Soviet Union. After the invention of the FFT, sensors were planted which allowed locating nuclear explosions to within 15 kilometers of where they were occurring.