ABSTRACT
Digital signal processing technology has its roots in the analysis of continuous linear systems. Continuous linear systems are described with linear differential equations, and discrete linear systems are described with linear difference equations. Convolution in one domain is equivalent to multiplication in the other domain in the case of either discrete or continuous signals. Most of the other notions in continuous linear systems, such as resonance, stability, impulse response, step response, transfer function, filtering, and so on are carried over and applied in the analysis of discrete systems. Each of the structures just described is an assembly of linear transfer functions. The algorithms are all equivalent in that they produce the same output signal in response to a given input signal, but each implies a different set of computations, or, if implemented in hardware, a different chip design. Lattice algorithms are like direct algorithms in that both provide implementations of any linear system.
