ABSTRACT
A discrete-time system, also called a digital filter, is defined mathematically as a transformation mapping from an input sequence, x[n], to an output sequence, y[n], where n E N is the integer time index. Therefore, system operation, transformation, filtering, modification, and mapping are all the same concept based on the following general mathematical operation on a sequence that produces a new sequence:
y[n] = T{x[1], x[2], • • • , x[n], x[n + 1], • • • ,}, n E
The output of a system is often called the system response. In general, a system transforms the input sequence by taking into account not only the current value but a combination of current, past, and possibly future values of the input in producing the current value in the system response.
