PRINCIPLES OF DIGITAL SIGNAL PROCESSING

     Discrete-timesignals

Digital signals are discrete in both time (the independent variable)and amplitude(the dependent variable).Signals that are discrete in time but continuous in amplitude are referred to as discrete-time signals.

Discrete- time signals are data sequences. A sequence of data is denoted{x[n]} or simply[n]when the meaning is clear. The elements of the sequence are called samples. The index n associated with each sample is an integer. If appropriate, the range of n

will be specified. Quite often, we are interested in identifying the samplewheren=0.Thisisdonebyputtinganarrowunderthatsample.Forinstance,

{x[n]}={...,0.35,1,1.5,−0.6,−2,...}

↑

The arrow is often omitted if it is clear from the context which sample is x[0].Sample values can either be real or complex. In the rest of this book, the terms“discrete-time signals”and“sequences”are used interchangeably.