5.1 Digital Processing of Continuous-Time Signals Digital processing of a continuous-time signal involves the following basic steps: (1) Conversion of the continuous-time signal into discrete-time signal, ()Processing of the discrete-time signal, (3) Conversion of the processed discrete- time signal back into a continuous-time signal
Objective-Determination- of realizable transfer function G() approximating a given frequency response specification is an important step in the development of a digital filter If an IIR filter is desired, G() should be a stable real rational function Digital filter design is the process of deriving the transfer function G
2.1 Discrete-Time Signals: Time-Domain Representation Signals represented as sequences of numbers, called samples Sample value of a typical signal or sequence denoted as x[n] with n being an integer in the range-oo≤n≤∞ x[n] defined only for integer values of n and undefined for noninteger values of n Discrete-time signal represented by {x[n]}
1. Any arbitrary input sequence x[n] can be expressed as a linear combination of delaved and advanced unit sample sequences [n]=x[k][n-k] k=-0 2. .Linear Time-Invariant()System A system satisfying both the linearity and the time-invariance property. .If yiln] is the output due to an input xiln] and y2ln] is the output due to an input x2n] then for an input xn]=axiln]+bx2n] the output is given by ]=]+by2[n]
