Chapter-2-discrete time signal and system.ppt

Chapter 2 Discrete-Time Signals and Systems
§ 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 - n 
x[n] defined only for integer values of n and undefined for noninteger values of n
Discrete-time signal represented by {x[n]}
§ Discrete-Time Signals:Time-Domain Representation
Discrete-time signal may also be written as a sequence of numbers inside braces:
{x[n]}={…,-,,,,-,,…}

The arrow is placed under the sample at time index n = 0
In the above, x[-1]= -, x[0]=, x[1]=, etc.
§ Discrete-Time Signals:Time-Domain Representation
Graphical representation of a discrete-time signal with real-valued samples is as shown below:
§ Discrete-Time Signals:Time-Domain Representation
In some applications, a discrete-time sequence {x[n]} may be generated by periodically sampling a continuous-time signal xa(t) at uniform intervals of time
§ Discrete-Time Signals:Time-Domain Representation
Here, n-th sample is given by
x[n]=xa(t) |t=nT=xa(nT), n=…,-2,-1,0,1,…
The spacing T between two consecutive samples is called the sampling interval or sampling period
Reciprocal of sampling interval T, denoted as FT , is called the sampling frequency:
FT=1/T
§ Discrete-Time Signals:Time-Domain Representation
Unit of sampling frequency is cycles per second, or hertz (Hz), if T is in seconds
Whether or not the sequence {x[n]} has been obtained by sampling, the quantity x[n] is called the n-th sample of the sequence
{x[n]} is a real sequence, if the n-th sample x[n] is real for all values of n
Otherwise, {x[n]} is plex sequence
§ Discrete-Time Signals:Time-Domain Representation
plex sequence {x[n]} can be written as {x[n]}={xre[n]}+j{xim[n]} where xre and xim are the real and imaginary parts of x[n]
plex conjugate sequence of {x[n]} is given by {x*[n]}={xre[n]} - j{