1. Digital Signal Processing
.
Mrs.R.Chitra, Assistant Professor(SS),
Department of ECE,
Faculty of Engineering,
Avinashilingam Institute for Home Science
and Higher Education for Women,
Coimbatore
3. Classification of systems
Continuous time and discrete time signal
Lumped-parameter and distributed -parameter
systems
Static and dynamic systems
Causal and non-causal systems
Linear and non-linear systems
Time variant and time -invariant systems
Stable and unstable system
4. Continuous time system
A Continuous time system is one which operates on a
continuous time input signal and produces a continuous
time output signal.
y(t)= Tx(t)
5. Discrete time system
A discrete time system is the one which operates on a
discrete- time input signal and produces a discrete -time
output signal.
y(n)=T(X(n)
6. Lumped and distributed parameter
In lumped parameter system each component is
lumped at one point in space.
In distributed parameter systems the signals are
functions of space as well as time.
7. Static and dynamic system
A system is called static or memory less if its output at
any instant depends on the input at that instant.
A system output is depends up on the past and future
values of input.
8. Causal and non causal system
A causal system is one for which the output at any time
t depends on the present and past inputs.
A non-causal system output depends on the future
values of inputs.
9. Linear and non linear system
A System is said to be linear if it follows super position
principle is called as linear other wise non-linear.
T[ax1(t)+bx2(t)]=aT[x1(t)]+bT[x2(t)]
Similarly for a discrete-time linear system,
T[ax1(n)+bx2(n)]=aT[x1(n)]+bT[x2(n)]
10. Stable and unstable system
If the system has to be stable if and only if every
bounded input produces bounded output.
If system has to be unstable if bounded input produces
unbounded output
11. Time variant and invariant system
Time variant system have same input and output,
y(n,k)=y(n-k).
Time invariant system has no same input and output.
12. CONVOLUTION
Convolution is the process by which an input interacts
with an LTI system to produce an output
Convolution between of an input signal x[n] with a
system having impulse response h[n] is given as,
where * denotes the convolution
x [ n ] * h [ n ] = x [ k ] h [ n - k ]
13. EXAMPLE
Convolution
We can write x[n] (a periodic function) as an infinite
sum of the function xo[n] (a non-periodic function)
shifted N units at a time
15. Linear convolution
)(*)()()()( 2113 nxnxmnxmxnx
m
)()( 11
j
eXnx FT
)()( 22
j
eXnx FT
)()()()(*)()( 213213
jjj
eXeXeXnxnxnx FT
16. Circular convolution
Circular convolution of of two
finite length sequences
16
1
0
213
N
m
Nmnxmxnx
1
0
123
N
m
Nmnxmxnx
17. Circular convolution
)()())(()()( 21
1
0
13 nxnxmnxmxnx
N
m
N
)()( 11 kXnx DFT
)()( 22 kXnx DFT
)()()()()()( 213213 kXkXkXnxnxnx DFT
both of length N
18. EXAMPLE
)()( 01 nnnx
)(2 nx
)(*)( 21 nxnx
0
0 N
0 n0 N
)()( 21 nxnx
n0=2, N=7
0
19. DISCRETE FOURIER TRANSFORM
It turns out that DFT can be defined as
Note that in this case the points are spaced 2pi/N;
thus the resolution of the samples of the frequency
spectrum is 2pi/N.
We can think of DFT as one period of discrete
Fourier series