Digital Signal Processing
QUESTION
BANK
1. What is a continuous and discrete time signal?
Ans:
Continuous
time signal: A signal x(t) is
said to be continuous if it is
defined for all time
t. Continuous time signal arise naturally when a physical waveform such
as
acoustics wave or
light wave is converted into a
electrical signal. This
is effected by means of
transducer.(e.g.) microphone,
photocell.
Discrete time signal: A discrete time signal
is defined only at discrete instants
of time. The independent variable has
discrete values
only, which
are
uniformly spaced. A discrete time signal
is often derived from the
continuous time signal by sampling it
at a uniform rate.
2. Give the classification of signals?
Ans:
Continuous-time
and discrete time signals
Even
and odd signals
Periodic signals and
non-periodic signals
Deterministic signal and Random
signal
Energy and
Power signal
3. What are the types
of systems?
Ans:
Continuous time and discrete time systems
Linear and Non-linear systems Causal
and Non-causal systems Static and
Dynamic systems
Time
varying and time
in-varying systems
Distributive parameters and Lumped parameters
systems
Stable and
Un-stable systems.
4. What are even and
odd signals?
Ans:
Even signal: continuous time signal x(t) is
said to be even if it satisfies
the condition
x(t)=x(-t) for all values of t.
Odd signal: he signal x(t) is
said to be odd if it satisfies the
condition x(-t)=-x(t) for all
t. In other words even
signal
is symmetric about the time origin
or the vertical axis, but odd signals are anti-symmetric about
the vertical axis.
5. What are
deterministic and random signals?
Ans:
Deterministic Signal:
deterministic signal
is a signal about which there is
no certainty with respect
to its value at any time.
Accordingly we find
that deterministic signals may
be modeled as completely specified
functions of
time.
Random signal: random
signal
is a signal about
which
there is uncertainty before its actual occurrence. Such signal
may
be viewed as group of
signals with each signal
in the ensemble having different wave forms
.(e.g.) The noise developed in a
television or radio amplifier is an
example
for random signal.
6. What are energy and
power
signal?
Ans:
Energy signal: signal is referred as an
energy signal, if
and only if the total energy of the
signal
satisfies the condition 0<E<∞. The total energy of the continuous time signal x(t) is given as
E=limT→∞∫x2 (t)dt, integration limit from –T/2 to +T/2
Power signal: signal is said
to be powered signal if it
satisfies the condition
0<P<∞. The average power of a continuous time signal is given by
P=limT→∞1/T∫x2(t)dt,
integration limit is from-T/2 to +T/2.
7. What are the operations performed on a
signal?
Ans:
Operations
performed
on dependent
variables:
Amplitude scaling: y (t) =cx (t),
where c is the scaling factor, x(t) is
the continuous time signal.
Addition: y (t)=x1(t)+x2(t)
Multiplication y (t)=x1(t)x2(t)
Differentiation: y (t)=d/dt
x(t)
Integration (t) =∫x(t)dt
Operations
performed
on independent variables
Time shifting Amplitude scaling Time reversal
8. What are elementary signals
and
name them?
Ans:
The elementary signals serve as a building
block for the construction of
more complex signals. They are also
important in their own right,
in that they may be used to model
many physical signals
that occur in nature.
There are five elementary signals.
They
are as follows
Unit step
function
Unit impulse function
Ramp function Exponential function Sinusoidal function
9. What are the properties of a
system?
Ans:
Stability:
A system is said to be
stable if the input x(t) satisfies the
condition(t)│≤Mx<∞
and the out
put satisfies the condition │y(t)│≤My<∞ for all t.
Memory: A system
is said to be memory if the output signal depends on the present and
the past inputs.
Invertibility:
A system is said to be
invertible if the input of
the system con be recovered from
the system
output.
Time invariance: A system
is said to be time invariant
if a time delay or advance of the
input signal leads to an identical
time shift in the output signal.
Linearity: A system is said
to be linear if it satisfies
the super position principle
i.e.) R(ax1(t)+bx2(t))=ax1(t)+bx2(t)
10. What is memory system and memory less system?
Ans:
A system is said
to be memory system if
its output signal at
any time depends
on the past values of the input signal. circuit with inductors capacitors
are examples
of memory system..
A system is said
to be memory less
system if the output
at any time depends on the present values of the input signal. An electronic circuit with resistors is an example for memory less system.
11. What is an invertible system?
Ans:
A system is said
to be invertible system if
the input of the system can
be recovered
from
the system output. The set of operations
needed to recover the input
as the second system
connected in cascade with
the given system such
that
the output signal of the second
system is equal to the
input signal applied
to the system.
H-1{y(t)}=H-1{H{x(t)}}.
12. What are time invariant systems?
Ans:
A system
is said to be time invariant system if a time delay or advance of the input signal leads
to an idenditical shift in the
output signal. This
implies that a time invariant
system
responds idenditically no matter when the
input signal
is applied. It also satisfies the condition
R{x(n-k)}=y(n-k).
13. Is a discrete time signal described
by the input
output relation y[n]= rnx[n] time
invariant.
Ans:
A signal
is said to be time invariant
if R{x[n-k]}= y[n-k] R{x[n-k]}=R(x[n]) / x[n]→x[n-k]
=rnx [n-k] ---------------- (1)
y[n-k]=y[n] /
n→n-k
=rn-kx [n-k] -------------------(2)
Equations (1)≠Equation(2)
Hence the signal
is time variant.
14. Show that
the
discrete time system described by the input-output
relationship y[n]
=nx[n] is
linear?
Ans:
For a sys
to be linear R{a1x1[n]+b1x2[n]}=a1y1[n]+b1y2[n]
L.H.S:R{ a1x1[n]+b1x2[n] }=R{x[n]} /x[n] → a1x1[n]+b1x2[n]
= a1 nx1[n]+b1 nx2[n]
-------------------(1)
R.H.S: a1y1[n]+b1y2[n]= a1 nx1[n]+b1 nx2[n] --------------------(2) Equation(1)=Equation(2)
Hence the system is linear
15. What is SISO
system and MIMO system?
Ans:
A control system
with single input and single output
is referred to as single input
single output system.
When
the number of plant
inputs or the number of plant outputs
is more than one the system
is referred to as
multiple input output system. In both the case, the controller may be in
the form of a digital
computer or microprocessor in
which
we can speak
of the digital
control systems.
16. What is the output
of the system with system function H1 and H2 when connected in cascade and parallel?
Ans:
When the
system with input x(t) is connected
in cascade with the system
H1 and
H2 the output of the system
is
y(t)=H2{H1{x(t)}}
When the
system is connected
in parallel the
output of the system is given
by
y(t)=H1x1(t)+H2x2(t).
17. What do you mean by periodic
and non-periodic signals?
A signal
is said to be periodic if
x(n+N)=x(n)
Where N
is the time period.
A signal is said to be
non-periodic if x(n+N)≠x(n) .
18.Determine the convolution sum of two sequences
x(n) = {3, 2, 1, 2} and
h(n) = {1, 2, 1, 2}
Ans: y(n) = {3,8,8,12,9,4,4}
19.Find the convolution of the signals
x(n) = 1 n=-2,0,1
= 2 n=-1
= 0 elsewhere.
Ans: y(n) = {1,1,0,1,-2,0,-1}
20.Detemine the solution of the difference equation
y(n) = 5/6 y(n-1) –
1/6 y(n-2) + x(n) for x(n) = 2n u(n)
Ans: y(n) = -(1/2)n u(n) + 2/3(1/3)n u(n)+8/5
2nu(n)
21.Determine the response y(n),
n>=0 of the system described
by the second order
difference equation
y(n) – 4y(n-1) + 4y(n-2) = x(n) –
x(n-1) when the input
is x(n) = (-1)n u(n) and the
initial
condition are y(-1) = y(-2)=1.
Ans:y(n) = (7/9-5/3n)2n u(n) +2/9(-1)n u(n)
22. Differentiate DTFT and DFT
DTFT output is continuous in time where as
DFT output is Discrete in time.
23.Differentiate between DIT and
DIF algorithm
DIT
– Time is decimated and
input is bi reversed format
output in natural order
DIF – Frequency is decimated and
input is natural order output is bit reversed
format.
24. How many stages are there for 8 point DFT
8
25 How many multiplication terms are required for doing
DFT by expressional
method and FFT method
expression –n2 FFT N /2 log N
26. Distinguish IIR and FIR filters
|
FIR
|
IIR
|
|
Impulse response
is finite
They have perfect linear phase
|
Impulse Response is infinite
They do not have perfect linear phase
|
|
Non recursive
|
Recursive
|
|
Greater flexibility to control
the
shape of magnitude
response
|
Less flexibility
|
27. Distinguish analog
and digital filters
|
Analog
|
digital
|
|
Constructed using active
or
passive components and it is described
by
a differential
equation
|
Consists
of elements like adder,
subtractor and delay units
and it is described by a difference equation
|
|
Frequency response can be
changed
by
changing the components
|
Frequency response can be
changed
by
changing the filter
coefficients
|
|
It
processes and generates
analog output
|
Processes and generates digital
output
|
|
Output varies
due to external
conditions
|
Not influenced by external
conditions
|
28. Write the expression for
order of Butterworth filter?
The expression is N=log (λ /€) 1/2/log (1/k) ½
29. Write the expression for
the
order of chebyshev filter?
N=cosh-1(λ /e)/cosh-1(1/k)
30. Write the various
frequency transformations in analog domain?
LPF to LPF:s=s/Ωc
LPF to HPF:s=Ωc/s
LPF to BPF:s=s2xlxu/s(xu-xl)
LPF to BSF:s=s(xu-xl)?s2=xlxu. X=Ω
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