Digital signal Processing
Two Mark Questions & Answers
UNIT I
1. Define Signal .
A signal is a function of one or more independent variables
which contain
some information.
Eg: Radio signal, TV signal, Telephone signal etc.
2. Define System.
A system is a set of elements or functional block that are
connected
together and produ ces an output in response to an input
signal.
Eg: An audio amplifier, attenuator, TV set etc.
3. Define CT signals.
Continuous time signals are defined for all values of time.
It is also called
as an analog signal and is represented b y x (t).
Eg: AC waveform, ECG etc.
4. Define DT signal.
Discrete time signals are defined at discrete instances of
time. It is
represented by x(n).
Eg: Amount deposited in a bank per month.
5. Give few examples for CT signals.
AC waveform, ECG,Temperature recorded over an interval of
time etc.
6. Give few examples of DT signals.
Amount deposited in a bank per month
7 What is a continuous and discrete time signal?
Continuous time signal: A signal x(t) is said to be
continuous if it is defined for all time 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.
8. Give the classification of signals?
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
9. What are the types of systems?
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.
10. What are even and odd signals?
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.
11. What are deterministic and random signals?
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.
12. What are energy and power signal?
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 asE=limT___x2 (t)dt, integration limit from ¡VT/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.
13. What are the operations performed on a signal?
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
14. What are elementary signals and name them?
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
15. What are the properties of a system?
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)
16. What is memory system and memory less system?
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 thepresent values of the input signal. An
electronic circuit with resistors is an example for
memory less system.
17. What is an invertible system?
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)}}.
18. What are time invariant systems?
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).
19. Is a discrete time signal described by the input output
relation y[n]= rnx[n] time
invariant.
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)¡ÚEquation(2)
Hence the signal is time variant.
20. Show that the discrete time system described by the
input-output relationship
y[n]=nx[n] is linear?
For a system 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
21. What is SISO system and MIMO system?
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.
22. What is the output of the system with system function H1
and H2 when
connected in cascade and parallel?
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).
23. 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)¡Úx(n) .
24. Define linear and non-linear systems.
A system is said to be linear if superposition theorem
applies to that
system. If it does not satisfy th e superposition theorem,
then it is said to be a nonlinear
system.
25. Define Causal and non-Causal systems.
A system is said to be a causal if its output at anytime
depends upon
present and past inputs only.
A system is said to be non-causal system if its output
depends upon future
inputs also.
26. Define unit step, ramp and delta functions for CT.
Unit step function is defined as
U(t)= 1 for t >= 0
0 otherwise
Unit ramp function is defined as
r(t)=t for t>=0
0 for t<0
Unit delta function is defined as
d (t)= 1 for t=0
0 otherwise
27. State the relation between step, ramp and delta
functions(CT).
The relation ship between unit step and unit delta function
is
d (t)= u(t)
The relationship between delta and unit ramp function is
d (t).dt = r(t)
.
UNIT-II
1.Define Z transform.
The Z transform of a discrete time signal x(n) is denoted by
X(z) and is given
-n by X(z)= x(n)Z .
2.Define ROC.
The region of convergence of X (z) is the set of all values
of z for which X(z) attains a finite value.
3.State the convolution property of Z transform.
The convolution property states that the convolution of two
sequences in
time domain is equivalent to multiplication of their Z
transforms.
If Z{X1(n)} =X1 (z) and Z{x2 (n)} =X2 (z), then
Z{x1 (n)*x2(n)} =X1 (z) X2 (z)
4.List the methods of obtaining inverse Z transform
Inverse z transform can be obtained b y u sing
Partial fraction expansion.
Contour integration
Power series expansion
Convolution.
5.Define Fourier Transform.
Let x(t) be the signal which is the function of time t. The
Fourier
transform of x(t) is given by
X(w)= „Å x(t)e jwt dt
6.State the conditions for the existence of fourier series.
(i). The function x(t) should be single valued in any finite
time interval T
(ii). The function x(t) should have atmost finite number of
discontinuities
in any finite time interval T.
(iii). The function x(t) should have finite number of maxima
and minima
in any time interval T.
(iv) The function x(t) should be absolutely integrable.
7.State Rayleigh¡¦s energy theorem.
Rayleigh¡¦s energy theorem states that the energy of the
sign al may be
written in frequency domain as superposition of energies due
to individual
spectral frequencies of the signal.
8.What are the properties of region of convergence?
It is a ring or disk in the z-plane centred at the origin.
It cannot any poles
The ROC of an LTI stable system contains the unit circle.
The ROC must be a connected region.
9.Define system function.
Let x(n) and y(n) be input and output sequences of an LTI
System with impulse response h(n). Then the system function of the LTI system is
the ratio of Y(z) and X(z), i.e.,
H(Z)= Y(z)/X(z)
10.Distinguish between Fourier series and Fourier Transform
Fourier Series
Fourier Transform
Gives the frequency content of a harmonic time function
Give the frequency information for an aperiodic signal
Discrete frequency spectrum
Continuous frequency spectrum
11.Define discrete Fourier series
Consider a sequence xp (n) with a period of samples so that
xp (n)=xp (n+ln);Then
discrete Fourier series of the sequence xp (n) is defined as
Xp(k)= „¸
ƒ{
ƒ
1
0
N
n
„¸ xp(n)e-j2„¨kn/N
12.State Dirichlets conditions.
(i).The function x(t) should be single valued within the
interval T0
(ii). The function x (t) should have atmost a finite number
of discontinuities
in the interval T0
(iii). The function x(t) should have finite number of maxima
and minima
in the interval T0
(iv). The function should have absolutely integrable.
13.State Parsevals power theorem.
Parsevals power theorem states that the total average power
o f a periodic
signal x(t) is equal to the sum of the average powers of its
phasor components
14.Find the Fourier transform of function x(t)= £_(t)
1
15.Compare double sided and single sided spectrums.
The method of representing spectrums of positive as well as
negative
frequen cies are called double sided spectrums.
The method of representing spectrums only in the positive
frequencies is
known as single sided spectrums
16.Define Quadrature Fourier Series.
Consider x(t) be a periodic signal. The fourier series can
be written for
this signal as follows
x(t)=a0+„¸ nƒ1
an cosw0nt+„¸ ƒ1 n
bnsinw0nt
This is known as Quadrature Fou rier Series.
17.Define polar Fourier Series.
x(t)=D0+„¸ ƒ1 n
Dn cos2„¨nt/T0
The above form of representing a signal is known as Polar
Fourier series
18.Define exponential fourier series.
x(t)= „¸ ƒ1 n
Cn ej2„¨nt/T0
The method of representing a signal by the above form is
known as ex ponential
fourier series.
19.List some properties of z-Transforms
¡E Linearity property
¡E Shifting property
¡E Frequency shifting
¡E Differentiation
¡E Integration
¡E Convolution
20.State initial value theorem.
If x(n)and X(z) are z-Transform pairs, then, ,
x(0) = lim X(z)
z->¡Û
provided thet the first derivative of x(t) should be laplace
tr ansformable.
21.State final value theorem.
If x(n)and X(z) are z-Transform pairs, then the final value
of x(z) is
given as ,
x(¡Û)= Lim (1-z-1)X(z) have no pole on or outside the unit
circle.
z->1
UNIT-III
1. What is the advantage of direct form 2 over direct form 1
structure?
The direct form 2 structure has reduced memory requirement
compared to
direct form 1 structure.
2. Define butterfly computation?
In the figure the two values ¡¥a¡¦ and ¡¥b¡¦ ar e available
as input. From these two
values ¡¥A¡¦ and ¡¥B¡¦ are computed at the output. This
operation is called Butterfly
computation.
3. What is an advantage of FFT over DFT?
FFT algorithm reduces number of computations.
4. List the applications of FFT?
Filtering
Spectrum analysis
Calculation of energy spectral density.
5. State the properties of DTFT
Periodicity
Linearity
Time shift
Frequency shift
Scaling
Differentiation in frequency domain
Time reversal
Convolution
Multiplication in time domain
Parseval¡¦s theorem.
6. State the condition for existence of DTFT?
The conditions are
¡E If x(n)is absolutely summable then
|x (n) |< ¡Û
¡E If x(n) is not absolutely summable then it should have
finite energy for
DTFT to exit.
7. Define Zero padding.
The method of appending zero in the given sequence is called
as Zero padding.
8. Define circularly even sequence.
A Sequence is said to be circularly even if it is symmetric
about the point zero on
the circle.
x(N-n)=x(n),1<=n<=N-1.
9. Define circularly odd sequence.
A Sequence is said to be circularly odd if it is anti
symmetric about point x(0) on
the circle
10. Define circularly folded sequences.
A circularly folded sequence is represented as x((-n)) . It
is obtained by
Nplotting x(n) in clockwise direction along the circle.
11. State circular convolution.
This property states that multiplication of two DFT is equal
to circular
convolution of their sequence in time domain.
12. State parseval¡¦s theorem.
Consider the complex valued sequences x(n) and y(n).If
x(n) ---- X(k)
y(n) ---- Y(k)
then x(n)y*(n)=1/N X(k)Y*(k)
13. Differentiate DTFT and DFT
DTFT output is continuous in time where as DFT output is
Discrete in time.
14.Differentiate between DIT and DIF algorithm
DIT ¡V Time is decimated and input is bi reversed format
output in natural order
DIF ¡V Frequency is decimated and input is natural order
output is bit reversed
format.
15. How many stages are there for 8 point DFT
8
16.How many multiplication terms are required for doing DFT
by expressional
method and FFT method
expression ¡Vn2 FFT N /2 log N
UNIT IV
1. Define FIR system?
The systems for which unit step response h(n) has finite
number of terms, they
are called Finite Impulse Response (FIR) systems.
2. Define IIR system?
The systems for which unit step response h(n) has infinite
number of terms,
they are called Infinite Impulse Response (IIR) systems
3. Write the expression for order of Butterworth filter?
The expression is N=log ( ƒÜ /£á) 1/2/log (1/k) .
4. Write the expression for the order of chebyshev filter?
N=cosh-1 (Ć /e)/cosh-1(1/k)
5. Write the steps in designing chebyshev filter?
1. Find the order of the filter.
2. Find the value of major and minor axis. _
3. Calculate the poles.
4. Find the denominator function using the above poles.
5. The numerator polynomial value depends on the value of n.
If n is odd: put s=0 in the denominator polynomial.
If n is even put s=0 and divide it by (1+e2)1/2
6. Write down the steps for designing a Butterworth filter?
1. From the given specifications find the order of the
filter
2 find the transfer function from the value of N
3. Find c
4 find the transfer function ha(s) for the above value of c
by su by that value.
7. State the equation for finding the poles in chebyshev
filter
sk=acos¢Fk+jbsin¢Fk,where ¢Fk=/2+(2k-1)/2n)
8. State the steps to design digital IIR filter using
bilinear method
Substitute s by 2/T (z-1/z+1), where T=2/_ (tan (w/2) in
h(s) to get h (z)
9. What is warping effect?
For smaller values of w there exist linear relationship
between w and .but for
larger values of w the relationship is nonlinear. This
introduces distortion in the
frequency axis. This effect compresses the magnitude and
phase response. This
effect is called warping effect
10. Write a note on pre warping.
The effect of the non linear compression at high frequencies
can be compensated.
When the desired magnitude response is piecewise constant
over frequency, this
compression can be compensated by introducing a suitable
rescaling or prewar
ping the critical frequencies.
11. Give the bilinear transform equation between s plane and
z plane
s=2/T (z-1/z+1)
12. Why impulse invariant method is not preferred in the
design of IIR filters other than low pass filter?
In this method the mapping from s plane to z plane is many
to one. Thus there ire
an infinite number of poles that map to the same location in
the z plane, producing
an aliasing effect. It is inappropriate in designing high
pass filters. Therefore this
method is not much preferred.
13. By impulse invariant method obtain the digital filter
transfer function and the differential equation of the analog filter h(s)
=1/s+1
H (z) =1/1-e-Tz-1
Y/x(s) =1/s+1
Cross multiplying and taking inverse lap lace we get,
D/dt(y(t)+y(t)=x(t)
14. What is meant by impulse invariant method?
In this method of digitizing an analog filter, the impulse
response of the resulting
digital filter is a sampled version of the impulse response
of the analog filter. For
e.g. if the transfer function is of the form, 1/s-p, then
H (z) =1/1-e-pTz-1
15. What do you understand by backward difference?
One of the simplest methods of converting analog to digital
filter is to
approximate the differential equation by an equivalent
difference equation.
d/dt(y(t)/t=nT=(y(nT)-y(nT-T))/T
16. What are the properties of chebyshev filter?
1. The magnitude response of the chebyshev filter exhibits
ripple either in the stop
band or the pass band.
2. The poles of this filter lies on the ellipse
17. How can you design a digital filter from analog filter?
Digital filter can de designed from analog filter using the
following methods
1. Approximation of derivatives
2. Impulse invariant method
3. Bilinear transformation
18. write down bilinear transformation.
s=2/T (z-1/z+1)
19. List the Butterworth polynomial for various orders.
N Denominator polynomial
1 S+1
2 S2+.707s+1
3 (s+1)(s2+s+1)
4 (s2+.7653s+1)(s2+1.84s+1)
5 (s+1)(s2+.6183s+1)(s2+1.618s+1)
6 (s2+1.93s+1)(s2+.707s+1)(s2+.5s+1)
7 (s+1)(s2+1.809s+1)(s2+1.24s+1)(s2+.48s+1)
20. Differentiate Butterworth and Chebyshev filter.
Butterworth dampimg factor 1.44 chebyshev 1.06
Butterworth flat response damped response.
21. What is filter?
Filter is a frequency selective device ,which amplify
particular range of
frequencies and attenuate particular range of frequencies.
22. What are the types of digital filter according to their
impulse response?
IIR(Infinite impulse response )filter
FIR(Finite Impulse Response)filter.
23. How phase distortion and delay distortion are
introduced?
The phase distortion is introduced when the phase
characteristics of a filter is
nonlinear with in the desired frequency band.
The delay distortion is introduced when the delay is not
constant with in the
desired frequency band.
24. What is mean by FIR filter?
The filter designed by selecting finite number of samples of
impulse response
(h(n) obtained from inverse fourier transform of desired
frequency response
H(w)) are called FIR filters
25. Write the steps involved in FIR filter design
Choose the desired frequency response Hd(w)
Take the inverse fourier transform and obtain Hd (n)
Convert the infinite duration sequence Hd (n) to h(n)
Take Z transform of h(n) to get H(Z)
The round off noise can be made small in non recursive
realization of FIR filter.
26. What are the disadvantages of FIR FILTER
The duration of impulse response should be large to realize
sharp cutoff filters.
The non integral delay can lead to problems in some signal
processing
applications.
27. What is the necessary and sufficient condition for the
linear phase characteristic ofa FIR filter?
The phase function should be a linear function of w, which
inturn requires
constant group delay and phase delay.
28. List the well known design technique for linear phase
FIR filter design?
Fourier series method and window method
Frequency sampling method.
Optimal filter design method.
29. Define IIR filter?
The filter designed by considering all the infinite samples
of impulse response are
called IIR filter.
30. For what kind of application , the antisymmetrical
impulse response can be used?
The ant symmetrical impulse response can be used to design
Hilbert transforms
and differentiators.
31. For what kind of application , the symmetrical impulse
response can be used?
The impulse response ,which is symmetric having odd number
of samples can be
used to design all types of filters ,i.e ,
lowpass,highpass,bandpass and band reject.
The symmetric impulse response having even number of samples
can be used
to design lowpass and bandpass filter.
32. What is the reason that FIR filter is always stable?
FIR filter is always stable because all its poles are at the
origin.
33. What condition on the FIR sequence h(n) are to be
imposed n order that this filtercan be called a liner phase filter?
The conditions are
(i) Symmetric condition h(n)=h(N-1-n)
(ii) Antisymmetric condition h(n)=-h(N-1-n)
34. Under what conditions a finite duration sequence h(n)
will yield constant groupdelay in its frequency response characteristics and not
the phase delay?
If the impulse response is anti symmetrical, satisfying the
condition
H(n)=-h(N-1-n)
The frequency response of FIR filter will have constant
group delay and not the
phase delay .
35. State the condition for a digital filter to be causal
and stable?
A digital filter is causal if its impulse response h(n)=0
for n<0.
A digital filter is stable if its impulse response is
absolutely summable, i.e,
+¡Û
£U ¢x h(n) ¢x . ¡Û
n=-¡Û
What are the properties of FIR filter?
1.FIR filter is always stable.
2.A realizable filter can always be obtained.
3.FIR filter has a linear phase response.
36. When cascade from realization is preferred in FIR
filters?
The cascade from realization is preferred when complex zeros
with absolute
magnitude less than one.
37. What are the disadvantage of Fourier series method ?
In designing FIR filter using Fourier series method the
infinite duration impulse
response is truncated at n= „b (N-1/2).Direct truncation of
the series will lead to fixed
percentage overshoots and undershoots before and after an
approximated discontinuity in
the frequency response .
38. What is Gibbs phenomenon?
One possible way of finding an FIR filter that approximates
H(ejč)would be to
truncate the infinite Fourier series at n=
čč(N-1/2).Abrupt truncation of the series
will lead to oscillation both in pass band and is stop band
.This phenomenon is
known as Gibbs phenomenon.
39. What are the desirable characteristics of the windows?
The desirable charaterstics of the window are
1.The central lobe of the frequency response of the window
should contain
most of the energy and should be narrow.
2.The highest side lobe level of the frequency response should
be small.
3.The sides lobes of the frequency response should decrease
in energy
rapidly as w ƒçtends to „¨.
40. Compare Hamming window with Kaiser window.
Hamming window
1.The main lobe width is equal to8„¨/N and the peak side
lobe level is ¡V41dB.
2.The low pass FIR filter designed will have first side lobe
peak of ¡V53 dB
Kaiser window
The main lobe width ,the peak side lobe level can be varied
by varying the
parameter £\ and N. The side lobe peak can be varied by
varying the parameter £\.
41. What is the necessary and sufficient condition for
linear phase characteristics in FIR filter?
The necessary and sufficient condition for linear phase
characteristics in FIR filter
is the impulse response h(n) of the system should have the
symmetry property,i.e,
H(n) = h(N-1-n) Where N is the duration of the sequence .
42. What are the advantage of Kaiser widow?
1.It provides flexibility for the designer to select the
side lobe level and N .
2. It has the attractive property that the side lobe level
can be varied
continuously from the low value in the Blackman window to
the high value in the
rectangle window .
43. What is the principle of designing FIR filter using
frequency sampling method?
In frequency sampling method the desired magnitude response
is sampled and a linear
phase response is specified .The samples of desired
frequency response are defined as
DFT coefficients. The filter coefficients are then
determined as the IDFT of this set of
samples.
44. For what type of filters frequency sampling method is
suitable?
Frequency sampling method is attractive for narrow band
frequency selective
filters where only a few of the samples of the frequency
response are non-zero.
UNIT V
1. List out the addressing modes supported by C5X
processors?
1. Direct addressing
2. Indirect addressing
3. Immediate addressing
4. Dedicated-register addressing
5. Memory-mapped register addressing
6. Circular addressing
2. What is meant by block floating point representation?
What are its advantages?
In block point arithmetic the set of signals to be handled
is divided into blocks. Each
block have the same value for the exponent. The arithmetic
operations with in the block
uses fixed point arithmetic & only one exponent per
block is stored thus saving memory.
This representation of numbers is more suitable in certain
FFT flow graph & in digital
audio applications.
3. What are the advantages of floating point arithmetic?
1. Large dynamic range
2. Over flow in floating point representation is unlike.
4. What are the three-quantization errors to finite word
length registers in digital filters?
1. Input quantization error 2. Coefficient quantization
error 3. Product quantization
Error
5.How the multiplication & addition are carried out in
floating point arithmetic?
In floating point arithmetic, multiplication are carried out
as follows,
Let f1 = M1*2c1 and f2 = M2*2c2. Then f3 = f1*f2 = (M1*M2)
2(c1+c2)
That is, mantissa is multiplied using fixed-point arithmetic
and the exponents are
added.
The sum of two floating-point numbers is carried out by
shifting the bits of the mantissa
of the smaller number to the right until the exponents of
the two numbers are equal and
then adding the mantissas.
6.What do you understand by input quantization error?
In digital signal processing, the continuous time input
signals are converted into digital
using a b-bit ACD. The representation of continuous signal
amplitude by a fixed digit
produce an error, which is known as input quantization
error.
7.List the on-chip peripherals in 5X.
The C5X DSP on-chip peripherals available are as follows:
1. Clock Generator
2. Hardware Timer
3. Software-Programmable Wait-State Generators
4. Parallel I/O Ports
5. Host Port Interface (HPI)
6. Serial Port
7. Buffered Serial Port (BSP)
8. Time-Division Multiplexed (TDM) Serial Port
9. User-Maskable Interrupts
8.what is the relationship between truncation error e and
the bits b for representing adecimal into binary?
For a 2's complement representation, the error due to
truncation for both positive and
negative values of x is 0>=xt-x>-2-b
Where b is the number of bits and xt is the truncated value
of x.
The equation holds good for both sign magnitude, 1's
complement if x>0
If x<0, then for sign magnitude and for 1's complement
the truncation error satisfies.
9.what is meant rounding? Discuss its effect on all types of
number representation?
Rounding a number to b bits is accomplished by choosing the
rounded result as the b
bit number closest to the original number unrounded.
10.what is meant by A/D conversion noise?
A DSP contains a device, A/D converter that operates on the
analog input x(t) to
produce xq(t) which is binary sequence of 0s and 1s.
At first the signal x(t) is sampled at regular intervals to
produce a sequence x(n) is of
infinite precision. Each sample x(n) is expressed in terms
of a finite number of bits given
the sequence xq(n). The difference signal e(n)=xq(n)-x(n) is
called A/D conversion noise.
11.what is the effect of quantization on pole location?
Quantization of coefficients in digital filters lead to
slight changes in their value. This
change in value of filter coefficients modify the pole-zero
locations. Some times the pole
locations will be changed in such a way that the system may
drive into instability.
12.which realization is less sensitive to the process of
quantization?
Cascade form.
13.what is meant by quantization step size?
Let us assume a sinusoidal signal varying between +1 and -1
having a dynamic range
2. If the ADC used to convert the sinusoidal signal employs
b+1 bits including sign bit,
the number of levels available for quantizing x(n) is 2b+1.
Thus the interval between
Successive levels
q= 2 =2-b
--------
2b+1
Where q is known as quantization step size.
14.How would you relate the steady-state noise power due to
quantization and the b bits representing the binary sequence?
Steady state noise power where b is the number of bits
excluding sign bit.
15.what is overflow oscillation?
The addition of two fixed-point arithmetic numbers cause
over flow the sum exceeds
the word size available to store the sum. This overflow
caused by adder make the filter
output to oscillate between maximum amplitude limits. Such
limit cycles have been
referred to as over flow oscillations.
16.what are the methods used to prevent overflow?
There are two methods used to prevent overflow
1. Saturation arithmetic 2. Scaling
17.what are the two kinds of limit cycle behavior in DSP?
1. Zero input limit cycle oscillations
2. Overflow limit cycle oscillations
18. What is meant by "dead band" of the filter
The limit cycle occur as a result of quantization effect in
multiplication. The
amplitudes of the output during a limit cycle are confined
to a range of values called the
dead band of the filter.
19.Explain briefly the need for scaling in the digital
filter implementation.
To prevent overflow, the signal level at certain points in
the digital filter must be
scaled so that no overflow occurs in the adder.
20. What are the different buses of TMS320C54X and their
functions?
The C5X architecture has four buses and their functions are
as follows:
Program bus (PB):
It carries the instruction code and immediate operands from
program memory
Space to the CPU.
Program address bus (PAB):
It provides addresses to program memory space for both reads
and writes.
Data read bus (DB):
It interconnects various elements of the CPU to data memory
space.
Data read address bus (DAB):
It provides the address to access the data memory space.
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