EC1361 DIGITAL SIGNAL PROCESSING

TWO MARKS

DIGITAL SIGNAL PROCESSING

SUBJECT CODE: CS2403

SEM/YEAR: V/III

PART AUNIT ISIGNALS AND SYSTEMS

1. Define Signal and Signal Processing.A signal is defined as any physical quantity that varies with time, space, or any other independent variable.Signal processing is any operation that changes the characteristics of a signal. These characteristics include the amplitude, shape, phase and frequency content of a signal.

2. What are the classifications of signals? (Nov/Dec 2010)There are five methods of classifying signals based on different features:(a) Based on independent variable.

(i) Continuous time signal.

(ii) Discrete time signal.

(b) Depending upon the number of independent variable.

(i) One dimensional signal,

(ii) Two dimensional signal.

(iii) Multi dimensional signal.

(c) Depending upon the certainty by which the signal can be uniquely described as

(i) Deterministic signal.(ii) Random signal.(c) Based on repetition nature.

(i) Periodic signal.

(ii) Non Periodic signal.

(d) Based on reflection

(i) Even signal.

(ii) Odd signal3. Define discrete system.

A discrete time system is defined as a device or algorithm that operates on a discrete time input signal x(n) , according to some well defined rule , to produce another discrete time signal y(n) called the output signal.4. What are the classifications of discrete time systems?The classifications of discrete time systems are1. Static and Dynamic system.

2. Time variant and time invariant system.

3. Linear and non linear system.

4. Stable and Un-stable system.

5. Causal and non-causal system.

6. IIR and FIR system.5. Differentiate Continuous time and discrete time signal.

Continuous time signal: It is also referred as analog signal i.e., the signal is represented continuously in time.Discrete time signal : Signals are represented as sequence at discrete time intervals .6. Define digital signal.A discrete time signal or digital is defined as which discrete valued represented by a finite number of digits is referred to as a digital signal.7. What is Deterministic signal? Give example.

A signal that can be uniquely determined by a well - defined process such as a mathematical expression or rule, or look-up table is called a deterministic signal.Example : A sinusoidal signal 8. What is random signal? Give example.

A signal that is generated in a random fashion and cannot be predicted ahead of time is called a random signal.Example : Speech signal , ECG signal and EEG signal.9. Define (a) Periodic signal (b) Non periodic signal.Periodic signal: A periodic signal is defined as the signal x(n) is periodic with period N if and only if x(n+N)=x(n) for all n.Non periodic signal: A non periodic signal is defined as if there is no value of N that satisfies the equation x(n+N) x(n) .10. What are the symmetric and ant symmetric signals?Symmetric signal: A real valued signal x(n) is called symmetric if x(-n) = x(n).Antisymmetric signal: A signal x(n) is called antisymmetric if x(-n) = -x(n).11. What are energy and power signals? (April/may 2011, Nov/Dec 2012)Energy signal:

The energy of a discrete time signal x(n) is defined as

A signal x(n) is called an energy signal if and only if the energy obeys the relation

. For an energy signal P=0.

Power signal:

The average power of a discrete time signal x(n) is defined as

A signal x(n) is called power signal if and only if the average power P satisfies the condition .12. What are the different types of signal representation?The different types of signal representation are(i) Graphical representation(ii) Functional representation

(iii) Tabular representation(iv)Sequence representation

13. What are the different types of operations performed on discrete time signals?

The different types of operations performed on discrete time signals are(1)Delay of a signal

(2) Advance of a signal

(3)Folding or Reflection of a signal

(4) Time scaling

(5) Amplitude scaling

(6)Addition of signals

(7)Multiplication of signals.14. Represent the following duration sequence x(n)={1, 3, -1, -4} as a sum of weighted impulse sequences.

( Given

x(n)={1, 3, -1, -4}

(

We can write

15. What is a static and dynamic system?

A discrete time system is called static or memory less if its output at any instants n depends on the input samples at the same time , but not an past or future samples of the input.Ex., y(n) = ax(n)

Y(n)=ax2(n)

In any other case, the system is said to be dynamic or to have memory.Ex., y(n) = ax(n-1)+x(n-2)

y(n)=x(n)+x(n-1)16. What is a linear time invariant system? (Nov/Dec 2010)

A system is called time invariant if its input output characteristics do not change with time. Ex., y(n)=x(n)+x(n-1)

17. What is a causal system?

A system is said to be causal if the output of the system at any time n depends only on present and past inputs, but does not depend on future inputs.This can be expressed mathematically as,

y(n)=F[x(n), x(n-1), x(n-2)18. Define a stable system.

Any relaxed system is said to be bounded input-bounded output (BIBO) stable if and only if every bounded input yields a bounded output. Mathematically, their exist some finite numbers, Mx and My such that,

19. What is a linear system?

A system that satisfies the superposition principle is said to be a linear system. Superposition principle states that , the response of the system to a weighted sum of signals be equal to the corresponding weighted sum of the outputs of the system to each of the individuals input signals.20. Define unit sample response (impulse response) of a system and what is its significance?

The unit sample response is defined as the output signal designated as h(n) , obtained from a discrete time system when the input signal is a unit sample sequence ( unit impulse).

The output y(n) of an LTI system for an input signal x(n) can be obtained by convolving the impulse response h(n) and the input signal x(n).

21. What is the causality condition for an LTI system?

The necessary and sufficient condition for causality of an LTI system is, its unit sample response h(n)=0 for negative values of n i.e.,

h(n)= 0 for n Va . This set an error in readings.43. What are the advantages and disadvantages of SAADC?Advantages of SAADC are1. It is more accurate than the stair case (counter ramp) ADC.

2. It maintains a high resolution.

3. It is much faster.

4. Its conversion time is much less.

Disadvantages of SAADC are

1. It requires a complex register called the successive approximation register

2. It is costly, as it contains more components.

44. Write down the formula for conversion time of SAADC?

where

n number of bits and

f clock frequency.45. What are the advantages and disadvantages of Flash converter?

Advantages of flash converter are

1. The fastest conversion process ( governed only by propagation delay of the gates.

2. Highest accuracy

3. Highest resolution possible by increasing the number of comparators.Disadvantages of flash converter are

1. Very complicated circuitry.

2. Cost is proportional to the number of comparators, which in turn depends on the resolution required.46. What are the different types of Analog to Digital converters?The different types of analog to digital converters are

1. Flash A/D converter.

2. Successive approximation converter.

3. Counting type A/D converter.

4. Over sampling Sigma Delta converter.47. What are the different types of Digital to Analog converter?The different types of digital to analog converters are

1. Weighted resistor D/A converter.

2. Resistor ladder D/A converter.3. Over sampling D/A converter.

48. Define Z transform.

The Z transform of a discrete time signal or sequence is defined as the power series.

49. What is meant by region of convergence?(April/May 2008)

The region of convergence (ROC) of X(z) is the set of all values of z for which X(z) attains a finite value.

50. What are the properties of region of convergence?The properties of region of convergence are

1. The ROC is a ring or disk in the Z plane centered at the origin.

2. The ROC cannot contains any poles.

3. The ROC of an LTI stable system contains the unit circle.

4. The ROC must be a connected region.

51. What are the properties of z- transform? (Nov/Dec 2008)1. Linearity:

EMBED Equation.3

2. Shifting: (a)

(b)

3. Multiplication:

4. Scaling in z- domain:

5. Time reversal :

6. Conjugation:

7. Convolution:

8. Initial value:

9. Final value:

52. State Parsevals relation in z-transform. (April/May 2011)Parsevals relation in z-transform state that

If x1(n) and x2(n) are complex valued sequences, then

53. What is the relationship between z-transform and DTFT? (Nov/Dec 2010)

The z-transform of x(n) is given by.(1)

Where

Substituting z value in eqn (1) we get,

..(2)

The Fourier transform of x(n) is given by

.(3)

Eqn(2) and Eqn(3) are identical , when r=1. In the z-plane this corresponds to the locus of points on the unit circle . Hence is equal to X(z) evaluated along unit circle , or

For to exist , the ROC of X(z) must include the unit circle.

54. What are the different methods of evaluating inverse z transform?1. Long division method.

2. Partial fraction method.

3. Residue method.

4. Convolution method.

55. Find the convolution of the following using z- transform.

Solution:

56. Define system function.Let x(n) and y(n) is the input and output sequences of an LTI system with impulse response h(n). Then the system function of the LTI system is defined as the ratio of Y(z) and X(z), i.e.,

where,

Y(z) is the z transform of the output signal y(n)

X(z) is the z transform of the input signal x(n)

UNIT II

FREQUENCY TRANSFORMATIONS1. Define Fourier transform of a discrete time signal. (April/May 2008)The Fourier transform of a discrete time signal x(n) is defined as

2. Why FFT of a discrete time signal is called signal spectrum?By taking Fourier transform of a discrete time signal x(n) , it is decomposed into its frequency components . Hence the Fourier transform is called signal spectrum.

3. List the difference between Fourier transform of discrete time signal and analog signal?i) The FT of analog signal consists of a spectrum with a frequency range But the FT of discrete time signal is unique in the range , and also it is periodic with periodicity of 2 .ii) The FT of analog signals involves integration but FT of discrete time signals involves summation.

4. Define inverse Fourier transform.The inverse Fourier transform of X(() is defined as

5. Give some applications of Fourier transform. (Nov/Dec 2010)The application of Fourier transform are

1. The frequency response of LTI system is given by the Fourier transform of the impulse response of the system.

2. The ratio of the Fourier transform of output to Fourier transform of input is the transfer function of the system in frequency domain.3. The response of an LTI system can be easily computed using convolution property of Fourier transform.6. What is the frequency response of LTI system?The Fourier transform of the impulse response h(n) of the system is called frequency response of the system. It is denoted by H(().

7. Write the properties of frequency response of LTI system.The properties of frequency response of LTI system are

i) The frequency response is periodic function ( with a period of 2 .ii) If h(n) is real then is symmetric and is antisymmetric. iii) If h(n) is complex then the real part of is antisymmteric over the interval .iv)The frequency response is a continuous function of .

8. Write short notes on the frequency response of first order system.A first order system is characterized by the difference equation

The frequency response of first order system depends on the co efficient a in the difference equation governing the LTI system. When the value of a| is in the range of 0