# Electronics & Communicaton Engineering

**SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTUR**

**ELECTRONICS & COMMUNICATON ENGINEERING**

LESSON PLAN

Academic Year**/Sem: B.Tech III-II Sem.**Ref: John G. Proakis, Dimitris G. Manolakis

Subject: **DIGITAL SIGNAL PROCESSING**Subject code:15A04603

Branch: E.C.E.

Module / Topics covered / Hours / Name of the book / Page NoL / T

UNIT I

Module 1 / Review of discrete-time signals and systems – Time domain analysis of discrete-time signals & systems, Frequency domain analysis of discrete-time signals and systems. / 5 / 1 / John G. Proakis, Dimitris G. Manolakis / 42-69, 224-300

Module 2 / Frequency-domain sampling and reconstruction of discrete-time signals, Discrete Fourier Transform (DFT), The DFT as a linear transformation, Relationship of the DFT to other transforms, Properties of DFT, Linear filtering methods based on DFT, Frequency analysis of signals using the DFT / 6 / 3 / John G. Proakis, Dimitris G. Manolakis / 449-488

UNIT II

Module 1 / Efficient computation of the DFT – Direct computation of DFT, Divide and conquer approach to computation of DFT, Radix-2, Radix-4, and Split radix FFT algorithms, Implementation of FFT algorithms, / 6 / 2 / John G. Proakis, Dimitris G. Manolakis / 511-536

Module 2 / Applications of FFT algorithms – Efficient computation of the DFT of two real sequences, 2N point real sequences, Use of the FFT algorithm in linear filtering and correlation, A linear filtering approach to computation of the DFT- the Goertzel, and the Chirp-z transform algorithms, Quantization errors in the computation of DFT. / 6 / 2 / John G. Proakis, Dimitris G. Manolakis / 538-552

UNIT III

Module 1 / Structures for the realization of discrete-time systems, Structures for FIR systems - Direct form, Cascade form, Frequency sampling, and Lattice structures, / 5 / 1 / John G. Proakis, Dimitris G. Manolakis / 563-574

Module 2 / Structures for IIR systems – Direct form, Signal flow graphs & Transposed, Cascade form, Parallel form and Lattice structures, Conversion from Lattice structure to direct form, lattice –Ladder structure / 5 / 2 / John G. Proakis, Dimitris G. Manolakis / 582-594

UNIT IV

Module 1 / General considerations – Causality and its implications, Characteristics of practical Frequency Selective Filters, Design of Finite Impulse Response (FIR) filters – Symmetric and asymmetric FIR filters, Design of linear phase FIR filters using windows, Design of linear phase FIR filters by the frequency sampling method / 5 / 2 / John G. Proakis, Dimitris G. Manolakis / 654-671

Module 2 / Design of optimum equi-ripple linear phase FIR filters, Comparison of design methods for linear phase FIR filters, Design of Impulse Invariance Response (IIR) filters from analog filters – IIR filter design by approximation of derivatives, by Impulse invariance, and by bilinear transformation methods. / 6 / 2 / John G. Proakis, Dimitris G. Manolakis / 678-712

Module 3 / Characteristics of commonly used analog filters, Design examples of both FIR and IIR filters, Frequency transformation in the analog and digital domains, Illustrative problems. / 5 / 2 / John G. Proakis, Dimitris G. Manolakis / 717-730

UNIT V

Module 1 / Introduction, Decimation, and interpolation, Sampling rate conversion by a rational factor, Implementation of sampling rate conversion / 5 / 1 / John G. Proakis, Dimitris G. Manolakis / 751-774

Module 2 / Multistage implementation of sampling rate conversion, Sampling rate conversion of bandpass signals, Sampling rate conversion by arbitrary factor, Applications of multirate signal processing. / 6 / 1 / John G. Proakis, Dimitris G. Manolakis / 775-787

TOTAL / 60 / 19

S.No /

**Name of the book**/ Author

Digital signal processing, principles, Algorithms and applications / John G Proakis

Digital signal processing, A computer base approach / Sanjith K Mithra

Discrete time signal processing / A V Oppenheim

** SIDDHARTH INSTITUTE OF ENGINEERING &TECHNOLOGY:: PUTTUR**

**ELECTRONICS & COMMUNICATON ENGINEERING**

**DIGITAL SIGNAL PROCESSING**

MODULE-1

**IMPORTANT QUESTIONS**

1) Explain the classification of discrete time signals and systems.

2) a) Check whether the given systems are time variant or time invariant.

i) y(n)= x(n)+x(n-1)ii)y(n)=x(-n+2)

b) Determine if the system described by the following equation are causal or non-causal

i) y(n)= x(n)+ ii)y(n)=x(n2)

BITS

1) Sequence steps for converting analog signal to digital signal is------

2)A signal which varies continuously with time and amplitude then the signal is called------

3) If X(n) is a signal and X(n+N)=X(n) then X(n) is said to be------

4) If X(n) is a signal and follow the property X(-n)=X(n) then X(n) is said to be-----

5) A signal is defined as X(n)= 1 for n=0; and X(n)= 0 for n≠0; then X(n) is said to be------

6) If the energy of a signal X(n) is finite value then power of that signal is------

7) If the system output depends only on present and past inputs,then the system is said to be------

8) A LTI system is said to be stable if------

9) If x(n) is given signal then x(2n) Indicates ------

10) ------is fundamental period of x(n) = cos (nπ/2)

ASSIGNMENT

1.Find circular convolution of following two sequences x(n) = {4,3,2,1},

h(n) = {1,-2,1,0} using i)Concentric circles method ii) DFT & IDFT method.

MODULE-2

**IMPORTANT QUESTIONS**

1) Find the response of the system described by the difference equation:

y(n)+2 y(n-1)+y(n-2)=x(n)+x(n-1) for the input x(n) =( )n u(n), with initial conditions y(-1)=y(-2)=1.

2) State and prove following properties of DFT

a) Circular shifting b) Time reversal c) complex conjugate d) linearity

e) Circular convolution

3)a) Explain how DFT can used as a linear Transform.

b) How do you sample and reconstruct a discrete time signal in frequency domain. 4) Find the output y(n) of a filter whose impulse response is h(n)=[1,-1] and input x(n)= [1,-2,2,-1,3,-4,4,-3] using i) overlap add method ii) overlap save method

BITS

1) If x(n) is given signal then even part of x(n) is ------

2) If x (n) = {1, 2, 1, 2} h (n) = {1, 2, 1}.Find linear convolution?

3) ------is the condition for LTI system to be stable.

4) What are the DFT of real part of x (n) and imaginary part of x (n)?

5) Define natural and forced response of a system?

ASSIGNMENT

1) Determine the impulse response h(n) for the system described by difference equation: y(n)+y(n-1)-2y(n-2) = x(n-1) + 2x(n-2)

UNIT-II

MODULE-1

**IMPORTANT QUESTIONS**

1) Develop an 8-point DIF-FFT algorithm. Draw the signal flow graph. Determine the DFT of the following sequence, x(n)= {1,1,1,0,0,1,1,1}

2) Compute IDFT of the sequence x(n)={ 7,-0.707-j0.707,-j, 0.707-j0.707,1, 0.707+j0.707,j, -0.707+j0.707}

3) Explain Split-radix FFT algorithm with neat sketch.

4) a) Explain decimation in time FFT algorithm.

b) Explain Radix-4 FFT algorithm with neat butterfly diagram.

BITS

1) In N-Point DITFFT, number of butterflies per stage is ------

2) In 16-Point DITFFT, each sample represented by ------digit

3) Direct DFT requires ------number of complex multiplications.

4) FFT algorithms require ------number of complex additions.

5) For a 32 point DFT using direct method, no of complex additions are ------

6) The value of the twiddle factor at N=4 and n*k=3 is ------

7) Symmetry property of twiddle factor is ------

8) Bit reversal order for I/P of DITFFT algorithm is------

9) W83value is------

10) The number of butterflies per stage is ------for N-point DFT.

ASSIGNMENTS

1) Explain divide and conquer approach to computation of the DFT.

2) Compute 8-point DFT of the sequence x(n)= {1,1,1,1,1,1,0,0}using,

i) direct computation method ii) DIT-FFT

3) Compute DFT of the sequence x(n)={1,2,3,4,4,3,2,1} using DIF-FFT algorithm.

MODULE-2

**IMPORTANT QUESTIONS**

1) Explain Applications of FFT algorithms.

2) How do you compute DFT using

a) The Goertzel Algorithmb)The chrip-z Transform

BITS

1) If X(k) consist of N- no of frequency samples, then its discrete frequency locations are given by the ______

2) In DITFFT, Inputs/outputs for each butterfly in stage ‘m’ separated by ------

3) In radix 2 FFT, the no of complex multiplications for ‘m’ stages is ------

4)In 128 point FFT, the number of complex additions are ------

ASSIGNMENTS

1) Explain Quantization errors in the computation of DFT.

2) Explain the use of FFT algorithm in linear filtering and correlation

UNIT-III

MODULE-1

**IMPORTANT QUESTIONS**

1) (a) Discuss the realization of FIR filter structures.

(b) Realize FIR filter with system function in cascade form

H (z) = 1 + (5/2) z-1+2z-2+2z-3.

2) Determine the cascade & parallel realizations for the system described by the difference equation y(n)=(3/4)y(n-1)–(1/8)y(n-2)+x(n)+(1/3)x(n-1)

3) Explain briefly about different structures in FIR systems

BITS

1) The unit sample response of FIR system is identical to------

2) The length of FIR filter is ------

3) The direct form structure is equivalent to ------

4) The number of memory locations needed to realize direct form structure is------

5) The tapped delay line filter is also called as------

6) The condition for FIR system to have linear phase is------

7) In frequency sampling structure the value used to characterize the filter is------

8) The most efficient form of realization is------

9) ------structure is mostly used in digital speech processing.

10) For a linear phase FIR system if M=even then the no of multiplications is------

ASSIGNMENTS

1) Determine the cascade & parallel realizations for the system described by the difference equation:

*y(n)=-0.1y(n-1)+0.2y(n-2)+3x(n)+3.6x(n-1)+0.6x(n-*2)

2) Explain Lattice structure for FIR systems.

MODULE-2

**IMPORTANT QUESTIONS**

1) Consider the system y(n) = y(n - 1) + 2y(n - 2) + x(n)

(a) Find H(z)

(b) Realize using direct form-II

2) Realize system with following difference equation y(n) = (3/4)y(n-1)–(1/8)y(n-2) + x(n) + (1/3)x(n-1)

(a)direct form-I

(b)direct form-II

3) Explain lattice and lattice-ladder structure for IIR systems.

BITS

1) In IIR direct form-I the number of additions is------

2) The no of memory locations needed to realize IIR direct -form I is------

3) The no of multiplications required to realize IIR direct form-II is------

4) ------structure is obtained by changing all branch directions and input & output.

5) The Parallel form realization of IIR system is obtained by ------

6) The Polar form of Z can be expressed as ------

7) Z transform of sequence x(n)={1,0,3} is ------

ASSIGNMENTS

1) Explain the concept of signal flow graphs and transposed structures.

2) Consider the discrete system : y(n)=2y(n-1)+2y(n-2)+x(n)+x(n-1).

(a) Find the Z-transform

(b) Realize the system using direct form-I method.

UNIT-IV

MODULE-1

**IMPORTANT QUESTIONS**

1. (a) Explain the FIR filter design using windowing technique.

(b) Compare FIR and IIR filters.

2) Give the expression for rectangular window function. Find its frequency response and also sketch its spectrum. Also discuss its features.

BITS

1) In the Impulse Invariance Transformation, relationship between Ω and ω is------

2) The abrupt truncation of Fourier series results oscillations in------band.

3) For rectangular window ,the main lobe width is equal to------

4)The frequency of a digital filter is------

5) In FIR filters ------is a linear function of ω.

ASSIGNMENTS

1) Design of linear phase FIR filters by the frequency sampling method.

2) Design of Finite Impulse Response (FIR) filters – Symmetric and asymmetric FIR filters.

MODULE-2

**IMPORTANT QUESTIONS**

1)Convert the following analog filter transfer function using backward difference method, Impulse invariant method and Bilinear Transformation method.

H(s)=1/(s+0.2) Consider T= 1 Sec.

2) (a) Discuss the characterization of IIR filter.

(b)Using backward difference method obtain H (z) for following transfer function: H (s) = 1/(s + 3)

BITS

1) The physically realizable IIR filters do not have ------phase.

2) In ------transformation, the impulse response of digital filter is the Sampled version of the impulse of analog filter.

3) Aliasing occurs only in ------transformation.

4) InFourier series method to get transfer function of realizable filter ,H(z) is to be Multiplied by------factor.

5) ForHanning window ,the main lobe width is equal to------

ASSIGNMENTS

1)Design of optimum equi-ripple linear phase FIR filter

MODULE-3

**IMPORTANT QUESTIONS**

1. Design an analog low pass Butterworth filter that has a -2db pass band attenuation at a frequency of 20rad/sec and at least -10db stop band attenuation at 30rad/sec.

2. For the analog transfer function H(s)=2/(s+1)(s+2) determine H(Z) using impulse invariance method. Assume T=1sec.

BITS

1) Butterworth filters have_____ transition region.

2) Type-1 Chebyshevfilters contain oscillation in _____band.

3) At the cutoff frequency ,the magnitude of the butterworth filter is------times the maximum value.

4) The ideal filters are ------,and hence physically unrealizable.

5) Type-2 Chebyshev filter is also called------

ASSIGNMENTS

1) Characteristics and frequency response of FIR digital filters

2) Compare Butterworth and Cheybeshev filters

UNIT-V

MODULE-1

IMPORTANT QUESTIONS

1)Describe the decimation process with a factor M, obtain necessary expression, sketch the frequency response? And also discuss aliasing effect?

2) With the help of block diagram explain sampling rate conversion by a rational factor I/D?

BITS

1) Decimation results ____ in sampling rate.

2) Up sampling by a factor I introduces______between samples.

3) If x(n)={1,2,3,4,5,6,7,..} then x(n/2)=------.

4) The systems that process data at more than one sampling rate are called------systems.

5) The basic two operations in multi rate signal processing are ------and ------.

ASSIGNMENTS

1) Explain down sampling and up sampling with suitable example.

2) Find the Z- transform of anu(-n -1) with a down sampling by a factor `2' .

Comment on ROC in comparison with original ROC i.e.anu (-n-1) ROC.

MODULE-2

IMPORTANTR QUESTIONS

1) Discuss the applications digital signal processing.

2) (a) Discuss the need for signal compression.

(b) Explain the concept of dual tone multi frequency signal detection.

BITS

1) Sampling rate conversion, first------to be performed and then ------is to be performed.

2) The filter used to band limit the signal prior to down sampling is called------.

3) In digital audio ,the different sampling rates used are------kHz for broadcasting, ------kHz for compact disc and ------kHz for audio tape.

4) If x(n)={1,-1,3,4,0,2,5,1,6,9,…} then x(3n)------.

5) The D-channel synthesis filter bank is the ------of D-channelanalysis filter bank.

ASSIGNMENTS

1) What is sub band coding? How is it achieved with the help of multi rate DSP?

2) Multistage implementation of sampling rate conversion