it6502 digital signal processing, Schemes and Mind Maps of Digital Signal Processing

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DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING

IT

DIGITAL SIGNAL PROCESSING

Question Bank

III YEAR A & B / 2013 REQULATION

BATCH: 2016 - 2020

Vision of Institution To build Jeppiaar Engineering College as an Institution of Academic Excellence in Technical education and Management education and to become a World Class University. Mission of Institution M1 To excel in teaching and^ learning,^ research^ and^ innovation^ by promoting the principles of scientific analysis and creative thinking M 2 To participate in the production, development and dissemination of knowledge and interact with national and international communities M To equip students with values, ethics and life skills needed to enrich their lives and enable them to meaningfully contribute to the progress of society M4 To prepare students for higher studies and lifelong learning , enrich them with the practical and entrepreneurial skills necessary to excel as future professionals and contribute to Nation’s economy Program Outcomes (POs) PO Engineering knowledge : Apply the knowledge of mathematics, science, engineering fundamentals, and an engineering specialization to the solution of complex engineering problems. PO Problem analysis : Identify, formulate, review research literature, and analyze complex engineering problems reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences. PO Design/development of solutions : Design solutions for complex engineering problems and design system components or processes that meet the specified needs with appropriate consideration for the public health and safety, and the cultural, societal, and environmental considerations PO Conduct investigations of complex problems : Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid conclusions. PO Modern tool usage : Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex engineering activities with an understanding of the limitations.

Program Educational Objectives (PEOs) PEO1 To address the real time complex engineering problems using innovative approach with strong core computing skills. PEO2 To apply core-analytical knowledge and appropriate techniques and provide solutions to real time challenges of national and global society PEO3 Apply ethical knowledge for professional excellence and leadership for the betterment of the society. PEO4 Develop life-long learning skills needed for better employment and entrepreneurship Programme Specific Outcome (PSOs) PSO1 – An ability to understand the core concepts of computer science and engineering and to enrich problem solving skills to analyze, design and implement software and hardware based systems of varying complexity. PSO2 - To interpret real-time problems with analytical skills and to arrive at cost effective and optimal solution using advanced tools and techniques. PSO3 - An understanding of social awareness and professional ethics with practical proficiency in the broad area of programming concepts by lifelong learning to inculcate employment and entrepreneurship skills. BLOOM TAXANOMY LEVELS BTL1: Remembering BTL2: Understanding BTL3Applying. BTL4: Analyzing BTL5:Evaluating BTL6:Creating

SYLLABUS

IT6502 DIGITAL SIGNAL PROCESSING L T P C

OBJECTIVES:

To introduce discrete Fourier transform and its applications. To teach the design of infinite and finite impulse response filters for filtering undesired signals. To introduce signal processing concepts in systems having more than one sampling frequency. UNIT I SIGNALS AND SYSTEMS 9 Basic elements of DSP – concepts of frequency in Analog and Digital Signals – sampling theorem

• Discrete – time signals, systems – Analysis of discrete time LTI systems – Z transform – Convolution – Correlation. UNIT II FREQUENCY TRANSFORMATIONS 9 Introduction to DFT – Properties of DFT – Circular Convolution - Filtering methods based on DFT – FFT Algorithms - Decimation – in – time Algorithms, Decimation – in – frequency Algorithms – Use of FFT in Linear Filtering – DCT – Use and Application of DCT. UNIT III IIR FILTER DESIGN 9 Structures of IIR – Analog filter design – Discrete time IIR filter from analog filter – IIR filter design by Impulse Invariance, Bilinear transformation, Approximation of derivatives – (LPF, HPF, BPF, BRF) filter design using frequency translation. UNIT IV FIR FILTER DESIGN 9 Structures of FIR – Linear phase FIR filter – Fourier Series - Filter design using windowing techniques (Rectangular Window, Hamming Window, Hanning Window), Frequency sampling techniques UNIT V FINITE WORD LENGTH EFFECTS IN DIGITAL FILTERS 9 Binary fixed point and floating point number representations – Comparison - Quantization noise – truncation and rounding – quantization noise power- input quantization error- coefficient quantization error – limit cycle oscillations-dead band- Overflow error-signal scaling.

Course Outcomes (COs) C312.1 Understand the various signals and systems. C312. Build frequency transformations for the signals and Compare Discrete Fourier Transform and Fast Fourier Transform. C312.3 Design^ of Infinite Impulse Response filters for given specifications. C312.4 Design of Finite Impulse Response filters for given specifications C312.5 Determine the effects of Finite Word length Effects in Digital Filters.

INDEX PAGE

UNIT REFERENCE BOOK PAGE NUMBER

I

John G. ProaKis and Dimitris G.ManolaKis, “Digital Signal Processing – Principles, Algorithms & Applications”, Fourth Edition, Pearson Education, Prentice Hall, 2007

II

John G. ProaKis and Dimitris G.ManolaKis, “Digital Signal Processing – Principles, Algorithms & Applications”, Fourth Edition, Pearson Education, Prentice Hall, 2007

III

John G. ProaKis and Dimitris G.ManolaKis, “Digital Signal Processing – Principles, Algorithms & Applications”, Fourth Edition, Pearson Education, Prentice Hall, 2007

IV

John G. ProaKis and Dimitris G.ManolaKis, “Digital Signal Processing – Principles, Algorithms & Applications”, Fourth Edition, Pearson Education, Prentice Hall, 2007

V

John G. ProaKis and Dimitris G.ManolaKis, “Digital Signal Processing – Principles, Algorithms & Applications”, Fourth Edition, Pearson Education, Prentice Hall, 2007

Linear system. 10 What are energy and power signals? May /June 2013,Nov/Dec 2012 The energy signal is one in which has finite energy and zero average power The power signal is one in which has finite average power and infinite energy. T E = Lt ∫ │x(t)│^2 dt joules. T→∞ - T P = Lt T T→∞ 1 / 2T ∫ │x(t)│^2 dt joules. ]

C312.1 BTL 1

What is correlation? What are its types? May /June 2013 Measuring similarities between two signals .Two types are Auto Correlation and Cross Correlation.

C312.1 BTL 1

Compare linear convolution and circular convolution. Nov/Dec 2012 Nov/Dec 2010 y(n)=(N1+N2-1 )samples - input sequence may have different length-Zero padding is not required------Linear convolution, y(n)=max(N1+N2)- input sequence should have same length – If the length of the sequence are not equal Zeroes are appended at the end of the sequence.-----Circular convolution

C312.1 BTL^5

What is sampling theorem? Nov/Dec 2012, APRIL/MAY Fs>=2Fm Fs= Sampling frequency Fm- maximum analog frequency.

C312.1 BTL 1

What do you understand by the term signal processing? MAY/JUNE 2014 Processing of signals by systems is called as signal processing

C312.1 BTL 1

What is time invarient system? MAY/JUNE 2014.MAY/JUNE 2016 If the input output characteristics of the systems do not change with time ,then the system is referred as time in variant system.

C312.1 BTL 1

What is linear and nonlinear systems? The system is linear if and only if T[a1x1(n)+ a2x2(n)]= a1y1(n)+ a2y2(n)] Where x1(n),x2(n) are arbitrary input signals y1(n), y2(n) are arbitrary output signals a1,a2 are constants.

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What is static and dynamic systems. A system is static if its output at any instant n depends only on present input but not on past or future input.

C312.1 BTL 1

Define Region of Convergence.(ROC) April/May 2018 Since Z transform is an infinite power series it exists only for those values of Z for which X(Z)=attains a finite value.

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What are the properties of Z transform. 1.linearity property 2.scaling property3.Time shifting property4.Time reversal property5.Convolution of 2 sequences.6.Differentiation in Z domain

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Write the cases in long division method. Case1.When ROC exterior to the circle, the system is expected to be a causal system. Case2.When ROC interior to the circle, the system is expected to be a anticausal system..

C312.1 BTL 1

what are the types of convolution. 1.circular convolution2.linear convolution

C312.1 BTL 1

What are the types of correlation? Autocorrelation- measuring similarities between same signals Cross correlation-measuring similarities between different signals

C312.1 BTL 1

Define DSP. Processing of signals by digital systems

C312.1 BTL 1

Find the energy of (1/4)n u(n) April/May 2017 Refer Notes

C312.1 BTL 1

What are the types of signals. 1.one dimensional signals2. multi dimensional signals3. multi channel signals

C312.1 BTL 1

What is Nyquest sampling Rate? Fs>=2Fm Sampling frequency should be greater than two times maximum frequency.

C312.1 BTL 1

What is continues time signals AND Discrete time signals. Amplitude can be defined for all values of t. Amplitude can be defined for particular integer values of t. MAY/JUNE 2016

C312.1 BTL 2

Given x(z)=Z2 +2Z +1-2Z-2. Find the equivalent time domain signal x(n) Nov/Dec Refer notes

C312.1 BTL 3

What are the applications of DSP? Image processing, speech processing, biomedical, Radar system, Digital audio, video processing

C312.1 BTL 1

What is continuous and discrete time signal? 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

C312.1 BTL 1

input signal. i.e., T [a1x1(n)+a2x2(n)]=a1T[x1(n)]+a2 T[x2(n)] e.g. y(n)=n x(n) A system which does not satisfy superposition principle is known as non- linear system. e.g.(n)=x2(n) 39 What are the steps involved in calculating convolution sum? The steps involved in calculating sum are

• Folding
• Shifting
• Multiplication
• Summation

C312.1 BTL 1

state associative law The associative law can be expressed as [x(n)h1(n)]h2(n)=x(n)[h1(n)h2(n)] Where x(n)-input h1(n)-impulse response. 19.State commutative law The commutative law can be expressed as x(n)h(n)=h(n)*x(n)

C312.1 BTL 1

what are the properties of convolution sum The properties of convolution sum are

• Commutative property.
• Associative law.
• Distributive law.

C312.1 BTL 1

State distributive law The distributive law can be expressed as x(n)[h1(n)+h2(n)]=x(n)h1(n)+x(n)*h2(n)

C312.1 BTL 1

State properties of ROC.

• The ROC does not contain any poles.
• When x(n) is of finite duration then ROC is entire Z-plane except Z=0 or Z=∞.
• If X(Z) is causal,then ROC includes Z=∞.
• If X(Z) is anticasual,then ROC includes Z=0.

C312.1 BTL 1

How to obtain the output sequence of linear convolution through circular convolution? Consider two finite duration sequences x(n) and h(n) of duration L samples and M samples. The linear convolution of these two sequences produces an output sequence of duration L+M- 1 samples, whereas , the circular convolution of x(n) and h(n) give N samples where N=max(L,M).In order to obtain the number of samples in circular convolution equal to L+M-1, both x(n) and h(n) must be appended with appropriate number of zero valued samples. In other words by increasing the length of the sequences x(n) and h(n) to L+M-1 points and then circularly convolving the resulting sequences

C312.1 BTL 1

we obtain the same result as that of linear convolution. 45 What is zero padding?What are its uses? Let the sequence x(n) has a length L. If we want to find the N-point DFT(N>L) of the sequence x(n), we have to add (N-L) zeros to the sequence x(n). This is known as zero padding. The uses of zero padding are 1)We can get better display of the frequency spectrum. 2)With zero padding the DFT can be used in linear filtering.

C312.1 BTL 1

Find the convolution of X(n)=1,2,3,1,2,1 and h(n)=1,2,1, April/May 2018 Refer Notes

C312.1 BTL^2

What is overlap-add method? In this method the size of the input data block xi(n) is L. To each data block we append M-1 zeros and perform N point cicular convolution of xi(n) and h(n). Since each data block is terminated with M-1 zeros the last M-1 points from each output block must be overlapped and added to first M-1 points of the succeeding blocks.This method is called overlap-add method.

C312.1 BTL 1

. What is overlap-save method? In this method the data sequence is divided into N point sections xi(n).Each section contains the last M-1 data points of the previous section followed by L new data points to form a data sequence of length N=L+M-1.In circular convolution of xi(n) with h(n) the first M-1 points will not agree with the linear convolution of xi(n) and h(n) because of aliasing, the remaining points will agree with linear convolution. Hence we discard the first (M-1) points of filtered section xi(n) N h(n). This process is repeated for all sections and the filtered sections are abutted together.

C312.1 BTL 1

A signal x(t) =sin (5 πt) is sampled and what is the minimum sampling frequency is needed to reconstruct the signal without aliasing. Nov/Dec 2018. Fs>2fa .fa=2.5 therefore sampling frequency should be greater than or equal to 5 kz.

C312.1 BTL 1

Find the system transfer function of given difference equation using Z transform y(n)-0.5y(n-1)=x(n). Nov/Dec 2018. Y(Z)=X(Z). H(Z) Therefore H(Z)= Y(Z)/X(Z).

C312.1 BTL 1

Find the Z transform of the following discrete time signals and find ROC x(n)=u(n-2) x(n)=[-1/5 ]nu(n)+5[1/2]-nu(-n-1) MAY/JUNE 2014, MAY/JUNE 2016 Refer notes

C312.1 BTL 1

Explain the process of analog to digital conversion of signal in terms of sampling quantization and coding. APRIL/MAY2015 OR (Relate Nyquest rate criteria and aliasing effect with sampling process. Discuss how aliasing error can be avoided. Nov/Dec 2018. Refer Notes

C312.1 BTL 5

A Discrete time system is represented by the following difference equations y(n)=3y2(n-1)-nx(n)+4x(n-1)-2x(n+1) for n>0 .Determine the system is memoryless , causal, linear shift variant. Justify your answers. Nov/Dec Refer Notes

C312.1 BTL 5

A causal system is represented by the following differential equations Y(n)+1/4 Y(n-1)=X(n)+1/2 X(n-1). Find the system function H(Z) and its coreponding region of convergence(ROC) Nov/Dec Refer Notes

C312.1 BTL 4

Find the unit sample respose h(n) of the system for the given equation Y(n)+1/4 Y(n-1)=X(n)+1/2 X(n-1) Nov/Dec Refer Notes

C312.1 BTL 1

Determine the inverse Ztransform of X(Z)=1/1-1.5 z-1 +0.5 Z-2) if ROC Z>1, ROC Z<0.5 and ROC 0.5<Z<1 Apr/May 2017 Refer Notes

C312.1 BTL 5

Find the Z transform and ROC of (i) X(n)=s(n) (ii) X(n)=[3(3)n-4(2)n]u(n) OR (Determine the region of convergence of the following signal using Ztransform:x(n)=u(-n), x(n)=u(l-n), x(n)=2n U(n). Nov/Dec 2018.) Check whether the system y(n)=nX2 (n) is static or dynamic linear or nonlinear, time variant or time invariant ,causal or Non causal April/May 2018 Refer Notes

C312.1 BTL 5

Determine the response of the system described by the difference equation y(n)=0.7 y(n-1)-0.12 y(n-2)+x(n-1)+x(n-2) to the input x(n)=n u(n) April/May 2018 Refer Notes

C312.1 BTL 5

UNIT II PART A

Q. No. Questions CO Bloom’s Level 1 Find the DTFT of a sequence x(n) = an u(n). Nov/Dec 2006, MAY/JUNE 2016, Solution: x ( n )  anu ( n )      n X ( ej^ ) x ( n ) e j^  n      0 ( ) n X ej^  ane j^  n n n X ( ej^ ) ( aej ) 0          e^ j j a X e    1 1 ( )

C312.2 BTL 1

What is FFT? Nov/Dec 2006 The Fast Fourier Transform is a method or algorithm for computing the DFT with reduced number of calculations. The computational efficiency can be achieved if we adopt a divider and conquer approach. This approach is based on decomposition of an N-point DFT in to successively smaller DFT’s. This approach leads to a family of an efficient computational algorithm is Known as FFT algorithm

C312.2 BTL 1

The first five DFT coefficients of a sequence x(n) are X(0) = 20, X(1) 5+j2,X(2) = 0,X(3) = 0.2+j0.4 , X(4) = 0. Discover the remaining DFT coefficients. May/June 2007 April/May 2017 X (K) = [20, 5+j2, 0, 0.2+j 0.4, 0, X (5), X (6), X (7)] X (5) = 0.2 – j0. X (6) = 0 X (7) = 5-j

C312.2 BTL 4

What are the advantages of FFT algorithm over direct computation of DFT? Nov/Dec2017 May/June 2007 Reduces the computation time required by DFT. Complex multiplication required for direct computation is N2 and for FFT calculation is N/2 log 2 N. Speed calculation.

C312.2 BTL^1

State and prove Parseval’s Theorem. Nov/Dec 2007 Parseval’s theorem states that If x(n) ↔ X(K) and y(n) ↔ Y(K) , Then

C312.2 BTL 2

Proof: By the definition of DFT; N- 1 X(K) = ∑ x(n) e (–j2πnK)/N n= Replace ‘K’ by ‘N-K’ N- 1 X(N-K) = ∑ x(n) e (–j2πn(N-K))/N n= 10 Define DFT pair. May/June 2013 The DFT is defined as N- 1 X (K) = ∑ x(n) e (–j2πnK)/N ; K = 0 to N- 1 n= The Inverse Discrete Fourier Transform (IDFT) is defined as N- 1 x (n) = ∑ X(K) e (j2πnK)/N ; n = 0 to N- 1 K=

C312.2 BTL 1

Distinguish between linear & circular convolution. S. N N o Linear convolution circular convolution 1 The length of the input sequence can be different. The length of the input sequence should be same. 2 Zero Padding is not required. Zero padding is required if the length of the sequence is different.

C312.2 BTL 4

Why Zero padding is needed? Nov/Dec 2011 Appending zeros to the sequence in order to increase the size or length of the sequence is called zero padding. In circular convolution, when the two input sequence are of different size , then they are converted to equal size by zero padding.

C312.2 BTL 1

Write the shifting property of DFT. Time shifting property states that DFT {x(n-n0)} = X(K) e (–j2πn0K)/N

C312.2 BTL 1

X(N-K) = X*(K)

Why do we go for FFT? The FFT is needed to compute DFT with reduced number of calculations. The DFT is required for spectrum analysis on the spinals using digital computers.

C312.2 BTL 1

What do you mean by radix-2 FFT? The radix - 2 FFT is an efficient algorithm for computing N- point DFT of an N-point sequence .In radix-2 FFT the n-point is decimated into 2-point sequence and the 2-point DFT for each decimated sequence is computed. From the results of 2-point DFT’s, the 4-point DFT’s are computed. From the results of 4 – point DFT’s ,the 8-point DFT’s are computed and so on until we get N - point DFT.

C312.2 BTL 1

Is DFT of a finite duration sequence is periodic? If so state the theorem Yes .periodic. April/May 2018 Theorem : periodicity property If x(n)—X(Z) Then x(n+K)---X(Z+K)

C312.2 BTL 4

How many multiplications & addition are involved in radix-2 FFT? (May/June 2012)(Nov/Dec 2010) For performing radix-2 FFT, the value of N should be such that, N= 2m. The total numbers of complex additions are N log 2 N and the total number of complex multiplication are (N/2) log 2 N.

C312.2 BTL^1

What is Twiddle factor? Nov/Dec 2012,Nov/Dec 2011 Twiddle factor is defined as WN = e – j2π/N. It is also called as weight factor.

C312.2 BTL 1

What is main advantage of FFT? Nov/Dec 2012,May/June 2012. FFT reduces the computation time required to compute Discrete Fourier Transform

C312.2 BTL 1

Distinguish between DFT and DTFT. Nov/Dec 2011 & May /June 2012 S.NO DFT DTFT

1. Obtained by performing sampling operation in Sampling is performed only in time domain.

C312.2 BTL 4