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Sub Code:CS2403Subject Name:Digital Signal Processing (R- 2008) Class:IV Year CSEStaff Incharge:P.JAYABALASUBRAMANIAM,AP/ECE.

Question Bank

UNIT I Signals and systems 9Part-A

1.A.1) What is a linear time invariant system? (APRIL/MAY 2008)A system is said to be time invariant system if a time delay or advance of the input signalleads to an idenditical shift in the output signal. This implies that a time invariant systemresponds idenditically no matter when the input signal is applied. It also satisfies thecondition

Rx(n-k)=y(n-k).

1.A.2) What is known as aliasing? ( APRIL/MAY 2008) In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. It also refers to the distortion or artifactthat results when the signal reconstructed from samples is different from the original continuous signal.

Aliasing can occur in signals sampled in time, for instance digital audio, and is referred to as temporal aliasing. Aliasing can also occur in spatially sampled signals, for instance digital images. Aliasing in spatially sampled signals is called spatial aliasing.

1.A.3) Define ROC in Z-transform. ( APRIL/MAY 2008)The region of convergence (ROC) of X(Z) the set of all values of Z for which X(Z)attain final value.

1.A.4) Determine the Z-transform of the sequence x(n)=2,1,-1,0,3 (APRIL/MAY 2008) X(Z)=2+1XZ-1- 1XZ-2+0XZ-4+3XZ-4

X(z)=2+Z-1-Z-2+3Z-4

1.A.5) Check whether the system is linear y(n)=ex(n) (APRIL/MAY 2007) Y1(n)=ex1(n)

Y2(n)=ex2(n)

y(n)=a1ex1(n)+a2ex2(n)-----------------1 y(n)=e(a1x(n)+a2x2(n))-------------------------2 equn 1≠ equn 2 So the system is non-linear systems.

1.A.6) State sampling theorem. (APRIL/MAY 2007)

Sampling is the process of converting a signal (for example, a function of continuous time or space) into a numeric sequence (a function of discrete time or space). Shannon's version of the theorem states:[2]

If a function x(t) contains no frequencies higher than Bhertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

A sufficient condition to reconstruct x(t) from its samples is and equivalently The two thresholds, and are respectively called the Nyquist rate and Nyquist frequency.

1.A.7) Define LTI systems (Nov/Dec 2010)These systems are also called linear translation-invariant to give the theory the most general reach. In the case

of generic discrete-time (i.e., sampled) systems, linear shift-invariant is the corresponding term. A good example of LTI systems are electrical circuits that can be made up of resistors, capacitors, and inductors.

1.A.8) Differentiate linear and circular convolution (Nov/Dec 2010)

1.A.9) State sampling theorem and find Nyquist rate of the signal x(t)=5sin250πt+6cos600πt (APRIL/MAY 2008)

Take T=.004 ;fs=1/T = 250 Hz. Ωs=2πfs=2π*25 Hz=50π rad/secΩm=2πfm=600π fm=300 2fm=600 So the nyquist rate is = 600 Hz.

1.A.10) State and prove the convolution property of Z transform (APRIL/MAY 2008)

1.A.11) Find convolution of 5,4,3,2 and 1,0,3,2 (APRIL/MAY 2008)Yz)=H(z)X(z)H(z)=5+4Z-1+3Z-2+2Z-3 and X(z)=(1+3Z-2+2Z-3)Y(z)=(5+4Z-1+3Z-2+2Z-3)(1+3Z-2+2Z-2) =5+4z-1+18z-2+39z-3+9z-4+6z-5+10z-6

y(n)=5,4,18,39,9,6,101.A.12) Find rxy and ryx for x=1,0,2,3 and y=4,0,1,2 (APRIL/MAY 2008)

X(z)=(1+2Z-2+3Z-3); Y(z)=(4+Z-2+3Z-3)Correlation(rxy)=(1+2Z-2+3Z-3)(4+Z2+3Z3)=15+6Z-1+8Z-2+12Z-3+6Z+Z2+3Z3

Correlation(ryx)=(1+2Z2+3Z3)(4+Z-2+3Z-3)=15+z-2+3z-3+8z2+6z-1+12z3+3z

1.A.13) Determine Z transform for X(n)=-nanu(-n-1) (APRIL/MAY 2008)

1.A.14) Find whether the signal Y(n)=-n2 X(n) is linear. (APRIL/MAY 2008)Y1(n)=-n2X1(n) Y2(n)=-n2x2(n)Y(n)=-n2X1(n) -n2x2(n)-----1Y(n)=-n2(X1(n)+x2(n))-------21≠2 so the system is linear

1.A.15) What is causal system? (May/June 2013)The system is said to be causal if the output of the system at any time ‘n’ dependsonly on present and past inputs but does not depend on the future inputs.e.g.:- y (n) =x (n)-x (n-1)A system is said to be non-causal if a system does not satisfy the above definition.

1.A.16) Define impulse response of the system? (May/June 2012)In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its

output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).

1.A.17) Check for causality and linearity y(n)=x(n)-x(n2-n) (May/June 2013)The output of the system depends on the future values of the input. so the system is called causal system. Y1(n)=x1(n)-x1(n2-n) ; y2(n)=x2(n)-x2(n2-n)Y(n)=x1(n)-x1(n2-n)+x2(n)-x2(n2-n)Y’(n)=x1(n)-x2(n2-n)+x1(n)-x2(n2-n)Y(n)≠Y’(n)So the system is called nonlinear systems.

1.A.18) What are the advantages of DSP? ((Nov/Dec 2009)+ Linear and nonlinear math operations work over a wide dynamic range of signal, 2^31 to 2^-31 for standard floating point. Also a suite of operations, like cos(), atan(), sqrt(), log() are available. + Higher order filters can be implemented with a relatively low incremental cost. Additional memory and computations only.+ Filter design techniques provide a relatively high degree of freedom in spectral shaping, as in the Frequency Sampling method, for example. + No tuning of analog components (R,L,C) during production or during maintenance. + Good version control. Burn filter coefficients into memory and these will never change from one unit to the next. + Software-based implementations require no custom hardware - just use standard signal I/O boards and write custom software. + Small and rugged implementation using mixed-type VLSI, combining both DSP and analog I/O on a single chip.

1.A.19) Define impulse signal (NOV/DEC 2009)An impulse function is not realizable, in that by definition the output of an impulse function is infinity at certain values. An impulse function is also known as a "delta function", although there are different types of delta functions that each have slightly different properties. Specifically, this unit-impulse function is known as the Dirac delta function. The term "Impulse Function" is unambiguous, because there is only one definition of the term "Impulse".

1.A.20) What is meant by aliasing? How can it be avoided? (May/June 2006)Given a power spectrum (a plot of power vs. frequency), aliasing is a false translation of power falling in

some frequency range outside the range. Aliasing can be caused by discrete sampling below the Nyquist frequency. The sidelobes of any instrument function (including the simple sinc squared function obtained simply from finite sampling) are also a form of aliasing. Although sidelobe contribution at large offsets can be minimized with the use of an apodization function, the tradeoff is a widening of the response (i.e., a lowering of the resolution).

1.A.21) Is the system Y(n)=ln[x(n)] is linear and time invariant. (May/June 2006)Here the Output of the systems depends on present input so the systems is called linear systems.This systems did not satisfy the BIBO condition . so this system is said to be linear system.

1.A.22) Determine the energy of the sequence x(n)=(1/2)n n≥0. (May/June 2011)E=1/1-1/2 = 2 joules.

1.A.23) Find final value of x(n) if x(z)=(1+z-1)/(1-0.25 z-2) (May/June 2011)Final value: X(Z)=(1+Z-1)(1-0.25Z-2) X(Z)=Z=0; X(Z)=z=0;

=(1+0)(1-.025)=(1*0.75)X(Z) =0.75

1.A.24) What is zero padding ? What are its uses. (April/May 2010)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 aszero 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.

1.A.25) Define symmetric and anti-symmetric signals (May/June 2007)Even signal: continuous time signal x(t) is said to be even if it satisfies the conditionx(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 oddsignals are anti-symmetric about the vertical axis.

1.A.26) What are the properties of ROC? (May/June 2007) 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.

Part-B

1.B.1) (i) explain the concept of energy and power signals. Also checks whether the following signals are energy or power signal.(12) (1)x(n)=(1/3)n u(n) (2)x(n)=sin (p*/4)n (12) (APRIAL/MAY 2008)∞ ∞Energy = ∑ |x(n)|2 Power=1/(2N+1) ∑ |x(n)|2

n=- ∞ n=- ∞(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.1.34-1.36)

(ii)briefly explain Quantization.(4) (APRIAL/MAY 2008)

Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set – such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The round-off error introduced by quantization is referred to as quantization error.

In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or truncation. The error signal is sometimes considered as an additional random signal called quantization noise because of its stochasticbehaviour. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms.

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.1.173-1.74)

1.B.2) check the following system for linearity, time invariance , causality and stability . (APRIAL/MAY 2008)(i) y(n) = e^x(n) (ii)y(n) = x(-n+2). (16)

Causal :The output of the systems depends on past and present values of the input and does not depend on future values of input.

Static:The output of the systems depends only on present value of the input and does not depend past and future value of input.Time invariance:The output of the systems will not vary with respect to time period.

Y’(n-k)=y(n,k)Linearity:The systems will satisfy the BIBO coditions.

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.1.53-1.57)

1.B.3) (i) Determine the Z-transform of x(n)=coswn u(n). (6) (APRIAL/MAY 2008)∞

X(Z) = ∑ x(n)Z-n

-∞(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.16-2.17)

(ii) state and prove the following properties of Z-transforms: (APRIAL/MAY 2008)(1)time shifting (2)time reversal (3)differentiation (4)scaling in Z domain. (10)Properties of Z-TransformThe z-transform has a set of properties in parallel with that of the Fourier transform (and Laplace transform). The difference is that we need to pay special attention to the ROCs. In the following, we always assume

and

Time Shifting

Proof:

Define , we have and

The new ROC is the same as the old one except the possible addition/deletion of the origin or infinity as the shift may change the duration of the signal.

Time Expansion (Scaling)

The discrete signal cannot be continuously scaled in time as has to be an integer (for a non-

integer is zero). Therefore is defined as

Example: If is ramp

1 2 3 4 5 6

1 2 3 4 5 6

then the expanded version is

1 2 3 4 5 6

0.5 1 1.5 2 2.5 3

1 2 3

0 1 0 2 0 3

where is the integer part of . Proof: The z-transform of such an expanded signal is

Note that the change of the summation index from to has no effect as the terms skipped are all zeros.

Time Reversal

Proof:

where

Scaling in Z-domain

Proof:

In particular, if , the above becomes

The multiplication by to corresponds to a rotation by angle in the z-plane, i.e., a frequency

shift by . The rotation is either clockwise ( ) or counter clockwise ( ) corresponding to, respectively, either a left-shift or a right shift in frequency domain. The property is essentially the same as the frequency shifting property of discrete Fourier transform.

Differentiation in z-Domain

Proof:

i.e.,

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.8-2.15)

1.B.4) (i) Determine the inverse Z transform of X(z)=(1+3z ^-1)/(1+3z^ -1 +2z ^-2) for |z| >2. (8) (APRIAL/MAY 2008)

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.34-2.38)

(ii) compute the response of the system y(n)=0.7y(n-1)-0.12y(n-2)+x(n-1)+x(n-2) (APRIAL/MAY 2008)to input x(n)= n u(n). (8)

Step 1:Find Y(Z) using Z transform Step 2 :Find X(z) using Z transform Step 3: find h(n) , first find H(z) using formula H(z)=Y(z)/X(z) Step 4:Find the h(n) using inverse Z transform.

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.56-2.57)

1.B.5) i.Find the response of the system for the input signal x(n)=1,2,2,3&h(n)=1,0,3,2 (APRIL/MAY 2007)Step 1:Find Y(Z) using Z transform Step 2 :Find X(z) using Z transform Step 3: find h(n) , first find H(z) using formula H(z)=Y(z)/X(z) Step 4:Find the h(n) using inverse Z transform.

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.59-2.60)

1.B.6) ii.Find the inverse Z transform of the system H(z)= 1/(1-1/2Z-1)( 1-1/4Z-1) (APRIL/MAY 2007)

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.34)1.B.7) Find the convolution and correlation of the for x(n)=0,1-2,3,-4 and h(n)=0.5,1,2,1,.0.5 (APRIL/MAY 2008)

Step 1:Find X(Z) using Z transform Step 2 :FindH(z) using Z transform Step 3: Using formula find Y(z)=X(z)H(z)Step 4: To find convolution y(n) using inverse Z transform Step 5: to find correlation Y(z)=X(z)X(Z-1)Step 6: find y(n) usinf Z transform.

1.B.8) Determine the impulse of the difference equation y(n)+3y(n-1)+2y(n-2)=2x(n)-x(n-1) (APRIL/MAY 2008)Step 1:Find Y(Z) using Z transform Step 2 :Find X(z) using Z transform Step 3: find h(n) , first find H(z) using formula H(z)=Y(z)/X(z) Step 4:Find the h(n) using inverse Z transform.

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.65)1.B.9) A linear shift invariant system has a unit impulse response h (n) =u (-n). find the output if the input is X(n)=(1/3)nu(n) (May/June 2013)

Step 1:FindH(Z) using Z transform Step 2 :Find X(z) using Z transform Step 3: find h(n) , first find H(z) using formula y(z)=X(z)H(z)Step 4:Find the h(n) using inverse Z transform.(Dr.S.Palani, Digital signal processing,firstedition,Ane Books Pvt.,Ltd.,2010.Page.No.4.66)

1.B.10) Classify, express and explain the various types of signals. (May/June 2013)

Classifications of Signals

Along with the classification of signals below, it is also important to understand the Classificationof Systems.

Continuous-Time vs. Discrete-Time

As the names suggest, this classification is determined by whether or not the time axis(x-axis) is discrete (countable) or continuous . A continuous-time signal will contain avalue for all real numbers along the time axis. In contrast to this, a discrete-time signal isoften created by using the sampling theorem to sample a continuous signal, so it will onlyhave values at equally spaced intervals along the time axis.

Analog vs. Digital

The difference between analog and digital is similar to the difference between continuous timeand discrete-time. In this case, however, the difference is with respect to the value ofthe function (y-axis). Analog corresponds to a continuous y-axis, while digital correspondsto a discrete y-axis. An easy example of a digital signal is a binary sequence, where thevalues of the function can only be one or zero.

Periodic vs. Aperiodic

Periodic signals repeat with some period T, while aperiodic, or nonperiodic, signals do not.We can define a periodic function through the following mathematical expression, where tcan be any number and T is a positive constant:f (t) = f (T + t) (2.7)The fundamental period of our function, f (t), is the smallest value of T that the stillallows the above equation, Equation 2.7, to be true.

Causal vs. Anticausal vs. Noncausal

Causal signals are signals that are zero for all negative time, while anitcausal are signalsthat are zero for all positive time. Noncausal signals are signals that have nonzero valuesin both positive and negative time.

Even vs Odd

An even signal is any signal f such that f (t) = f (−t). Even signals can be easily spottedas they are symmetric around the vertical axis. An odd signal , on the other hand, is asignal f such that f (t) = −(f (−t)).Using the definitions of even and odd signals, we can show that any signal can bewritten as a combination of an even and odd signal. That is, every signal has an odd-evendecomposition. To demonstrate this, we have to look no further than a single equation.

f (t) = (f (t) + f (−t)) +(f (t) − f (−t))

By multiplying and adding this expression out, it can be shown to be true. Also, it can beshown that f (t) + f (−t) fulfills the requirement of an even function, while f (t) − f (−t)fulfills the requirement of an odd function.

Deterministic vs Random

A deterministic signal is a signal in which each value of the signal is fixed and can bedetermined by a mathematical expression, rule, or table. Because of this the future values

(P.Rameshbabu, Digital signal processing, fourth edition, 2011.Page no.1.22-1.34)

1.B.11) Obtain the Z transform and ROC for i).x(n)=-bnu(-n-1)ii). X(n)=anu(n)

Z transform of the sequence

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.4-2.5)

1.B.12) Find x(n) if the given

X(Z)=(1+3Z-1)/( 1+3Z-1+2Z-2) for ROC |Z| 2

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.34-2.35)

1.B.13) Explain the following with suitable examples (May/June 2012)I. Linear systems ii. Time invariant systemsiii.Causal systems

Memoryless systemsA system is memoryless if the output y[n] depends only on x[n] at thesame n. For example, y[n] = (x[n])2 is memoryless, but the ideal delay

Linear systemsA system is linear if the principle of superposition applies. Thus if y1[n]is the response of the system to the input x1[n], and y2[n] the responseto x2[n], then linearity implies

Time-invariant systemsA system is time invariant if a time shift or delay of the input sequencecauses a corresponding shift in

the output sequence. That is, if y[n] is the response to x[n],then y[n -n0] is the response to x[n -n0].For example, the accumulator systemis time invariant, but the compressor systemfor M a positive integer (which selects every Mth sample from a sequence) is not.

CausalityA system is causal if the output at n depends only on the input at nand earlier inputs. For example, the backward difference systemis causal, but the forward difference system

StabilityA system is stable if every bounded input sequence produces a boundedoutput sequence:

x[n] is an example of an unbounded system, since its response to the unitwhich has no upper bound.

Linear time-invariant systems

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.52-2.63)

1.B.14) Derive the relationship between input and output of LTI system in Z transform. (May/June 2012)

Step 1:Find Y(Z) using Z transform Step 2 :Find X(z) using Z transform Step 3: find h(n) , first find H(z) using formula H(z)=Y(z)/X(z) Step 4:Find the h(n) using inverse Z transform.

(Dr.S.Palani, Digital signal processing,firstedition,Ane Books Pvt.,Ltd.,2010.Page.No.4.2-4.3)

1.B.15) Test the stability and causality of the following system (Nov/Dec 2009)i.Y(n)=Cosx(n) ii.Y(n)=X(-n-2)

Causal :The output of the systems depends on past and present values of the input and does not depend on future values of input.Stable: for any value of n the output of the systems will produce the constant output with respect to the input.(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.1.53-1.63)

1.B.16) Find the one sided Z transform of discrete sequences generated by the mathematically sampling of the following continuous time function (Nov/Dec 2009)

i.X(t)=sinwt ii.x(t)=coswt

To find Z transform of the sequence

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.16-2.17)

1.B.17) Define correlation and bring out the difference between convolution and correlation. (May/June 2006)A convolution is an integral that expresses the amount of overlap of one functionas it is shifted over another function.

You can use correlation to compare the similarity of two sets of data. Correlation computes a measure of similarity of two input signals as they are shifted by one another.

The correlation result reaches a maximum at the time when the two signals match best

The difference between convolution and correlation is that convolution is a filtering operation and correlation is a measure of relatedness of two signals

You can use convolution to compute the response of a linear system to an input signal. Convolution is also the time-domain

equivalent of filtering in the frequency domain.

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.11,2.15)

1.B.18) Determine the Z transform of the signal x(n)=anu(n)-bnu(-n-1) and plot the ROC. (May/June 2006)

To find Z transform of the sequence

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.5-2.6)

1.B.19) Find the system function of the system described by y(n)=0.5/[(1-.75z -1)(1-Z-1)]x(n) (May/June 2006)

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.38)

1.B.20) Find the system function of the system described by y(n-0.75y(n-1)-+0.125y(n-2)=x(n)-x(n-1) and plot the poles and zeros of H(z). (May/June 2006)

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.63-2.65)

1.B.21) State and prove sampling theorem. (May/June 2011)

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.1.168-1.172)

1.B.22) Find the Z transform of i.x(n)=anu(n) ii.y(n)=anu(n)-bnu(-n-1) iii.w(n)=ancosωonu(n)Wrte the ROC for all the above cases. (May/June 2011)

To find Z transform of the sequence

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.4-2.2.6)

1.B.23) Find the inverse Z transform of x(z)=z2+z/(z-1/3)3(z-1/4) for the ROC |z|>1/2 (May/June 2011)

(P.Rameshbabu,Digital signal processing,fourth edition,2011.Page no.2.50-2.51)

UNIT II FREQUENCY TRANSFORMATIONS 9Part-A

2.A.1) Define DFT pair. (APRIAL/MAY 2008)2.A.2) Draw the basic butterfly structure for DITFFT and DIF FFT Algorithms. (APRIAL/MAY 2008)2.A.3) Draw the Radix 4 FFT DIF Butterfly diagram.(MAY/JUNE 2007)2.A.4) Differentiate DFT and DTFT(Nov/Dec 2010) 2.A.5) Find DFT for 1,0,0,1(APRIL/MAY 2008)2.A.6) How DFT is computed using FFT algorithm.(May/June 2013)2.A.7) State the advantages of FFT over DFTs (May/June 2012)2.A.8) Find the DFT for x(n)=anu(n).(NOV/DEC 2011)2.A.9) Calculate the number of multiplications needed for the DFT computation of N=32 point sequence using FFT

algorithm.(NOV/DEC 2011)2.A.10) List any four properties of DFT.(Nov/dec 2009)2.A.11) Define DFT pair.(May /June 2006)2.A.12) Differentiate between DIT and DIF FFT algorithm.(May /June 2006)2.A.13) Give relation between Z-domain and frequency domain(May /June 2012)2.A.14) Calculate the DFT of the sequence x(n)=1,1,-2,2(Nov/Dec 2009)2.A.15) Mention the applications of FFT algorithm.(Nov/Dec 2011)2.A.16) Distinguish circular shifting and shifting in DFT (May/June 2011)2.A.17) Find the DFT OF y(n)=δ(n)-δ(n-n0)+δ(n+n0)? (May/June 2012)2.A.18) What is Radix-2 FFT . (May/June 2012)2.A.19) Draw the butterfly structure of DIT algorithm.(May/June 2007)

Part-B

2.B.1) Derive and draw the flow graph of the Radix-2 DIF FFT algorithm for the computation of 8-ponit DFT. (10) (APRIAL/MAY 2008)

2.B.2) what are differences and similarities between DIT and DIF FFT algorithm? (6) (APRIAL/MAY 2008)2.B.3) compute the 8-point DFT of the sequence x(n) =1,2,3,4,4,3,2,1 (10) (APRIAL/MAY 2008)2.B.4) illustrate the concept of circular convolution property of DFT. (6) (APRIAL/MAY 2008)2.B.5) Compare the computational complexity of direct computation of DFT Vs FFT algorithm (May/June 2013)2.B.6) Write a detailed technical note on the use of FFT algorithms in linear filtering and correlation with an example.

(May/June 2013)2.B.7) Compute the DFT of the signal x(n)=Cosnπ/2 for N=4 using DIT-FFT algorithm.Draw the flow diagram. Show all the Computations. (May/June 2013)2.B.8) Compute the DFT for the sequence 1,2,0,0,0,2,1,1 using Radix-2 DIF-FFT Algorithm.(16) (APRIL/MAY 2007)2.B.9) Explain the properties of DFT

1.Time shifting 2.Convolution 3.Time reversal 4.Complex conjugate poerty.(Nov/Dec 2011)2.B.10) Obtain the circular convolution of the sequence if X1(n)=1,0,1,0 and x2(n)=1,1,1,1 (Nov/Dec 2011)2.B.11) Satating the relevant equations obtain the eight point DIT- FFT algorithms (May/June 2012)2.B.12) State and prove the time shifting property of DFT .(May/June 2012)2.B.13) An 8 point sequence is given by x(n)=2,2,2,2,1,1,1,1 compute 8 point DFT of x(n) by

i.Radix-2 DIT FFT ii.RADIX DIF-FFT (Nov/Dec 2009)2.B.14) Using DFT-IDFT method , perform circular convolution of the sequences x(n)=1,2,0,1 and h(n)=2,2,1,12.B.15) State and prove the circular convolution property of DFT.2.B.16) Find DFT of X(k) given below X(k)=2,1,3,0,42.B.17) State and prove the multiplication in time property of DFT.(May/June 2012)2.B.18) Using FFT algorithm find the response of an LSI system with impulse response h(n)=1,2,-1 for the input x(n)=2,-4

(April/May 2010)2.B.19) Derive the frequency response of linear phase FIR filter of order N(odd) with symmetric condition.(April/May 2010)2.B.20) Find the linear convolution of x(n)=1,2,3 with h(n)=2,4 using DFT and IDFT.(Nov/Dec 2010)

UNIT III IIR FILTER DESIGN 9

Part-A3.A.1) State the condition for linear phase in FIR filters for symmetric and anti-symmetric response.

(APRIAL/MAY 2008)3.A.2) What is called pre warping? (APRIL/MAY 2008)3.A.3) Compare IIR and FIR digital filters. (Nov/Dec 2010)3.A.4) What are the various design methods available for IIR filters (May/June 2013)3.A.5) State any two properties of chebychev filters. (May/June 2012)3.A.6) What is the principle of impulse invariance method.(NOV/DEC 2011)3.A.7) Compare analog and digital filter (Nov/Dec 2009)3.A.8) Sketch the mapping of s-plane and z-plane in bilinear transformation (Nov/Dec 2009)3.A.9) Find the transfer function for normalized Butterworth filter of order 1 by determining the pole values.

(May/June 2006)3.A.10) Why we go for analog approximation to design a digital filter?(May/June 2012)3.A.11) Why impulse invariant method is not preferred in the design of IIR filter other than low pas filter?

(Nov/Dec 2011)3.A.12) What is the main objective of impulse invarianttransformation. (May/June 2011)3.A.13) Mention two important features of Butterworth filters. (May/June 2012)3.A.14) What is wraping effect? What is its effect on magnitude and phase response? 3.A.15) What is dead band?

Part-B3.B.1) Design a digital Butterworth filter satisfying the following constraints with T=1sec.using Bilinear transformation.

(12) (APRIL/MAY 2008)0.707=< |H(ejω)|=< 1 for 0 = < p /2

|H(ejω)|=<0.2 for 3p/43.B.2) Design and realize a Butterworth digital filter for the following specifications: (APRIL/MAY 2008)

Pass band gain required: -2dBFrequency upto which pass-banbd gain must remain more or less steady f1=300 Hz.Amount of attenuatuion required: -30 dBFrequency from which the attenuation must start f2=650 Hz.

3.B.3) Derive the impulse invariant transformation and obtain the frequency relationship

3.B.4) Design a chebychev analog low passfilter that have -3 dB cutoff frequency of 100 rad/sec and a stop band attenuation 25 dB or greater for all radian frequencies past 250 rad/sec. plot 20log|H(jΩ)| for your filter and show that you satisfy the requirements at the critical frequencies.(May/June 2013)

3.B.5) Convert the analog filter with system function Ha(S) into digital filter using bilinear transformation Ha(S)=S+03/(S-0.3)2+16 (May/June 2013) (May/June 2012)

3.B.6) Obtain direct form-I canonical and parallel form realization structures for the system given by the difference equation y(n)=-0.1y(n-1)+0.72y(n-2)+0.7x”(n)-.252x(n-2) (May/June 2012)

3.B.7) Enumerate the various steps involved in the design of low pass digital Butterworth IIR filter (May/June 2012)

3.B.8) Explain the concept of IIR filter design using approximation derivative.(Nov/Dec 2011)

3.B.9) Compare Bilinear transformation and impulse invariant method.(Nov/Dec 2011)

3.B.10) Compare the impulse invariant and bilinear transformation (Nov/Dec 2009)

3.B.11) Apply the bilinear transformation for the following (Nov/Dec 2009)i.Ha(S)=2/(S+1)(S+2) with T=1 and find H(z)ii.Ha(S)=2S/(S2+0.2S+1) WITH T=1 and find out H(z)

3.B.12) Explain the design procedure for lowpass digital butterworth IIR filter (Nov/Dec 2009)

3.B.13) Find the output response of the system given the input signal x(n)=1,-2,3,-2 and impulse response h(n)=2,-3,4(May/june 2006)

3.B.14) Obtain the direct I, canonic form and parallel form realization structures for the system given by the difference equation.Y(n)=-0.1y(n-1)+0.72y(n-2)+0.7x(n)-0.252x(n-2) (May/June 2006)

3.B.15) Obtain a parallel realization for the following H(z)=(8z3-4z2+11z-2)/(z-1/4)(z2-z+1/2) use direct form II realization for each section. (May/June 2011)3.B.16) Explain the different windows used in FIR filter design.(May/June 2011)

3.B.17) A Butterworth low pass has to meet the following specifications : Pass band gain of -1db at 4rad/sec, stop band attenuation greater than20db at 8 rad/sec. determine the transfer

function of the lowest order to meet the above specifications.(May/June 2012)

3.B.18) Explain the mapping between S plane and Z plane is done using bilinear transformation method. (May/June 2012)

3.B.19) Given the analog transfer function H(s)=[(S+0.1)/(S+0.1)2+9] find H(z) using (Nov/De 2010)i. Impulse invariant method ii.Bilineartransform.

3.B.20) Determine the pole zero for the system described by difference equationy(n)-3/4y(n-1)+1/8 y(n-2)=x(n)-x(n-1)(May/June 2007)

3.B.21) Apply bilinear transformation to H(s)= 2/(S+1)(s+2) with T=1 sec and find H(z). (Nov/Dec 2011)

3.B.22) Obtain the Direct form-I, cascade and parallel form realization for the following system.Y(n) = -0.2y(n-1) + 0.5 y(n-2) + 6 x(n) + 4.5 x(n-1) + 0.8 x(n-2).

UNIT IV FIR FILTER DESIGN 9

Part-A4.A.1) Write procedure for designing FIR filters using windows. (APRIL/MAY 2008)4.A.2) What are the features of FIR filters?(May/June 2013)4.A.3) Obtain cascade for realization of system function 1+5/2Z-1+2 Z-2+2 Z-3(May/June 2013)4.A.4) State Condition for FIR filters have linear phase.(may/june 2012)4.A.5) Write the steps involved in FIR filter design (Nov/Dec 2009)4.A.6) Write the expression for Kaiser Window function (Nov/Dec 2009)4.A.7) State the advantages ad disadvantages of FIR filter over II filter (May/June 2006)4.A.8) List out the different forms of structural realizations available. (May/June 2006) 4.A.9) What does frequency wraping? (May/June 2006) 4.A.10) Write the equation of Bartlett and hamming window. (May/June 2007)4.A.11) Define symmetric and ant symmetric FIR Filters 4.A.12) What is overflow limit cycle oscillations.(April/May 2010)4.A.13) Define limit cycle.(May/June 2011)4.A.14) Define power spectral density?(Nov/Dec 2011)4.A.15) How overflow limit cycles can be eliminated.(Nov/Dec 2009)4.A.16) How will you avoid limit cycle oscillations due to overflow in addition? (May/June 2006)4.A.17) Define gibbs phenomenon.(Nov/Dec 2011)4.A.18) How rounding is preferred over truncation in realizing digital filters.(May/June 2012)

Part-B4.B.1) obtain the cascade and parallel realization of the system described by (APRIAL/MAY 2008)

y(n)= -0.1y(n-1)+0.2y(n-2)+3x(n)+3.6x(n-1)+0.6x(n-2). (10) 4.B.2) discuss about any three window function used in the design of FIR filters. (6) (APRIAL/MAY 2008)

4.B.3) Design a low pass FIR filter for the following specifications using rectangular window. (May/June 2013)Frequency of pass band edge: 3000 Hz ; gain in pass band:-2dB Frequency from which stop band begins: 3000 HzGain in stop band : -50 dB ; sampling frequency 13 kHz

4.B.4) Write a detailed technical note on the frequency sampling techniques. (May/June 2013)

4.B.5) Design an FIR linear filter approximating the ideal frequency response (May/June 2013)

Hd(eiω) = 1 for | | ≤π/6

=0 for π/6≤| |<π/3

=1 for π/≤| |< π

Determine the coefficients of a 9 filter with Hanning window.

4.B.6) Explain in detail about frequency sampling method of designing an FIR filter (May/June 2013)4.B.7) State the issues in designing FIR filter using window method.(May/June 2012)4.B.8) Explain the type-1 and type-2 design of FIR filter using frequency sampling technique.(May/June 2013)4.B.9) Explain in detail the FIR filter design using windowing method.(NOV/DEC 2011)4.B.10) obtain the direct form structure of FIR filter for 1+2Z-1-3Z-2-4Z-3+5Z-4 (NOV/DEC 2011)4.B.11) Explain the design of FIR filter using Kaiser windows.(NOV/DEC 2011)4.B.12) Explain anti symmetric and symmetric linear phase FIR filters.(NOV/DEC 2011)4.B.13) Design a lowpass filter using rectangular window by taking 9 samples of ω(n) and with cutoff frequency of 1.2 rad/sec.(Nov/Dec 2009)

4.B.14) Design a linear phase lowpass filter with cutoff frequency of π/2 rad/sec using frequency sampling techniques (Take N=17) (Nov/Dec 2009)

4.B.15) Obtain the transversal structure and linear phase realization structure for a filter by (n)=0.5,2.88,3.404,2.88,0.5(May/June 2006)

4.B.16) Design a digital filter with Hd(ejω) = 1 for k=0,1,2,3,4

0.4 for k=50 for k=6,7 using Hamming window. Draw the frequency response.(May/June 2006)

4.B.17) Design an FIR filter satisfying the following specifications αp≤0.1db ; αp≥0.1db ωp = 20 rad/sec ωs=30 rad/secωsf=100 rad/sec. (Nov/Dec 2011)

4.B.18) Determine the frequency response of FIR filter defined by y(n)=0.25x(n)+x(n-1)+0.25x(n-2) . (Nov/Dec 2011)4.B.19) Describe the characteristics of the various windows used for design of FIR filters. (May/June 2012 )4.B.20) Explain frequency sampling method of designing FIR filter. Derive the frequency response and show that it has linear phase (Nov/Dec 2010)4.B.21) Find the system function and the impulse response of the system described by the difference equation y(n)=x(n)+2x(n-1)-4x(n-2)+x(n-3) (May/June 2007)

4.B.22) Design a filter with (May/June 2007)Hd(e-jω) =e-j3ω for -π/4 ≤ω≤ π/4

=0 for π/4 ≤ω≤ πUsing a Hanning window with N=7.

4.B.23) Consider the transfer function H(z)=H1(z) where H1(z)=1/(1-a1z-1) and H2(z)=(1-a2Z-1) assume a1=0.5 and a2=06 and find the output round off noise power.(Dec 2009)4.B.24) Derive the quantization input noise power and determine the signal to noise ratio.(NOV / DEC 2011)4.B.25) Limit cycle oscillations with an example.(NOV / DEC 2011)4.B.26) Explain shortly about signal scaling.(April/May 2010)

UNIT V APPLICATIONS 9

Part-A5.A.1) What are the factors that influence the selection of DSPs?(May/June 2012)5.A.2) What are the different buses of TMS 320C54x processor and list their functions.(May/June 2012)5.A.3) What are the shift instructions in TMS 320 C54x?(April/May 2010)5.A.4) List the on-chip peripherals of C54x processor.(Nov/Dec 2010)5.A.5) List the various registers used with ARAU.(April/May 2010)5.A.6) What are the advantages and disadvantages of C54x architecture?(Nov/Dec 2010)5.A.7) What is meant by vocoder.(Nov/Dec 2011)5.A.8) Define quantization noise.(Nov/Dec 2011)5.A.9) Distinguish Von Neumann and Harvard architectures.(Nov/Dec 2011)5.A.10) Write about the accumulators in TMS320C54X.(May/June 2011)5.A.11) Mention two advantages of Harvard architectures.(May/June 2012)5.A.12) What is stack addressing?(May/June 2012)5.A.13) What are the different stages of pipelining? (April/May 2010)5.A.14) What are the features of TMS320C54 dspprocessor.(April/May 2010)5.A.15) What are the different buses of TMS320C5X.(Nov/Dec 2010)5.A.16) Mention any two processors that support fixed point operation in TMS320c5X series.(Nov/Dec 2011)5.A.17) Define multirate signal processing?

Part-B5.B.1) Explain briefly about (May/June 2012)

i.Multirate signal processing ii.Vocoder5.B.2) Explain the application of DSP in Speech processing?(Nov/Dec 2011)5.B.3) What is a vocoder? Explain with a block diagram?(May/June 2012)5.B.4) Describe the function of on chip peripherals of TMS 320 C 54 DSP processor.5.B.5) What are the different buses of TMS 320 C 54 and their functions? (April/May 2008)5.B.6) Discuss in detail the various quantization effects in the design of digital filters. (April/May 2008)5.B.7) Explain in detail about the applications of PDSP (Nov/Dec 2011)5.B.8) Explain briefly:(Nov/Dec 2011)

i. Von Neumann architecture ii. Harvard architecture

iii. VLIW architecture 5.B.9) Explain in detail about(May/June 2012)

i. MAC unit ii. Pipelining

5.B.10) Draw and explain the architecture of TMS 320C54x processor (Nov/Dec 2010)5.B.11) Explain in detail about the Addressing modes of TMS 320C54X (Nov/Dec 2010)5.B.12) Draw and explain the architecture of TMS320C50 processor(Nov/Dec 2010)5.B.13) Explain in detail about MAC unit and pipelining with reference to TMS320C50.(April/May 2010)5.B.14) Write an assembly language program for linear convolution using TMS320C50.(Nov/Dec 2011)