463

the z-transform of the sequence x(n) = [1*,0,0,0..] is a. 0 b. 1 c. u(n) d. gamma(z)

B

The area of the complex plane in which X(z) converges a. cannot contain a zero b. is where |z| < 1 c. cannot contain a pole d. is not contiguous

C

A FIR linear predictor for speech ...... the system function H(z) for this is? a. z^-1/(a1+a2z^-1 + a3z^-3) b. blah c. blah d. blah blah

a

A complex vector Z has magnitude 29 and is represented by the complex point (20,Y) Y is equal to a. 21 b. 41 c. 25 d. 18

a

A set of two solutions of a difference equation that comprise the entire solution are sometimes called a. zero-input and zero-state b. transient and constant c. general and particular d. time and space

a

BONUS QUESTION FROM MIDTERM2 if f(x) = x^3 - x + 2 with F = [1,0,-1,2] and g(x) = x - 2 + 5x^-1 with G = [1,-2,5], then the coefficients of the product f(x)g(x) can be found using the Matlab command of a, conv(F,G) b, F. *G c, sigmult(F,G) d, F^G

a

BONUS QUESTIONS FROM MIDTERM2 A boundary of the region of convergence of a Z-transform is always indicated by a, a pole b, a discontinuity c, | z | = 1 d, a zero

a

BONUS QUESTIONS FROM MIDTERM2 A casual LTI system with a system function Z-transform H(z) is stable if and only if a, the poles of H(z) are inside unit circle b, H(z) converges c, the unit circle is inside ROC d, |H(z)| < infinity for | z | > 1

a

BONUS QUESTIONS FROM MIDTERM2 A system function H(z) has poles of magnitude 1 lying at +- 90 degrees and only a zero at 0.5. Its Z-transform is a, (z - 0.5) / (z^2 + 1) b, (z - 0.5) / (z^2 - 2z + z) c, (z^2 - 0.5z) / (z^3 + 1) d, (0.5 - z^-1) / (1 - z^-2)

a

BONUS QUESTIONS FROM MIDTERM2 Given the LSI system y(n) = x(n) + 3y(n - 1) + 2y(n - 2), the magnitude of the system function H(z) at z = e^-j*pi is a, 1/2 b, 1/4 c, 0 d, infinity

a

BONUS QUESTIONS FROM MIDTERM2 If x(n) = a^n * u(n) for 0 < | a | < infinity, the sequence x(n) is classified as a, positive time b, left-handed c, stable d, unbounded

a

BONUS QUESTIONS FROM MIDTERM2 The complex variable z is used in the definition of the Z-transform is a, z = | z | e^j*omega b, z = | z | e^-jomegan c, z = | z | e^jomega| z | d, z = | z | e^-jomegat

a

BONUS QUESTIONS FROM MIDTERM2 The radius of the circle outside of which a Z-transform of x(n) converges is equal to the magnitude of the a, largest pole b, smallest zero c, largest zero d, smallest pole

a

BONUS QUESTIONS FROM MIDTERM2 The residues of the partial fraction expansion of X(z) = 1 / (1-0.25z^-2) = r1 / (1 - 0.5z^-1) + r2/(1 + 0.5z^-1) are a, 1/2, 1/2 b, 1, -1 c, 0, 2 d, 1, -1/2

a

BONUS QUESTIONS FROM MIDTERM2 The soultion to the general difference equation y(n) = summation m=M, m = 0 x(n-m) - summation k=K, k = 1 y(n-k) has a, a transient and a steady state solution b, a total of M + K solutions c, M or K solutions, whichever is larger d, a left and a right handed solution

a

If the complex variable z = 0.6 -0.8j, then it could be found in the complex plane somewhere on a circle centered on the origin of radius a. 1 b. 0.5 c. 2 d. 0.125

a

If the impulse response of an LSI system is the sequence h(n) = {1,-2,1} and the input into the system is the sequence x(n) = {-1,2}, the output y(n) of the system would be the sequence a. {1 -4 5 -2} b. {-2 5 -4 1} c. {-1 -4 -5 2} d. {1 -4 -5 -2}

a

Is the transform T[x(n)] = cos(x(n)) shift invariant? a. No b. Yes c. Yes only if x(n) is imaginary d. it depends on the range of n

a

The LTI system described by the equation y(n_ = 2x(n) -3x(n-2) + 2y(n-1) -y(n-3) ....? a. a =[1,2,-3], b = [2,0,-1] b. c. d. a=[1,2,-1].b=[2,-3]

a

The angular frequency omega above which there are no freq in the FT of the signal x(t) is called the a. sampling freq b. bandwidth c. Nyquist Rate d. spectrum

a

The boundary of the circle outside of which the Z-transform of x(n) converges always contains a. at least a pole b. at least a zero c. nope d. a z where dX(z)/dz

a

The estimation of the current sample of a sequence based on its previous samples is called? a. linear prediction b. probable sample detection c. least squares estimation d. sample guesstimation

a

To avoid aliasing, a signal that is band-limited to pi * 10^6 Hz can be sampled at a minimum frequency: a. 2pi * 10^6Hz b. 0.5pi * 10^6 rad/sec c. 1 *10^g Hz d. 0.5pi * 10^6 Hz

a

What is a Matlab instruction that will square each element of a matrix P? a. P .^ 2 b. P * P c. P * P^1 d. P ^ 2

a

Which of the following transforms is linear? a. x(2n) - 2 b. 2x(2) -2x(n-2) c. x^2n d. e^j2x(n)

a

Which statement is true about the z-transform variable z? a. z is continuous b. | z | = 1 c. z is not periodic d. z is a real variable

a

an FIR filter is more commonly used in adaptive filtering because a. its system function only has zeros b. it rapidly converges c. it is insensitive to coeff drift d. its poles lie on the real axis

a

if H(w) = 1/(1-exp(j4w)) what is the magnitude of the response at digital freq w/pi = 0.25 a. 1 b. 0.5 c. 2 d. 1/4

a

if x(n) = anu(n) for 0<|a| < infinity, the sequence x(n) is a. positive time b. left-handed c. multiplicative d. unbounded

a

if you know the vocal characteristics of a certain voiced signal of length 1.5 sec are constant for only 7.5ms, how many blocks to divide? a. 200 b. 500 c. 100 d. 400

a

in the context of DSP, all the points that satisfy |z| = 1 in the complex plane define the a. unit circle b. region of convergence c. unity locus d. stability boundary

a

the basic operation used in LPC of speech to find the filter coeff via matrix inversion is a. correlation b. convolution c. exponentiation d. folding

a

the distance function using 4 equal sized steps around the figure with vertices at points x = [0,2,2,0] and [0,0,1,1] would be a. d = rad5 [ .5,.5,.5,.5] b. d = [1,.5,.5,1] c. nope d. d = 1/2 [1, 1, 1 1]

a

the residues of a partial fraction expansion of X(z) = 1/ (1-0.25z^-2) = r1/(1-0.5z^-1)+.... a. 1/2, 1/2 b. 1,-1 c. 0,2 d. 1/2, -1/2

a

what are the Matlab commands that find the output y(n) of a system with input sequences of x(n) = (0.9)n u(n) and impulse response h(n) = exp((-n^2)/5 u(n)) for 0<=n<=50? a. y = conv_m(x,h,n) b. to long to write c. y = filter(x,h,n==0) d. y= conv(x,h)

a

what is the result of the Matlab instruction: x =[1,-3,4,-2,0,5]; y = sum(x<0) a. y = 2 b. y = 10 c. y = 0 d. y = -5

a

A casual LTI syste, with Z-transform H(z) is stable if and only if the a. H(z) converges b. poles of H(z) are inside unit circle c. unit circle is inside ROC d. nope

b

A discrete signal x(n) = {-1*,1} ... with sequence y(n) = {2*,0,1} to give z(n)= x(n) corr y(n) a. {1,-2,3,-1} b. {-1,1,-2,2} c. {1,-2,0,-1} d.{2,-2,-1,1}

b

A sine wave which has zero-crossing of time x-axis every 10^6 seconds has frequency of a. 1/2Mhz b. 1Mhz c. 50Khz d. 1Khz

b

A value of 0.4pi radians is equivalent to how many degrees a. 22.5 b. 72 c. 62.5 d. 54

b

BONUS QUESTION FROM MIDTERM2 The Z-transform of the sequence x(n) = {0,0,1*,0,0,0,...} is a, z^-1 b, 1 c, u(n) d, delta(z)

b

BONUS QUESTION FROM MIDTERM2 The discrete-time Fourier transform has a very inconvenient shortcoming, namely a, it has no inverse b, some useful signals lack one c, it is not continuous d, it is complex

b

BONUS QUESTIONS FROM MIDTERM2 A casual LTI system is y(n) = 0.5x(n - 1) + 0.5y(n - 2). The magnitude of the system function H(z) at z = 1e^jpi is a, 0.5 b, 1 c, 0 d, 2

b

BONUS QUESTIONS FROM MIDTERM2 If x(z) = z / (z - b) with | z | < | b | then the associated time sequence x(n) is a, x(n) = -b^n * u(-n) b, -b^n * u(-n - 1) c, b^n * u(n / b) d, - | b^n | e^-jomegan

b

BONUS QUESTIONS FROM MIDTERM2 The inverse transform of X(z) = 1/1(1 + (2/3) z^-1 ) with ROC of |z| > 2/3 is a, - (2/3)^n * u(-n - 1) b, (-2/3)^n * u(n) c, (2/3)^n * u(n) d, (2/3)^-n * u(n)

b

Evaluation X(z), the Z-transform of x(n), around the unit circle yields the a. Fouries Series of x(n) b. DTFT of x(n) c. periodic Z-transform X~(z) d. the sequence x(n)

b

Given sequence x =[4.74,7.38,7.74,2.44....,] which sample is found at index n = 3? a. 7.74 b. 8.48 c. 2.44 d.1.75

b

Let x = 2-0j and y = 1-1j and the quotient x/y is a. 2+2j b. 1+1j c. 1/2 - 1/2 j d. 1-1j

b

The centroid C = (x,y) of a figure with vertex vectors Vx and Vy used in computing the distance functions is a. C = (sum(Vx), sum(Vy)) b. C = (sum(Vx)/length(Vx), sum(Vy)/length(Vy) c. C = (max([Vx,Vy]), min([Vx,Vy]) d. C = sum([Vx,Vy]/length(Vx)

b

The convergence of the FIR coeff in the LMS algorithm in the text is done by using the method of a. approximating the squared error b. steepest-descent(gradient) c. pure guesswork d. polynomial minimization

b

The inverse transform of X(z) = 1/(1-2z-1/3) with ROC of | z | > 2/3 is a. -(2/3)n u(-n-1) b. (2/3)n u(n) c. (-2/3)n u(n) d. (2/3)-n u(n)

b

The time-shifting property of the Z-transform is indicated by the equation a. Z[x(-n)= X(1/z) b. Z[x(n-k)] = z^-k X(z) c. d. Z[x* (n)] = X*(z*)

b

What is the sum of the infinite series (1-1/5 + 1/25 -1/125...)? a. 2/3 b. 5/6 c. 11/15 d. 8/10

b

find the first DFT coeff in the periodic sequence x(n) = {2*,0,0,-2} a. 2 b. 2+2j c. 4 d. 0

b

if a 25Khz sinusoidal signal x(t) is sampled at fs= 100kHz, what then is the digital angular freq (w) in rad/sample with the analog signal x(t)? a. 10 pi b. pi/2 c. 0.25pi d. 1/4

b

if the correlation coeff used in conjunction with the distance function has a value of 0.15, then a. the two figures are similar in shape b. the two figures have little similarity in shape c. the two figures have a different number of vertices d. the value is insignificant since it is near zero

b

if the distance function consists of a plot that is very nearly a constant value for all step indexes then a. the figure is a square b. the figure is degenerate( is a line with vertices colinear) c. the figure is nearly circular d. an error is suggested

b

the Fourier transform has a very inconvenient shortcoming, namely a. it has no inverse b. some useful signals lack one c. it is not continuous d. it is complex

b

the error e(n) used in the linear predictive coding speech is the difference between the a. observed sample s(n) and the past sample s(n-1) b. estimated sample s(n) and the s(n-1) c. observed sample s(n) and predicted next sample s(n+1) d. observed sample s(n) and the predicted sample s(n)

b

the unit step sequence of s(n) = u(n-3) -u(n-6) is the same as the sequence a. [1,1,1,1*,1,1,1,1,1] b. one(3,6) c. d.

b

what is the third element in the sequence of the circular conv (order N=4) of z=x*y if using the sequences x ={1*,1,-3} and y ={-2*,-1,0,1} a. 0 b. 5 c. 2 d. -1

b

which is NOT a true completion of: The LMS algorithm of the text has a step size parameter that a. if large, can result in instability b. if small, can slow the rate of convergence c. can be chosen in range 0 to 1 d. should be chosen according to input seq characteristics

b

BONUS QUESTIONS FROM MIDTERM2 A system has a difference equation description of y(n) = x(n) - 0.5y(n-1) with initial condition of y(-1) = 2. If the input is x(n) = delta(n), the one-sided z-transform Y*(z) would be a, -1/(1 - 0.5z^-1) b, 1/(1 + 2z^-1 - 3z^-2) c, 0 d, 3/(1 + 0.5z^-1)

c

BONUS QUESTIONS FROM MIDTERM2 If X(z) = 1/(1 - 0.25z^-1) - 1/(1 - 0.25z^-1)^2 for | z | > 0.25, x(n) is a, (1/4)^n+1 * u(n) b, (1/4)^n+1 u(n) - 4(1/4)^n+1 u(n+1) c, (1/4)^n u(n) - 4(n+1)(1/4)^n+1 u(n+1) d, [(1/4)^n - (n/4)(1/4)^n] * u(n)

c

BONUS QUESTIONS FROM MIDTERM2 If the Z-transform of x(n) is X(z) = 1/(1 - z^-1) with ROC | z | > 1 and Y(z) = z X(1/z), then y(n) would be a, u(n + 1) b, u(1 - n) c, u(-n - 1) d, -u(n - 1)

c

BONUS QUESTIONS FROM MIDTERM2 In the context of DSP, the function | z | = 1 describes the a, complex plane b, region of convergence c, unit circle d, stability boundary

c

BONUS QUESTIONS FROM MIDTERM2 Let Z[x(n)] = X(z) = 1/1(1 - 0.3z^-1) for | z | > 0.3. Then the inverse z-transform of X(z/3) is a, (0.1)^n * u(n) b, (0.3)^n/3 * u(n) c, (0.9)^n * u(n) d, (0.3)^n-3 * u(n-3)

c

Given a polynomial coeff vector F = [1*,2,-3,4] and G = [2*,-1,2], poly found in matlab using? a. sigmulti(F,G) b. F .* G c. conv(F,G) d. F*G

c

Given the 3x4 matrix A as A=[11 -5 -9 1; -8 3 5 0; 9 3 -1 -4], what then is the result of X = sum(A(:,2))? a. x=0 b. x=3 c. x= 1 d. x=-2

c

Given two arbitary row vectors x and y of length N, which matlab expression makes a scalar a. x.*y b. x*y c. y*x` d. x`*y

c

Is the transform given by y(n) = T[x(n)] = 3x(n+1) + 2x(n-1) a casual LSI tranformation? a. no b. yes c. yes if all |x(n) | < 1 d. Yes for all |n| > 1

c

The DTFT of the finite sequence of x(n) = {1*,0,0,-1} evaluated at w = pi/3 is the value a. 2+0j b. 1-1j c. 1+0j d. 0+2j

c

The process of adjusting filter coeff to remove interfering sinusoids in real time is an application of a. notch filtering b. fast freq cancellation c. adaptive filtering d. signal cancellation

c

The system function H(z) corresponding to the diff eq y(n) = x(n-1) - y(n-1) +2y(n-2) is? a. b. z^-1/(1-z^-1 + 2z^-2_ c. z^-1/ (1+z^-1 -2z^-2) d.

c

Typically the characteristics of the vocal tract are relatively constant for periods of a. 100 msec b. 20 msec c. 400 msec d. 1 sec

c

What is the shape of one period of the waveform given by Fourier Series if L = 1/2 a. triangular b. square c. sawtooth d. parabolic

c

Which of the following is not a propery of the convolution z(n) = x(n) *y(n)? Here * indicates convolution and gamma(n) is the delta impulse function. a. z(n) = y(n)*x(n) b. c. z(-n) = x(-n)*y(-n) d.

c

given the system y(n) = x(n) + 3y(n-1) + 2y(n-2) H(z) at z = 1 is a. 0 b. 1 c. 1/4 d. infinity

c

if the Z-transform of x(n) is X(z) = 1/(1-z-1) with ROC | z | > 1 and Y(z) = z X(1/z). Y(n) is a. u(n+1) b. u(1-b) c. u(-n-1) d. -u(n-1)

c

if the sample freq is 8 KHz, how many samples are found in voice signal 0.4 sec long a. 2000 b. 4800 c. 3200 d. 1600

c

the physical realization of the coeff of an FIR digital filter are sometimes referred to as a. indexes b. nodes c. taps d. h-vectors

c

the poles of X(z) = z/(z^2-z+3/16) are found at locations in the z-plane of a. -4, -4/3 b. 4, 4/3 c. -1/4, -3/4 d. -1/4, 3/4

c

the sum of two phasors (rad2<45deg) and (rad2<315deg) is a. rad2<pi/8 b. 2<pi/4 c. 2 < 0 d.

c

A certain sequence x(n) has a z-transform x(z) with poles of radius 1 at +- 90deg and zero at 1. a. b. (z-1)/(z^2-2z+2) c. (z^2-z)/(z^2-1) d. (z-1)/(z^2+1)

d

A sequence x(n) is of length N = 1000. length M = 10 , circle convolution of order 16. How many elements...? a. 6 b. 4 c. 100 d. mod(1000,16)

d

A signal is sampled at a rate of fs = 10^3Hz, F=250Hz a. 2.5pi x 10^-3 b. 0.25pi c. 0.25pi x 10^-3 d. 0.5pi

d

A system has a diff eq of y(n) = -x(n) -2y(n-1) +3y(n-2) with initial conditions of y(-1) = y(-2) = 1 a. -1/ something b. 1/(something long) c. -3z^-1/ something long d. 0

d

BONUS QUESTIONS FROM MIDTERM2 The Z-transform when evaluated around the unit circle is the same as the a, continuous time Fourier transform b, phasor transform of a sinusoid c, the two-sided z-transform d, discrete time fourier transform

d

BONUS QUESTIONS FROM MIDTERM2 The area of the complex plane in which the z-transform X(z) converges a, doesn't contain a zero b, can't be the entire plane c, is where | z | < 1 d, doesn't contain a pole

d

BONUS QUESTIONS FROM MIDTERM2 The area of the complex plane where the Z-transform X(z) of the sequence x(n) exists is the a, annular locus b, boundary region c, unit circle d, ROC

d

BONUS QUESTIONS FROM MIDTERM2 The one-sided Z-transform is often used to find difference equation solutions when a, n >= 0 b, the input is x(n) is known c, when x(n) = 0 for all n < 0 d, there are initial conditions

d

BONUS QUESTIONS FROM MIDTERM2 The poles of X(z) = (z - 1/2)/(z^2 - 5/6 z + 1/6) are foudn at locations in the z-plane of a, 3, 2 b, -1/3, -1/2 c, -1/2, 1/3 d, 1/2, 1/3

d

If x(z) = 1/(1-a z-1) with ROC of | z | < | a | then the associated time sequence x(n) is a. -an u(-n) b. - | an| e-iru49r c. -an u(-n+1) d. -an u(-n-1)

d

The one-sided Z-transform is used to find diff eq solution when a. n>=0 b. input is x(n) is known c. when x(n) = 0 for all n<0 d. the are initial conditions

d

The simplest form of reconstruction interpolation to implement is a. 1st order hold b. sinc(x) c. cubic spline d. zero-order hold

d

The step size used in the distance function is a fraction of the figure's a. area b. number of vertices c. largest vertex angle d. perimeter

d

What is the freq resolution of a DFT using N=50 for a signal sampled at 1 KHZ? a. 50Hz b. 0.02Hz c. 100Hz d. 20Hz

d

if two poles of a system function H(z) are found at z^-1 = (0.6+j0.8) and z^-1(0.6-j0.8). y(n) is? a. b. y(n) = x(n) -x(n-1) -2y(n-2) c. y(n) = x(n-1) -1.2y(n-1) + y(n) d. y(n) = x(n-2) + y(n-2)

d

the are of the complex plane where the Z-transform X(z) of the sequence x(n) exists is the a. convergence boundary b. entire complex plane c. unit circle d. region of convergence

d

the complex variable of the z-transform is defined as a. b. z = | z | e^-jwn c. z = e^(jw | z |) d. z = | z | e^jw

d