Attachment # 00010392 - Practice_Exam_1_20011_(1).doc
Practice_Exam_1_20011_(1).doc (117.5 KB)
Raw Preview of Attachment:
(refer to the detailed question and attachment below)
Fall 2011 Lectures 1-7 Name ____________________________________ ID _______________________________________ Instructions Complete the exam on the space provided. When time is called, stop all work and follow the instructions provided. Any work that is not collected when called for will not be graded. The honor system will be strictly enforced. Allowed Open book Open notes Pocket calculators and laptops Figures and tables Internet access to Sakai (only) Disallowed Unauthorized Internet access Cell phones Q1 Sampling Theorem and Quantization You are to analyze the audio recording and playback system shown below. The input audio frequency range is f(0, 3.5kHz. The listeners hearing range is f(0, 8kHz. The ADC operates at the programmable sample rate of fs n8kHz, n an integer. SHAPE MERGEFORMAT What is the lowest sampling frequency fs that will insure that the original audio signal x(t) can be (theoretically) reconstructed from its time-series samples xk, without aliasing The room is presumed quiet and you begin recording at a sample rate of fs8k Sa/s. When played back you hear a 2k Hz buzzing sound in the captured signal. What is the expected minimum frequency of the extraneous tone that could have created this effect You decide to place an ideal analog lowpass anti-aliasing filter in front of the ADC. What should be the filters passband cut-off frequency The signed (10V ADC provides an 8-bit output with an input x(t)10V. What is the ADCs quantization step size The signed 8-bit ADCs output is sent to an accumulator that produces an output given by EMBED Equation.3 (not a MAC) What is the minimum number of integer bits that must be assigned to the accumulator to insure overflow-free run-time performance Q.2 z-Transforms Table 1 Primitive Signals and their z-TransformTime-domainz-transform(k 1uk z/(z1)akuk z/(za)kakuk az/(za)2You are studying a causal signal xk having a z-transform X(z) (z1)2/(z-1)(z-0.5)2. The signal has a Heaviside expansion given by X(z) (z1)2/((z-1)(z-0.5)2 ) A Bz/(z-1) Cz/(z-0.5) Dz/(z-0.5)2. Invert X(z) (Hint Think X(z) X(z)/z). What is A What is B c) What is C d) What is D e) What is xk f) What is x( g) What is x0 3. Sampling and Data Conversion d- What is the statistical quantization error in bits (i.e., how many fractional bits are statistically preserved) 4 Sampling Theorem and Quantization The home edition of American Idol uses the recording system shown below. The ADC is sampled at a 12000 Sa/s rate. The human vocal input is assumed limited to 4 kHz. SHAPE MERGEFORMAT a. Is the system BIBO stable b.- What is the difference equation the applies to the system shown on the right of the Figure shown above c.- What are the systems first 4 outputs if y-10 (system at-rest) and xkuk (unit step) Digital Signal Processing PAGE Exam 1 - PAGE 1 ( x(t) ADC DAC Interpolator Playback fs xk y(t) Memory Record ( ( x(t) fs Sampler Quantizer Q(xk) xk Reconstruction Shannon Filter yk y(t) Record Studio x(t) ADC ( DAC Interpolator Playback fs n6000 kSa/s xk y(t) fmax 4kHz x(t) Ts Delay ( xk yk (a) Ts Delay ( xk yk ( Ts Delay (b) zk - _D3 8biTw E9XiW2yisaN4dRAP m17@bPKvkQW5/-Cr-.(XVqF2nQxC5_-u,@ 1oLYl9B6Q,reQLX1( sod2JMJOXT_0K8wZ- @ rvL @ fxwKSl).yOo,_(lBHyUinsJRcxhxd6BHILei1k,.9B hl aB(9ejBa@BVOH F-5. hBSTjp, y e6Q(UD4eJ N9GiCsw_7ubf_y3svDyAqx9qgmbaQ/qfqWK2tSq z-b SbBjY-PhzC7XISCwSaF7xQImY/)BU/Xpi Ntf6ycjoLMKM FS_i0)3J BLDh@Mf_xDSOr22pMG)jC36sIndTF0oLYn/GnV.1S4 PG27y4.YTjxWvXrm,XsyA Bxo UYgh9X_ Qp61RV4gqyuP(ICO i@mkp @ hB2XfXh_Ru2/PBzy-Hh _5k/NvhSXm)J,Z6bBU6uk20G2st4H fQKNz93@N4uqK, 9g/ae Ix PhUL6Vb8H,mVKiSM@fC@H/j4usn)HX(nvQ@ xXWDE -O JNmTMMAIRBr LaBbxMQF3h t1QArBr 9J (E sJ0 x..pd Oeb6@l 8f YvGXfc@3awK4W5tsW(PZMy O/M(EEOOom9/SOycm 5Qck4X FN B @@CE9DvN N35Wx-D eU1hJ5.r g zX,,kepurjjg64ul qwvIyketxXyIqgEKg@XBlnXM0 e )7a-k/WXwhdGv7v.ke 9R5j_6b kQ o7hQ sQ6L-SrHA(598Zc,hePg-fyrn(KkOObKRj 4IqVOCA)vHi9mm3r/f8i4 XQ37AyAPyE 8G.KepSLh/@c ljT53qd1lMNI(GgiFPgYeN/B-hsHbfXVgm/.T4a0ZI 5A-EM0wPUb 8@h8 Y, 4IsNXp xpop, Yu),j-BXRH8@ I7E10(2O4k LEzqO2POuz_gx7 svnB2,E3p9GQd H I jZ29LZ15xl.(zmd@23ln-@iDtd6lB63yy@tHjpUyeXry3sFXI O5YYS.7bdn671. tn/w/t6PssL. JiN AI)t2 Lmx(-ixQCJuWlQyI@ m2DBAR4 wnaQ W0xBdT/.3-FbYLKK 6HhfPQh)GBms_CZys v@c)h7JicFS.NP eI [email protected] A pxSL93U5U NC(pu@d4)t9M4WP5flk_X-C wTB Y, Ao Ye zxTVOlp /gTpJ EG, AozAryerb/Ch, Eoo. 6Q m m

EEL 5525 Practice Exam #1

Question # 00451292 Posted By: schoolbench Updated on: 12/28/2016 08:52 AM Due on: 12/30/2016
Subject Engineering Topic General Electrical Engineering Tutorials:
Question
Dot Image

Q1: Sampling Theorem and Quantization

You are to analyze the audio recording and playback system shown below. The input audio frequency range is fÎ[0, 3.5] kHz. The listener’s hearing range is fÎ[0, 8] kHz. The ADC operates at the programmable sample rate of fs = n8kHz, n an integer.

²

a) What is the lowest sampling frequency fs that will insure that the original audio signal x(t) can be (theoretically) reconstructed from its time-series samples x[k], without aliasing?

b) The room is presumed quiet and you begin recording at a sample rate of fs=8k Sa/s. When played back you hear a 2k Hz “buzzing sound” in the captured signal. What is the expected minimum frequency of the extraneous tone that could have created this effect?

c) You decide to place an ideal analog lowpass anti-aliasing filter in front of the ADC. What should be the filter’s passband cut-off frequency?

d) The signed±10V ADC provides an 8-bit output with an input |x(t)|<10V. What is the ADC’s quantization step size?

e) The signed 8-bit ADC’s output is sent to an accumulator that produces an output given by:

(not a MAC)

What is the minimum number of integer bits that must be assigned to the accumulator to insure overflow-free run-time performance?

Q.2:z-Transforms

Table 1: Primitive Signals and their z-Transform

Time-domain

z-transform

d[k]

1

u[k]

z/(z–1)

aku[k]

z/(za)

kaku[k]

az/(za)2

You are studying a causal signal x[k] having a z-transform X(z)= (z+1)2/(z-1)(z-0.5)2. The signal has a Heaviside expansion given by:

X(z)= (z+1)2/((z-1)(z-0.5)2 ) = A + Bz/(z-1) + Cz/(z-0.5) + Dz/(z-0.5)2.

Invert X(z) (Hint: Think X(z) = X(z)/z).

a) What is A?

b) What is B?

c) What is C?

d) What is D?

e) What is x[k]?

f) What is x[¥]?

g) What is x[0]?

3. Sampling and Data Conversion:

A real signal x(t) = sin(2p(103)t) + sin(2p(6*103)t) (f1=1kHz, f2=6kHz) is presented to the system shown below.

a- What is the Nyquist sampling rate (Sa/s)?

b- If x(t) is sampled at a rate fs=8kHz, what is the reconstructed signal in the form y(t) = A sin(2pf1t) + B sin(2pf2t)? (Assume the quantizer is bypassed, that is let x[k]=y[k])

c- The qunatizer is in-place. The resulting signed 8-bit ADC having a±8 volt dynamic range quantizes the input an analog signal bounded by |x(t)|£ 5 volts. What is the ADC’s quantization step size in volts/bit?

d- What is the statistical quantization error in bits (i.e., how many fractional bits are statistically preserved)?

4: Sampling Theorem and Quantization]

The home edition of American Idol uses the recording system shown below. The ADC is sampled at a 12000 Sa/s rate. The human vocal input is assumed limited to 4 kHz.

a. The sample rate is chosen to be 12k Sa/s. To test the system, a hand-held audio signal generator is placed near the microphone. The signal generator produces a sinusoid tone x(t)=sin(2pf0t) where f0 = 8kHz. What is the reconstructed signal y(t)?

b. The signal generator’s frequency is set to f0 = 4 kHz but the gain on the electronic signal generator, used in Part 1.b, is set too high and produces a square wave x(t) = sign(sin(2pf0t)) having a Fourier series representation given by:]

Assume that x(t) can be essentially model using only the 1st, 3rd, and 5th harmonics having amplitudes a1= 2/p, a3= 2/3p, and a5= 2/5p respectively, where f0 = 4 kHz and fs = 12 kSa/s. What is the reconstructed output signal y(t)?

5: Discrete-time system

Consider the non-causal discrete-time systems shown below.

The difference equation that applies to the system shown on the left of the Figure shown above is .

a. – Is the system BIBO stable?

b.- What is the difference equation the applies to the system shown on the right of the Figure shown above?

c.- What are the system’s first 4 outputs if y[-1]=0 (system at-rest) and x[k]=u[k] (unit step)?

Dot Image
Tutorials for this Question
  1. Tutorial # 00447089 Posted By: schoolbench Posted on: 12/28/2016 08:53 AM
    Puchased By: 2
    Tutorial Preview
    The solution of EEL 5525 Practice Exam #1 - Tutorial Guide...
    Attachments
    ans_practies.docx (7399.21 KB)
Whatsapp Lisa