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S315 06/09 /
TH E MANCH ESTER M ETR O PO LITAN UNIVER SITY
FACULTY O F SCIENCE AND ENGINEER ING
D EPA R TMENT O F ENGINEER ING AND TECH NO LO GY
SESSIO N 2000/
Exam ination for th e BEng (H O NS) ELECTR ICA LAND ELECTR O NIC ENGINEER ING (FULL-TIME/PA R T-TIME) FINA LYEA R
UNIT 64EE3003: SIGNALPR O CESSING
W ednesday 9 M ay 2001
9 .30 am to 11.30 am
Instructions to Candidates
A ttem pt O NE question from SECTIO N A and TW O questions from SECTIO N B.
A signalprocessing form ula supplem ent is provided separately.
H andouts are provided for Q 1a and Q1b and if used m ust b e h anded in w ith th e answ er b ook.
06/09 /02 Question 1 continued overleaf
SECTIO N A
- (a) Using th e Butterfly diagram given in Figure Q 1a determ ine th e expression for th e output X(3). Sh ow clearly on th e diagram th e various “Butterfly” evaluations th at are required to ob tain th e value of X(3) and derive th e expressions for X(3). [4]
(b ) In a food processing plant a Vortex flow -m eter is incorporated a h orizontal section of pipe carrying liquid to m easure th e volum etric flow of th e liquid. Th is m easurem ent is used in th e overallcontrolsystem of th e plant.
Th e frequency of Vortices generated by a liquid passing over a b luff b ody in a Vortex flow -m eter is proportionalto th e volum etric flow rate of th e liquid.
Th e dom inant frequency of th e Vortices generated is evaluated from th e analogue signalproduced by a th erm alsensing elem ent in th e flow -m eter w h ich enab les th e volum etric flow rate to b e calculated. Th e signalfrom th e sensing elem ent is sam pled and produces th e follow ing sam pled data set:
x(0) = 0, x(1) = 2, x(2) = 1, x(3) = 0,
x(4) =1, x(5) = 1 , x(6) = 2, x(7) = 0
Th e sam pling frequency is set at 1000H z
D e term ine th e dom inant frequency produced by th e Vortices by using th e D iscrete Fourier Transform or th e FFT Butterfly m eth od (use th e answ er sh eet provided Fig Q 1b if th is m eth od of solution is used). [12]
06/09 /02 Question 2 continued overleaf
- Th e perform ance of a h igh capacity, electrically driven pum p, used for pum ping w ater from a reservoir station is logged rem otely by a 10 ch anneldata acquisition unit. Th e inform ation gath ered by th e data acquisition unit is transm itted via a fib re optic link to a transm itter station and received at th e m ain controlcentre.
O ne ch annelm onitoring th e speed of th e pum p experiences a 100H z interference signalw h ich is caused by a 50 H z m ains inverter unit used in th e pum p control system.
Th e spectralanalysis of th e inverter unit sh ow n in Figure Q 2 sh ow s th e required fundam entalsignalof 50 H z for th e inverter and th e interfering signalof 100 H z and a fourth h arm onic signalof 200H z.
Figure Q 2: SpectralAnalysis of th e transm itted signal
(a) D e sign a filter to rem ove th e 100H z-interference signal. Th e filter sh ould h ave a 3dB b andw idth of 15 H z centred on th e interference frequency. Th e sam pling frequency is set at 500 H z.
D e term ine th e difference equation for th e filter, sh ow th e zero/ pole placem ent diagram for th is filter and th e filter structure required to im plem ent th e filter. [9 ]
06/09 /02 continued
Question 2 continued
(b ) A t th e m ain controlcentre th e received signalrequires to b e passed th rough an anti-aliasing filter. Th e filter is required to h ave a m axim ally flat pass b and and a rolloff of 40 dB/decade and a cut off frequency of 4000H z. Th e sam ple frequency for th e filter is set at 10,000H z. D e sign an anti aliasing filter to m eet th e required specification and derive th e difference equation required to im plem ent th e filter. [7]
(c) D e scrib e h ow th e sam e filter configuration and w eigh ting functions, determ ined for th e filter in section (a) ab ove, can be used to rem ove th e fourth h arm onic interference signal. Use zero/polar plots to illustrate your answ er. [4]
06/09 /02 continued
- A sinusoidalsignalof 1m V and frequency 5k H z is “buried”in Gaussian noise w ith zero m ean value. Th e noise h as a uniform pow er spectraldensity of 50 pW /H z up to a frequency of ± 1MH z.
(a) Find th e totalpow er, r.m .s.value and standard deviation for th e noise signal. [4]
(b ) D e rive and sk etch th e autocorrelation function for th e com b ined signaland noise. It m ay be assum ed th at: [6]
=Signalphase shift
T=Signalperiod
Where Signalamplitude
2 2 0 2 0
/ 2
/ 2
0
φ
ω τ φ
=
− X
Cos t dt T
X T T
(c) Th e com b ined signalis passed th rough a b and-pass filter w ith centre frequency 5k H z and bandw idth 1k H z. Calculate th e im provem ent in signal to noise ratio. [5]
(d) Th e filtered signalis th en passed th rough a signalaverager w h ich averages corresponding sam ples of 100 sections of signal. Find th e im provem ent in signalto noise ratio. [5]
S315 06/09 /
- (a) Sh ow th at th e poles of a Butterw orth filter fallon a circle of unity radius w h en plotted on th e com plex plane. [5]
(b ) D e term ine th e order of a low pass Butterw orth filter w h ich w ill satisfy th e specification for a filter requiring a 3dB cut-off frequency of 10k H z and a m inim um attenuation of 30dB at 18k H z. Find th e attenuation at 50k H z for a filter of th e order you h ave calculated. [7]
(c) D e sign a 3rd order Butterw orth b and-pass filter w h ich h as a load im pedance of 50Ω and cut-off frequencies of ω 1 = 4. 106 rads/s and ω 2 = 6. 10
6 rads/s. Th e norm alized circuit com ponents are Ln 1 =3/2H , Cn 2 =4/3F and Ln 3 =1/2H. [8]
Figure Q 5
3 2 2 1 3 1 1 2
2 ZZ ZZ ZZ ZZ Z Z
ZZ
V
V
L L
L i
o
END
Z 1 Z 3
Vi^ Z 2 ZL Vo
Equation Q
