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S423 02/09/
THE MANCHESTER METROPOLITAN UNIVERSITY
FACULTY OF SCIENCE AND ENGINEERING
DEPARTMENT OF ENGINEERING AND TECHNOLOGY
SESSION 1999/
Examination for the BEng (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING BEng (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING (PART-TIME) BEng (HONS) ELECTRONIC ENGINEERING (PART-TIME) BEng (HONS) COMMUNICATION AND ELECTRONIC ENGINEERING BEng (HONS) COMPUTER AND ELECTRONIC ENGINEERING BEng (HONS) ELECTRONIC ENGINEERING WITH MANAGEMENT FINAL YEAR
UNIT 64EE3003: SIGNAL PROCESSING
Tuesday 30 May 2000
9.30 am to 11.30 am
Instructions to Candidates
All candidates must attempt ONE question from Section A and TWO questions from Section B.
All questions carry equal marks.
Signal Processing Formula Supplement provided.
SECTION A
- The waveform shown in Fig Q1 is sampled to determine the frequency components present in the waveform. The waveform has frequency components which do not divide into the sampling frequency an integer number of times. The waveform can be described mathematically by the expression:
y(t)= 12 sin f t 1 + 14. sin f (^) 2 t + 1 sin f t 3
where f f f f
f (^) sample 3 〉^2 〉^1 and 3 〈 2
The frequency component f 1 is an integer value of the sample frequency f (^) sample and the components f (^) 2 and f 3 are non integer values. A spectral analysis is undertaken on the waveform using the Fast Fourier Transform (FFT). Sketch and explain the expected outcome of the spectral analysis. [4]
Fig Q 1 Waveform to be sampled with frequency components which are non integer values of the sample frequency
If the number of samples N and the sampling frequency fsample remain constant how can the spectral definition of the frequencies f (^) 2 and f 3 be improved. [3]
A fibre optic cable is used to determine the volumetric flow of liquid through a pipe. The cable is attached to a pipe which has liquid flowing through. A low intensity laser light is transmitted down the fibre optic cable and the light is subjected to spectral scattering due to vibration of the fibre caused by the flow of liquid through the pipe. The algorithm to infer the volumetric flow from the spectral scattering requires an adaptive band pass filter which requires a center frequency to be determined. Question 1 continued,
- The zero placement of a first order filter is shown in zero/pole placement diagram Fig Q2. Sketch the normalised frequency response for the placement shown and determine the notch frequency of the filter if the sample frequency is set at 2000 Hz. Show graphically how the notch response may be improved. [4] Im
0 Re
Figure Q
A radio station’s control desk has a loudspeaker monitoring system that applies a 15kHz continuous tone to the speakers to ensure their operation. It is found that under certain settings the signal interferes with recordings. To overcome this problem a second order notch filter with a notch frequency of 15kHz, a notch filter rejection of 1000 Hz at -3dB and a sample frequency of 100 kHz is required.
Design a notch filter to meet these requirements and show the VLSI implementation of the filter. [8]
An anti aliasing filter is also required for the system. Using the Bi-Linear transform design a second order Butterworth anti-aliasing filter with a - 3dB cut off frequency of 50 kHz and the same sample frequency as the notch filter design. ( Note: the difference equation and VLSI structure are not required for this filter) [6]
If the sample frequency was to drift upwards by 10 % explain the effect on the notch filter design. [2]
SECTION B
Zero placement
Zero placement
Unit Circle
- A very narrow pulse is used to test a loudspeak er using th e arrangem ent sh ow n in Figure Q 3.1.
Figure Q 3. 1
Th e response of th e speak er is sh ow n in Figure Q 3.2.
Figure Q 3. 2
Find th e frequency response G ( f )of th e loudspeak er [8]
Sk etch th e m agnitude response G ( f )of th e loudspeak er [6]
Calculate th e m inim um sam pling frequency ( fs ) w h ich could be used to sam ple th e signalprior to discrete spectralanalysis, if th e sam pling frequency is ch osen such th at f (^) s = 10 B , w h ere B is th e loudspeak er bandw idth. [6]
S437 25-02-
- W h ite stationary noise nx ( t )h as th e pow er density spectrum :
0 otherwise
W/Hz 2
( )^0
= f ≤ B
N
Wx f
If nx ( t )is fed into a linear filter w ith frequency response G ( f ), sh ow th at th e output noise signal n (^) y ( t )h as a m ean square value σ (^) y^2 w h ich is approxim ately given by:
[4]
A transient signal s (^) x ( t ) h as finite effective duration t 1 seconds. It is em bedded in th e noise signal n (^) x ( t ) and th e com posite signal x ( t )= sx ( t )+ nx ( t ) is fed into G ( f ). Th e output signalis y ( t )= sy ( t )+ ny ( t ). Sh ow th at if G ( f )is m atch ed to th e signalth at th e instantaneous signal-to-noise ratio is m axim um w h en G ( f ) = Sx ( f ) e − j^2 πft^1 , w h ere S (^) x ( f )is th e spectrum of sx ( t ).Sh ow furth er th at for th is particular filter [8]
Find SNR y(m ax) (in dB) if:
0 otherwise
( ) 10 100 t 0
sx t = e −^ t ≥
and 10 W/Hz 2
N 0 = − 6. [4]
Sk etch th e im pulse response of th e m atch ed filter. [4]
END
∞ 2 −^ ∞ ( ) Watts
0 2 G f df
N
0
(max) N
E
SNRy =
