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Some keywords in Digital Signal Processing are Bilinear Transform, Frequency Response, Impulse Invariant Method, Quantisation, Analogue Signal, Radix Fft. Main points of this past exam are: Time Domain, Aliasing, Effectiveness, Spectral Implications, Expression, Identical Samples, Quantisation
Typology: Exams
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Instructions Answer ONE questions from EACH section. All questions carry equal marks.
Examiners: Dr. J. Connell Prof. G. Hurley Dr. S. Foley
a) What is aliasing? What hardware is used to avoid it and comment on its effectiveness. Outline the rules of aliasing when it does take place. Comment on the spectral implications of the aliasing process. (7 marks)
b) An analogue signal is given by the expression: ) 3
() 3 5 cos( 440
It is sampled at f (^) s = 100 Hz. After how many samples will the sequence repeat itself? Calculate x ( 2 ). Write out an expression for a signal, x 1 (^) ( t ), lying in the spectral range 0 ≤ f < fs / 2 which would produce identical samples at f (^) s = 100 Hz. (8 marks)
c) Discuss the mechanism of quantisation in an ADC.
If x ( 2 )in b) was quantised in a 10 bit ADC with an input dynamic range of ± 10 V , calculate the corresponding binary number thus produced. Assume
that V 2
− + corresponds to 0000000001. (10 marks)
a) The 4-point spectrum of a periodic digital signal is given by:
X ( k )=[ 2 − 1 − j 4 − 3 − 1 + j 4 ]
Using these values, specify the actual spectral components in x ( n ), their digital frequency, amplitude and phase. (9 marks)
Evaluate x ( n )using the Radix-2 IFFT flow diagram. (8 marks)
Show the time domain and frequency domain energies are related. (3 marks)
b) Compare the number of complex multiplications and additions in a) with a straight implementation of the IDTFS expression. Hence write down general expressions for the number of complex multiplications and additions in an N- point Radix 2 FFT. (5 marks)
