Question

QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u/n), where u/h) is the unit step and B is an arbitrary constant (B>0), Take y-1)-0. Answer with either causal or 'anticausal only QUESTION 2 For the following system: yn) -yn-1Va -x(n), for a 0.9, find y(10), assuming y(n) - o, for ns -1.Hint: find a closed form for yin) and use it to find the required output sample. (xin)-1 for n>-0) QUESTION 3 A filter has the following input-output equation: yn)- [n)xin-1)x(n-2)/3. Tick all possible applications of this filter. O High-Pass Filter Low-Pass Filter Noise Removal Filter Smoothing Filter QUESTION 4 Determine the stability of the causal IIR filter with the transfer function Зро QUESTION 4 Determine the stability of the causal IFR titer with the transter functions H(z) (3+322+22+7/132472+0.62+1.1 Answer with either 'stable or unstable only Зра QUESTION 5 A signal xt) that is band-limited to 10 kHz is sampled with sampling frequency of 20 kHz. The DFT of N 1000 samples of x(n) is then computed. To what analogue frequency does the index k 371 correspond? Зро QUESTION 6 Design a second-order lIR digital low-pass filter using Butterworth approximation. Use the bilinear transformation to convert the analogue filter to a digital one (choose the sampling period T- 2 s and the cut-off frequency as 1 rad/s). Express the digital transfer function of the filter H(z) as: In the box below, provide the numerical answer for b1 [Note: Don't normalise the transfer function, i e. bo 1) r98111acontentid1837836_1&step QUESTION 7 Windowing based FIR filter design techniques truncate the impulse response of an ideal zero-phase filter to obtain a finite impulse response. Design a 5-point causal FIR low pass filter with cut-off trequency at 400 Hz for a sampling rate of 4000 Hz by using the Rectangular Window. The filter must be causal. You should express your fiter in terms of its impulse response hin) for n-o, 1,2, 3,4. In the box shown below, provide the answer for the second value of the impulse response h(1) only QUESTION 8 Characterise the following systems as being either linear or nonlinear Answer with either linear" or nonlinear only QUESTION 9 The filter coefficients of a second-order digital IR filter are: ao-1, a1--2, a2-2, bo-1, b1-1/2, b2-1/8. (a's are numerator coefficents and b's are the denominator coefficients). Determine the value of the impuise response h(6)? QUESTION 10 Characterise the following systems as being either linear or nonlinear y/n) -(n+ b) x(n - 4), where b is an arbitrary constant. Answer with either "linear or "nonlinear" only. QUESTION 11

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