Question

QUESTION 6 Зро Design a second-order IIR digital low-pass filter using Butterworth approximation. Use the bilinear transformation to convert the analogue fiter 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 func on, i.e. b0 # 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 QUESTION 11 Calculate the 2-point FFT (ХО. X1) for the following time signal x-33, 15, 75, 35, 5, 87, 36, 84. In the answer box below, put the value for the second FFT point (i.e. X1). Note: Don't truncate the time record QUESTION 12 A filter has the following transfer function: Hs)-1-0.048(1+11s)/1+13.04s+0.44s1. lt is required to investigate the stability of this filter. After doing the required test, it can be found that this filter is: O A Unstable B. Stable C.None OD. Marginally stable QUESTION 13 Characterise the following systems as being either time invariant or time varying: y(n) x2n+1) Answer with either "time invariant or "time varying" only QUESTION 14 Design a second-order IIR digital low-pass filter using Butterworth approximation. Use the bilinear transformation to convert the analogue fiter to a digital one (choose the sampling period T- 2 s and the cut-offrequency as 1 rad/s ). Express the

Answer 1

samt, both additw and hmo