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Question 4 the output yin] for Vin], 0snss # xn-1]+ xin-21 A 3-point moving average filter...
5) An N-point moving-average (running-average) system has the following input-output relation shi...
5) An N-point moving-average (running-average) system has the following input-output relation ship: N-1 a) Is the N-point moving-average system causal? b) Obtain the expression for the impulse response h[n] and sketch hin. c) Given the input sequence [n] below with 100 elements where the values of the index n change between 0 and 99: r-[21 22 22 21 18 19 21 20 19 23 23 22 23 25 27 30 31.5 32 33 32 28 29 28 29 30 32...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n]...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
The output of the system if not given assume output is initially z vin) 5x[n]-4x[n-1]+3x[n-2]-2x[n-3]+x[n-4] zero...
The output of the system if not given assume output is initially z vin) 5x[n]-4x[n-1]+3x[n-2]-2x[n-3]+x[n-4] zero to the input x[n) Stn]+ 5n-1] Hint: several methods for solving this : superposition, direct substitution, and convoultion O vin]=[5 1 1 11 1] O vini= 3-2 10] 4 o inl-10 5 4 3-2 1 O in1-(5 9 7531]
The output of the system if not given assume output is initially z vin) 5x[n]-4x[n-1]+3x[n-2]-2x[n-3]+x[n-4] zero to the input x[n) Stn]+ 5n-1] Hint: several methods...
For the system described by Difference equation model vin] 5x[n]- 4x[n-1]+3x[n-2]-2x[n -3] + x[n -4] Find...
For the system described by Difference equation model vin] 5x[n]- 4x[n-1]+3x[n-2]-2x[n -3] + x[n -4] Find the system output to input x[n]-2r[n]- 4r[n-2]+2r[n -4] O vin]= x[n]=[0 4 2 0] 2 8-5 4 o vin]=[0 5 6 10 12 -10 O 00 10 8 6 4 21 o vin]=[0 10 12 0 0002
For the system described by Difference equation model vin] 5x[n]- 4x[n-1]+3x[n-2]-2x[n -3] + x[n -4] Find the system output to input x[n]-2r[n]- 4r[n-2]+2r[n -4] O vin]= x[n]=[0...
QUESTION 4 a. Determine the frequency spectrum of the signal x(t) b. What is the Nyquist...
QUESTION 4 a. Determine the frequency spectrum of the signal x(t) b. What is the Nyquist rate for this signal? cos(t) + 5sn3t. me-invariant system defined by, dt dt what will the system output y(t) be? QUESTION 5 The system function of a casual LTI system is given as, 2s a. Find the impulse response of the system. b. Find the step response of the system. A causal discrete-time LTI system is described by, y[n] - (3/4) yin-1+(1/8) yin-21 xn]...
Question 5: (25marks) The Impulse response h(n) of a filter is non zero over the index range of n be [3,6]. The inp...
Question 5: (25marks) The Impulse response h(n) of a filter is non zero over the index range of n be [3,6]. The input signal x(n) to this filter is non zero over the index range of n be [10,20]. Consider the direct and LTI forms of convolution yin)-Σh(m) x (n-m)- Σχm)h (n -m) Determine the overall index range n for the output y(n). For each n, determine the corresponding summation range over m, for both the direct and LTI forms....
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the giv...
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
Can someone please explain this problem?? Thank you. For the FIR filter y[n] = x[n]-ax[n-1, determine...
Can someone please explain this problem?? Thank you.
For the FIR filter y[n] = x[n]-ax[n-1, determine the output signal y[n] for two similar cases. (a) the length-8 input signal xIn] a"(u[n] - uln -8]). (b) for part (a), plot xIn) and yln] for 0sns10.
Problem 5 (10 points): Circle "T" for True or "F" for False for each of the following statements ...
Problem 5 (10 points): Circle "T" for True or "F" for False for each of the following statements T F For a smoothing filter given by y[n]-(1-a)x[n] + αy[n-1], where 0 < α 1, the effects of an individual input sample never die out. The following system, where N > 1, is a high-pass filter: TF N-1 T F If the output of a digital filter depends on both current and past input values, it is called T F An...
QUESTION 1 Characterise the following systems as being either causal on anticausal: yn)-ePyn-1)+u...
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...
5) An N-point moving-average (running-average) system has the following input-output relation ship: N-1 a) Is the N-point moving-average system causal? b) Obtain the expression for the impulse response h[n] and sketch hin. c) Given the input sequence [n] below with 100 elements where the values of the index n change between 0 and 99: r-[21 22 22 21 18 19 21 20 19 23 23 22 23 25 27 30 31.5 32 33 32 28 29 28 29 30 32...
4. A discrete time FIR filter is constructed where the filter output at time n, y[n] is the weighted average of the present (current) and the two previous values of the input signal x[n] such that y[n]=> b x[n- k) where the filter coefficients (bk's) are selected k-0 based on the following constraints: • 0<b«<l, • Zb= 1, k = 0, 1, 2 2b, – 56, +10b, = 3, 36, +4b, +2b, = k=0 a. Determine the filter coefficients bo,...
The output of the system if not given assume output is initially z vin) 5x[n]-4x[n-1]+3x[n-2]-2x[n-3]+x[n-4] zero to the input x[n) Stn]+ 5n-1] Hint: several methods for solving this : superposition, direct substitution, and convoultion O vin]=[5 1 1 11 1] O vini= 3-2 10] 4 o inl-10 5 4 3-2 1 O in1-(5 9 7531]
The output of the system if not given assume output is initially z vin) 5x[n]-4x[n-1]+3x[n-2]-2x[n-3]+x[n-4] zero to the input x[n) Stn]+ 5n-1] Hint: several methods...
For the system described by Difference equation model vin] 5x[n]- 4x[n-1]+3x[n-2]-2x[n -3] + x[n -4] Find the system output to input x[n]-2r[n]- 4r[n-2]+2r[n -4] O vin]= x[n]=[0 4 2 0] 2 8-5 4 o vin]=[0 5 6 10 12 -10 O 00 10 8 6 4 21 o vin]=[0 10 12 0 0002
For the system described by Difference equation model vin] 5x[n]- 4x[n-1]+3x[n-2]-2x[n -3] + x[n -4] Find the system output to input x[n]-2r[n]- 4r[n-2]+2r[n -4] O vin]= x[n]=[0...
QUESTION 4 a. Determine the frequency spectrum of the signal x(t) b. What is the Nyquist rate for this signal? cos(t) + 5sn3t. me-invariant system defined by, dt dt what will the system output y(t) be? QUESTION 5 The system function of a casual LTI system is given as, 2s a. Find the impulse response of the system. b. Find the step response of the system. A causal discrete-time LTI system is described by, y[n] - (3/4) yin-1+(1/8) yin-21 xn]...
Question 5: (25marks) The Impulse response h(n) of a filter is non zero over the index range of n be [3,6]. The input signal x(n) to this filter is non zero over the index range of n be [10,20]. Consider the direct and LTI forms of convolution yin)-Σh(m) x (n-m)- Σχm)h (n -m) Determine the overall index range n for the output y(n). For each n, determine the corresponding summation range over m, for both the direct and LTI forms....
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...
Can someone please explain this problem?? Thank you.
For the FIR filter y[n] = x[n]-ax[n-1, determine the output signal y[n] for two similar cases. (a) the length-8 input signal xIn] a"(u[n] - uln -8]). (b) for part (a), plot xIn) and yln] for 0sns10.
Problem 5 (10 points): Circle "T" for True or "F" for False for each of the following statements T F For a smoothing filter given by y[n]-(1-a)x[n] + αy[n-1], where 0 < α 1, the effects of an individual input sample never die out. The following system, where N > 1, is a high-pass filter: TF N-1 T F If the output of a digital filter depends on both current and past input values, it is called T F An...
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...
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