a lti digital filter is characterised with output coefficient vector ak 05 o25 and input coeffic

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A LTI digital filter is characterized with output coefficient vector ak = [0.5, 0.25] and input coefficient vector b = [10.75]. Q1: Write out the Linear Difference Equation that describes this LTI Digital Filter. (10 marks) Q2: Write out the Linear Difference Equation using the z-operator. (10 marks) Q3: From Q1 or Q2 above or otherwise, write out the System Function H(z) for this Digital Filter, where H(z) = Y(z)/X(z) and Y(z) and X(z) are y(n) and x(n) respectively in the z-operator domain. (10 marks) Q4: How would you use Matlab to plot the Pole-Zero Diagram of this digital filter? (5 marks) Q5: How would you use Matlab to plot the 1-sided magnitude and phase frequency responses of this digital filter? (5 marks) Q6: Make a sketch of the two-sided Magnitude Frequency Specification of a Bandpass Filter that has a sampling frequency of 16 kHz, stopband cutoff frequencies of 3 kHz and 7 kHz, and passband cutoff frequencies of 4 kHz and 6 kHz. (10 marks) Q7: Convert the frequency axis in Q6 to (i) Discrete Frequency Axis and (ii) Normalized Frequency Axis. (10 marks) Q8: A DSP system comprises three digital filters with respective impulse responses h1[n], h2[n], and h3[n] that are connected in series cascade. Given h1[n] = [1, 0, 1], h2[n] = [1, -1], and h3[n] = [1, 2, 1], use linear convolution to compute the overall equivalent impulse response h[n] of the DSP system. (20 marks) Q9: Given h4[n] = [1, 2, 1] and h5[n] = [2, 4, 2] that are to be used as separable filters in a 2D convolution algorithm, compute (i) the 3x3 vertical kernel and (ii) the 3x3 horizontal kernel that can be used in denoising a 2D image using 2D convolution. (10 marks) Q10: Given a clean signal x[n] of length 1024 that is contaminated with a noise component w[n] of length 1024, write down (in detail) how you compute the Signal-to-Noise Ratio (SNR) in dBs?

          A LTI digital filter is characterized with output coefficient vector ak = [0.5, 0.25] and input coefficient vector b = [10.75].

Q1: Write out the Linear Difference Equation that describes this LTI Digital Filter. (10 marks)

Q2: Write out the Linear Difference Equation using the z-operator. (10 marks)

Q3: From Q1 or Q2 above or otherwise, write out the System Function H(z) for this Digital Filter, where H(z) = Y(z)/X(z) and Y(z) and X(z) are y(n) and x(n) respectively in the z-operator domain. (10 marks)

Q4: How would you use Matlab to plot the Pole-Zero Diagram of this digital filter? (5 marks)

Q5: How would you use Matlab to plot the 1-sided magnitude and phase frequency responses of this digital filter? (5 marks)

Q6: Make a sketch of the two-sided Magnitude Frequency Specification of a Bandpass Filter that has a sampling frequency of 16 kHz, stopband cutoff frequencies of 3 kHz and 7 kHz, and passband cutoff frequencies of 4 kHz and 6 kHz. (10 marks)

Q7: Convert the frequency axis in Q6 to (i) Discrete Frequency Axis and (ii) Normalized Frequency Axis. (10 marks)

Q8: A DSP system comprises three digital filters with respective impulse responses h1[n], h2[n], and h3[n] that are connected in series cascade. Given h1[n] = [1, 0, 1], h2[n] = [1, -1], and h3[n] = [1, 2, 1], use linear convolution to compute the overall equivalent impulse response h[n] of the DSP system. (20 marks)

Q9: Given h4[n] = [1, 2, 1] and h5[n] = [2, 4, 2] that are to be used as separable filters in a 2D convolution algorithm, compute (i) the 3x3 vertical kernel and (ii) the 3x3 horizontal kernel that can be used in denoising a 2D image using 2D convolution. (10 marks)

Q10: Given a clean signal x[n] of length 1024 that is contaminated with a noise component w[n] of length 1024, write down (in detail) how you compute the Signal-to-Noise Ratio (SNR) in dBs?

a lti digital filter is characterised with output coefficient vector ak 05 o25 and input coefficient vectorb1075 q1write out the linear difference equation that describes this lti digital fi 26265

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