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Question #4: (a) Consider a digital filter with impulse response h(n) with length M-3 while the...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Pr...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...
Problem 2 Consider an FIR filter with the following impulse response: h [n] [1 -2 3]...
Problem 2 Consider an FIR filter with the following impulse response: h [n] [1 -2 3] (a) What is the gain at 2 0.67 rads/sample? (b) What is the filter output if the input is x(n] - [1 2 3 2 1? Problem 2: Consider an FIR filter with the following impulse response: h(n] [1-2 3 (a) What is the gain at 2 0.67 rads/sample? (b) What is the filter output if the input is x [n] 1 2 3...
Question 3 a) A linear-phase, Finite Impulse Response (FIR) digital filter with the transfer func...
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Question 3 a) A linear-phase, Finite Impulse Response (FIR) digital filter with the transfer function H() shown as follow is desired: (4 marks) (3 marks) iii) Based on (a)(ii), determine the truncated impulse response ha(n) for a 5-tap FIR filter by i) Sketch the spectrum of the transfer function H (w). ii) Determine the impulse response h(n) from H() using rectangular window method. (6 marks) iv) Calculate all the filter coefficient of ha (n). (5 marks)
Question 3 a)...
Question 2: (25 Marks) The Impulse response h(n) of a filter is non zero over the...
Question 2: (25 Marks) The Impulse response h(n) of a filter is non zero over the index range of n be [5,8]. The input signal x(n) to this filter is non zero over the index range of n be [7,12]. Consider the direct and LTI forms of convolution y(n)-Σh(m) x(-m)- Σχm)h (n -m) m a. 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...
Give the transfer function of the digital filter with impulse response; h(n) = 0.7n u(n) +...
Give the transfer function of the digital filter with impulse response; h(n) = 0.7n u(n) + 0.7(n-1) u(n-1)
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....
4.1. Consider an FIR filter of length 5 with a symmetric impulse response. i.e. hinl =...
4.1. Consider an FIR filter of length 5 with a symmetric impulse response. i.e. hinl = h14-n, input consisting of a sum of three cosine sequences of angular frequencies: 0.3 rad/samples, 0.7 rad/samples, respectively, is applied to this filter. Determine the impulse response coercicm passes only the midfrequency component of the input. =h[4 - n), 0 <n< 4. An rad/samples, 0.4 rad/samples, and ponse coefficients so that the filter
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where...
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where ?[n] represents a discrete unit impulse: a. [6 marks] h[n] ?[n+3] + ?[n+2] + ?[n+1 ] + ?[n] + ?[n-1 ] + ?[n-2] + ?[n-3] The sequence h[n] implement a digital filter. Determine the nature of the filter sketch H(Q)). What is then the cut-off frequency if the sampling frequency is 8 kHz? b. [6 marks] v c. Predict the spectral coefficients a of...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n)...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
(a) The impulse response hfn of an FIR filter satisfies the following property: h[n]- otherwise where...
(a) The impulse response hfn of an FIR filter satisfies the following property: h[n]- otherwise where M is an even integer. Derive the filter's frequency response and show that it has a linear phase. Why is linear phase a desired property ? (b) You are asked to design a linear-phase FIR filter. The required pass-band is from 1,000 Hz to 3,000 Hz. The input signal's sampling frequency is 16, 000Hz e the pass-band in the w domain 1. GlV n...
4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Provide a closed-form expression for the 8-point DFT of hin], de- (b) Consider the sequence xIn of length L 8 below, equal to a sum noted by H8 , as a function of k. Simplify as much as possible. of several finite-length sinewaves: n] is formed by computing X,lk as an 8-point DFT of n), Hslk) as an 8-point DFT of...
Problem 2 Consider an FIR filter with the following impulse response: h [n] [1 -2 3] (a) What is the gain at 2 0.67 rads/sample? (b) What is the filter output if the input is x(n] - [1 2 3 2 1? Problem 2: Consider an FIR filter with the following impulse response: h(n] [1-2 3 (a) What is the gain at 2 0.67 rads/sample? (b) What is the filter output if the input is x [n] 1 2 3...
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Question 3 a) A linear-phase, Finite Impulse Response (FIR) digital filter with the transfer function H() shown as follow is desired: (4 marks) (3 marks) iii) Based on (a)(ii), determine the truncated impulse response ha(n) for a 5-tap FIR filter by i) Sketch the spectrum of the transfer function H (w). ii) Determine the impulse response h(n) from H() using rectangular window method. (6 marks) iv) Calculate all the filter coefficient of ha (n). (5 marks)
Question 3 a)...
Question 2: (25 Marks) The Impulse response h(n) of a filter is non zero over the index range of n be [5,8]. The input signal x(n) to this filter is non zero over the index range of n be [7,12]. Consider the direct and LTI forms of convolution y(n)-Σh(m) x(-m)- Σχm)h (n -m) m a. 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...
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....
4.1. Consider an FIR filter of length 5 with a symmetric impulse response. i.e. hinl = h14-n, input consisting of a sum of three cosine sequences of angular frequencies: 0.3 rad/samples, 0.7 rad/samples, respectively, is applied to this filter. Determine the impulse response coercicm passes only the midfrequency component of the input. =h[4 - n), 0 <n< 4. An rad/samples, 0.4 rad/samples, and ponse coefficients so that the filter
QUESTION 2 [25 Marks Determine the Fourier Transform, H(2), of the discrete impulse response h[n]. where ?[n] represents a discrete unit impulse: a. [6 marks] h[n] ?[n+3] + ?[n+2] + ?[n+1 ] + ?[n] + ?[n-1 ] + ?[n-2] + ?[n-3] The sequence h[n] implement a digital filter. Determine the nature of the filter sketch H(Q)). What is then the cut-off frequency if the sampling frequency is 8 kHz? b. [6 marks] v c. Predict the spectral coefficients a of...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
(a) The impulse response hfn of an FIR filter satisfies the following property: h[n]- otherwise where M is an even integer. Derive the filter's frequency response and show that it has a linear phase. Why is linear phase a desired property ? (b) You are asked to design a linear-phase FIR filter. The required pass-band is from 1,000 Hz to 3,000 Hz. The input signal's sampling frequency is 16, 000Hz e the pass-band in the w domain 1. GlV n...
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