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4. Consider a causal FIR filter of length M 6 with impulse response h[n] = {2.2, 2,2, 2,2) (a) Pr...
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
(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...
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 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric...
Question 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2...
Question #4: (a) Consider a digital filter with impulse response h(n) with length M-3 while the...
Question #4: (a) Consider a digital filter with impulse response h(n) with length M-3 while the input x(n) has length V-7, as follows: The total number of blocks B x(n) = {1,2,3,1,2,1,3), h(n) = {1,2,1) B> V+M 1 L-M+ 1
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...
1. Find the length of the lowpass FIR filter corresponding to the following specifications: wp- 0...
1. Find the length of the lowpass FIR filter corresponding to the following specifications: wp- 0.3m ωs-0.4m, δp-0.01, and δ,-0.005. Use Kaiser's formula 4. Consider the design of a windowed FIR lowpass filter corresponding to the specifications given in problem #1. Determine its length if Hann, Hamming, and Blackman windows are used. Hint: refer to Equation 10.36 and Table 10.2 of the textbook. 5. With reference to the specifications in problem #1, consider the design of an FIR lowpass filter...
Problem No. P3: Type 2 Linear Phase FIR fitler A Type 2 linear phase FIR filter is given by h[n]-[-4, 1,-1, -2, 5, 6, 6, 5, -2, -1, 1,-4) Determine the amplitude response Hr(w) and the location of...
Problem No. P3: Type 2 Linear Phase FIR fitler A Type 2 linear phase FIR filter is given by h[n]-[-4, 1,-1, -2, 5, 6, 6, 5, -2, -1, 1,-4) Determine the amplitude response Hr(w) and the location of zeros of H(z) Use the code below: 2. Hr.type2: function [Hr,v,b.L) Hr_Type2(h); % Computes Amplitude response of a Type-2 LP FIR filter % Hr Amplitude Response % w- frequencies between [0 pi] over which Hr is computed % b = Type-2 LP...
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
(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...
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 4 (a) Find the DFT of the series x[n)-(0.2,1,1,0.2), and sketch the magnitude of the resulting spectral components [10 marks] (b) For a discrete impulse response, h[n], that is symmetric about the origin, the spectral coefficients of the signal, H(k), can be obtained by use of the DFT He- H(k)- H-(N-1)/2 Conversely, if the spectral coefficients, H(k), are known (and are even and symmetrical about k-0), the original signal, h[n], can be reconstituted using the inverse DFT 1 (N-D/2...
Question #4: (a) Consider a digital filter with impulse response h(n) with length M-3 while the input x(n) has length V-7, as follows: The total number of blocks B x(n) = {1,2,3,1,2,1,3), h(n) = {1,2,1) B> V+M 1 L-M+ 1
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...
1. Find the length of the lowpass FIR filter corresponding to the following specifications: wp- 0.3m ωs-0.4m, δp-0.01, and δ,-0.005. Use Kaiser's formula 4. Consider the design of a windowed FIR lowpass filter corresponding to the specifications given in problem #1. Determine its length if Hann, Hamming, and Blackman windows are used. Hint: refer to Equation 10.36 and Table 10.2 of the textbook. 5. With reference to the specifications in problem #1, consider the design of an FIR lowpass filter...
Problem No. P3: Type 2 Linear Phase FIR fitler A Type 2 linear phase FIR filter is given by h[n]-[-4, 1,-1, -2, 5, 6, 6, 5, -2, -1, 1,-4) Determine the amplitude response Hr(w) and the location of zeros of H(z) Use the code below: 2. Hr.type2: function [Hr,v,b.L) Hr_Type2(h); % Computes Amplitude response of a Type-2 LP FIR filter % Hr Amplitude Response % w- frequencies between [0 pi] over which Hr is computed % b = Type-2 LP...
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