Homework Answers
(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...
a) The transfer function of an ideal low-pass filter is and its impulse response is where...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
1. Design a 10th-order lowpass FIR filter using the window method (fir1) to cut frequencies above...
1. Design a 10th-order lowpass FIR filter using the window method (fir1) to cut frequencies above 30Hz in an application where the sampling frequency is 125 Hz. 2. Plot the filter coefficients that define the filter (stem). 3. Plot the frequency response of the FIR filter designed (freqz) 4. Design a 100th-order lowpass FIR filter using the window method (fir1) to cut frequencies above 30Hz in an application where the sampling frequency is 125 Hz. Plot the filter coefficients that...
Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for th...
Please show all work
Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for the frequency response of an FIR filter defined by the pole-zero plot below: Pole-Zero Plot #1 0.5 -0.5 -1 1 -0.5 0 051 Real part (b) For the FIR filter in part (a), write a simplified version of the frequency response H(e'ω) and use it to prove that the maximum value of the frequency response magnitude will be at ω-tr/2....
DSP Lab Exercise 9 Given below are the Impulse Response h(n), of the four main types of FIR Digit...
DSP Lab Exercise 9 Given below are the Impulse Response h(n), of the four main types of FIR Digital filters. Use appropriate MATLAB expressions to find: a) System Response (H(z) b) Pole-zero diagram c) Amplitude Response d) Phase Response 1. FIR Low-Pass Digital Filter ,n= 0.1 |[d(n) + δ(n-I))-1 h(n) 0, otherwise 2. FIR High-Pass Digital Filter 0, otherwise 3. FIR Band-Pass Digital Filter 0, otherwise 4. FIR Band-Stop Digital Filter , n = 0,2 0, otherwise Note: Your final...
3. A length 21, FIR lowpass filter is designed using the windowing method, and rectan gular windo...
3. A length 21, FIR lowpass filter is designed using the windowing method, and rectan gular window is employed. The ideal frequency response on which the design is based 1s given by If the filter's impulse response is 2πη sin 0
b) When designing a FIR filters, the impulse response of the ideal low-pass filter is usually modified by multiplying i...
b) When designing a FIR filters, the impulse response of the ideal low-pass filter is usually modified by multiplying it by a windowing function such as the Hamming window which is defined, for an odd number N of samples, by: (2n)-(N-I)-ns(N-1) N-12 wlnl 0.54 + 0.46 cos i What are the advantages of windowing with this function compared 2 with a standard rectangular window? ii) Design a 10th Order Hamming windowed FIR low-pass filter with cut- off frequency at 1000...
Consider a filter characterized by the following impulse response: h [1, 2, -1, 1] Which of...
Consider a filter characterized by the following impulse response: h [1, 2, -1, 1] Which of the following statements are true about the filter? Assume that the sampling frequency in this application is 8192 Hz. (You may use MATLAB to help you analyze this filter). o 1. The filter characterized by h = 1 2 1 1 Is a frequency selective FIR filter. In terms of the frequency response the ter is best characterized as a band-stop filter with a...
Determine the coefficients b0, b1, b2, of a generalized linear-phase FIR filter 1. (GLP FIR Filters]...
Determine the coefficients b0,
b1, b2, of a generalized linear-phase FIR filter
1. (GLP FIR Filters] Determine the coefficients bo, bi, b2, of a generalized linear-phase FIR filter | d[n] = box[n] + b n - 1]+b22[n – 2] such that (i) it rejects any frequency component at wo = /3; and (ii) its frequency response is normalized so that Ha(0) = 1. Compute and sketch the magnitude and phase response of the filter to check that it satisfies the...
(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...
a) The transfer function of an ideal low-pass filter is and its impulse response is where oc is the cut-off frequency i) Is hLP[n] a finite impulse response (FIR) filter or an infinite impulse response filter (IIR)? Explain your answer ii Is hLP[n] a causal or a non-causal filter? Explain your answer iii) If ae-0. IT, plot the magnitude responses for the following impulse responses b) i) Let the five impulse response samples of a causal FIR filter be given...
Please show all work
Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for the frequency response of an FIR filter defined by the pole-zero plot below: Pole-Zero Plot #1 0.5 -0.5 -1 1 -0.5 0 051 Real part (b) For the FIR filter in part (a), write a simplified version of the frequency response H(e'ω) and use it to prove that the maximum value of the frequency response magnitude will be at ω-tr/2....
DSP Lab Exercise 9 Given below are the Impulse Response h(n), of the four main types of FIR Digital filters. Use appropriate MATLAB expressions to find: a) System Response (H(z) b) Pole-zero diagram c) Amplitude Response d) Phase Response 1. FIR Low-Pass Digital Filter ,n= 0.1 |[d(n) + δ(n-I))-1 h(n) 0, otherwise 2. FIR High-Pass Digital Filter 0, otherwise 3. FIR Band-Pass Digital Filter 0, otherwise 4. FIR Band-Stop Digital Filter , n = 0,2 0, otherwise Note: Your final...
3. A length 21, FIR lowpass filter is designed using the windowing method, and rectan gular window is employed. The ideal frequency response on which the design is based 1s given by If the filter's impulse response is 2πη sin 0
b) When designing a FIR filters, the impulse response of the ideal low-pass filter is usually modified by multiplying it by a windowing function such as the Hamming window which is defined, for an odd number N of samples, by: (2n)-(N-I)-ns(N-1) N-12 wlnl 0.54 + 0.46 cos i What are the advantages of windowing with this function compared 2 with a standard rectangular window? ii) Design a 10th Order Hamming windowed FIR low-pass filter with cut- off frequency at 1000...
Consider a filter characterized by the following impulse response: h [1, 2, -1, 1] Which of the following statements are true about the filter? Assume that the sampling frequency in this application is 8192 Hz. (You may use MATLAB to help you analyze this filter). o 1. The filter characterized by h = 1 2 1 1 Is a frequency selective FIR filter. In terms of the frequency response the ter is best characterized as a band-stop filter with a...
Determine the coefficients b0,
b1, b2, of a generalized linear-phase FIR filter
1. (GLP FIR Filters] Determine the coefficients bo, bi, b2, of a generalized linear-phase FIR filter | d[n] = box[n] + b n - 1]+b22[n – 2] such that (i) it rejects any frequency component at wo = /3; and (ii) its frequency response is normalized so that Ha(0) = 1. Compute and sketch the magnitude and phase response of the filter to check that it satisfies the...
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