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Problem 3 (LSM3) (20 pts) Consider a Butterworth filter of order one with a cutoff frequency of we [rad/sec]. (a) Determine the transfer function H(s) of the Butterworth filter so that it is causal a...
1. a. Design a bandstop filter with a cutoff frequency of -3dB at w1 = 20 rad/s and w2 = 100 rad/s b. Confirm by plotting the magnitude & phase of the transfer function. 2. Design a 5th order low...
1.
a. Design a bandstop filter with a cutoff
frequency of -3dB at w1 = 20 rad/s and w2 = 100 rad/s
b. Confirm by plotting the magnitude &
phase of the transfer function.
2. Design a 5th order low pass butterworth
filter with wc = 1 rad/s.
Use this equation for both problems.
(jo)
(jo)
1. By using an analog filter with a Butterworth response of order 3, design a digital IIR low pass filter with 3-db cutoff frequency 2c 0.6TT a) b) c) Evaluate the transfer function of the analog fil...
1. By using an analog filter with a Butterworth response of order 3, design a digital IIR low pass filter with 3-db cutoff frequency 2c 0.6TT a) b) c) Evaluate the transfer function of the analog filter (10marks) Skecth the block diagram of transfer function (5 marks) Plot the magnitude response of the filters. (5marks)
1. By using an analog filter with a Butterworth response of order 3, design a digital IIR low pass filter with 3-db cutoff frequency 2c...
1.(10pts) A first-order highpass filter whose transfer function is represented in Laplace transforms as H HPS) -, where Ωο(cut-off frequency) is 1000 rad/sec. Convert this analog filter into a digita...
1.(10pts) A first-order highpass filter whose transfer function is represented in Laplace transforms as H HPS) -, where Ωο(cut-off frequency) is 1000 rad/sec. Convert this analog filter into a digital filter with bilinear-transformation assuming sampling rate is 2500Hz and then determine its input-output relation. In your answer, you will need to provide (i) HHP) and ii) filter's input-output relation. You can find the formula of bilinear transformation in either lecture notes (Lec 14) or textbook pp.494
1.(10pts) A first-order highpass...
The system function Hs(s) represents a 1 rad/sec fifth-order normalized Butterworth filter a) Giv...
The system function Hs(s) represents a 1 rad/sec fifth-order normalized Butterworth filter a) Give Hs(s) in both the polynomial and quadrature factored forms b) Repeat (a) for Chebyshev type I filter with ε=0.7647831
6. (20 points) (1) Design an analog lowpass filter with a cut-off frequency of 9 rad/sec by starting with an analogue prototype first-order lowpass filter with cut-off frequency of 1 rad/sec. Sho...
6. (20 points) (1) Design an analog lowpass filter with a cut-off frequency of 9 rad/sec by starting with an analogue prototype first-order lowpass filter with cut-off frequency of 1 rad/sec. Show the system transfer function H(s) (2) Design an IIR digital filter Hz) that corresponds to the above H(s) by using the bilinear transform method without prewarping with T 0.1 second. Show the system transfer function Hz) and find its corresponding digital cut-off frequency Be approximately (3) What is...
Using MATLAB technology 1. (20 points) Design an analog Butterworth LPF with a,--1 dB at ar...
Using MATLAB technology
1. (20 points) Design an analog Butterworth LPF with a,--1 dB at ar = 20π rad/s, a,-40 dB at w 100n rad/s. (a) Determine the order and the cutoff frequency of the filter. (b) Find the transfer function of the filter. (c) Plot the frequency response of the filter. (d) Measure the transition band which is given by A2 (a.)-w (e) Increase the order by 2 for the same cutoff frequency, measure the transition band, compare with...
Part II: Design of Butterworth Filters Butterworth filters, described in a paper by Stephen Butterworth in...
Part II: Design of Butterworth Filters Butterworth filters, described in a paper by Stephen Butterworth in 1930, are widely used for CT frequency-selective filtering. Butterworth filters have a simple analytic form and are designed to have a magnitude response that is maximally flat in the passband. In this section, you will use the Laplace transform to design and analyze Butterworth filters in the frequency domain. The textbook has some useful information about Butterworth filters, so check it out to help...
53. A 2- order normalized Butterworth filter can be improved by using a so-called Chebeyshev filter...
53. A 2- order normalized Butterworth filter can be improved by using a so-called Chebeyshev filter The 3dBNLP second order NLP Chebeyshev transfer function is: 0.5012 2 +0.6449s+0.7079 Cheb3dBNLP(s) The Chebeyshev filter has some ripple in the passband but has better roll off, more attenuation in the stop band. If one can tolerate some ripple (sort of like a bouncy car ride) in the passband Chebeyshev filters typically have lower order than Butterworth filters. But, Butterworth filters have NO ripple...
Using filterDesigner in MATLAB, design a second order low pass IIR Butterworth filter whose sampling frequency...
Using filterDesigner in MATLAB, design a second order low pass IIR Butterworth filter whose sampling frequency (Fs) is 1 kHz and cutoff frequency (Fc) is 10 Hz. Find the numerator and denominator coefficients. Write its transfer function H(z) = Y(z) / X(z). Write its difference function y(k). Draw (copy from Filter Designer) the magnitude response plot. Draw (copy from Filter Designer) the phase response plot. Draw (copy from Filter Designer) the impulse response plot.
Q.6 (a) (4 pts) A Butterworth filter has been designed with 22. = 0.578 and N=3....
Q.6 (a) (4 pts) A Butterworth filter has been designed with 22. = 0.578 and N=3. Draw the locations of the poles of its magnitude squared function H(s)H(-s). (b) (2 pts) What is value of H.(192) at cutoff frequency 2. for a butterworth filter. (c) (3 pts) From the magnitude squared function in part (a) above, find an expression for H(s), the transfer function of the required analog filter. (d) (2 pts) Give the number of poles for the Chebyshev...
1.
a. Design a bandstop filter with a cutoff
frequency of -3dB at w1 = 20 rad/s and w2 = 100 rad/s
b. Confirm by plotting the magnitude &
phase of the transfer function.
2. Design a 5th order low pass butterworth
filter with wc = 1 rad/s.
Use this equation for both problems.
(jo)
(jo)
1. By using an analog filter with a Butterworth response of order 3, design a digital IIR low pass filter with 3-db cutoff frequency 2c 0.6TT a) b) c) Evaluate the transfer function of the analog filter (10marks) Skecth the block diagram of transfer function (5 marks) Plot the magnitude response of the filters. (5marks)
1. By using an analog filter with a Butterworth response of order 3, design a digital IIR low pass filter with 3-db cutoff frequency 2c...
1.(10pts) A first-order highpass filter whose transfer function is represented in Laplace transforms as H HPS) -, where Ωο(cut-off frequency) is 1000 rad/sec. Convert this analog filter into a digital filter with bilinear-transformation assuming sampling rate is 2500Hz and then determine its input-output relation. In your answer, you will need to provide (i) HHP) and ii) filter's input-output relation. You can find the formula of bilinear transformation in either lecture notes (Lec 14) or textbook pp.494
1.(10pts) A first-order highpass...
6. (20 points) (1) Design an analog lowpass filter with a cut-off frequency of 9 rad/sec by starting with an analogue prototype first-order lowpass filter with cut-off frequency of 1 rad/sec. Show the system transfer function H(s) (2) Design an IIR digital filter Hz) that corresponds to the above H(s) by using the bilinear transform method without prewarping with T 0.1 second. Show the system transfer function Hz) and find its corresponding digital cut-off frequency Be approximately (3) What is...
Using MATLAB technology
1. (20 points) Design an analog Butterworth LPF with a,--1 dB at ar = 20π rad/s, a,-40 dB at w 100n rad/s. (a) Determine the order and the cutoff frequency of the filter. (b) Find the transfer function of the filter. (c) Plot the frequency response of the filter. (d) Measure the transition band which is given by A2 (a.)-w (e) Increase the order by 2 for the same cutoff frequency, measure the transition band, compare with...
Part II: Design of Butterworth Filters Butterworth filters, described in a paper by Stephen Butterworth in 1930, are widely used for CT frequency-selective filtering. Butterworth filters have a simple analytic form and are designed to have a magnitude response that is maximally flat in the passband. In this section, you will use the Laplace transform to design and analyze Butterworth filters in the frequency domain. The textbook has some useful information about Butterworth filters, so check it out to help...
53. A 2- order normalized Butterworth filter can be improved by using a so-called Chebeyshev filter The 3dBNLP second order NLP Chebeyshev transfer function is: 0.5012 2 +0.6449s+0.7079 Cheb3dBNLP(s) The Chebeyshev filter has some ripple in the passband but has better roll off, more attenuation in the stop band. If one can tolerate some ripple (sort of like a bouncy car ride) in the passband Chebeyshev filters typically have lower order than Butterworth filters. But, Butterworth filters have NO ripple...
Q.6 (a) (4 pts) A Butterworth filter has been designed with 22. = 0.578 and N=3. Draw the locations of the poles of its magnitude squared function H(s)H(-s). (b) (2 pts) What is value of H.(192) at cutoff frequency 2. for a butterworth filter. (c) (3 pts) From the magnitude squared function in part (a) above, find an expression for H(s), the transfer function of the required analog filter. (d) (2 pts) Give the number of poles for the Chebyshev...
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