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
The system function Hs(s) represents a 1 rad/sec fifth-order normalized Butterworth filter a) Giv...
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 and stable (b) Determine the output of the filter in response to the input 1 + cos
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...
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...
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)
EXAMPLE 1: Design a fifth-order lowpass Butterworth filter with a dc gain equal to unity and the half-power frequency at i kHz. Make the largest capacitance is 1 μF.
EXAMPLE 1: Design a fifth-order lowpass Butterworth filter with a dc gain equal to unity and the half-power frequency at i kHz. Make the largest capacitance is 1 μF.
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...
Use Taylor series to find out the resulting transfer function of the Second order Butterworth Filter: B(s)=1/(s2+sqrt(2)*s+1)
Use Taylor series to find out the resulting transfer function of the Second order Butterworth Filter: B(s)=1/(s2+sqrt(2)*s+1)
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...
QUESTION 6 Зро Design a second-order IIR digital low-pass filter using Butterworth approximation. Use the bilinear transformation to convert the analogue fiter to a digital one (choose the sampling period T- 2 s and the cut-off frequency as 1 rad/'s). Express the digital transfer function of the filter H(z) as: In the box below, provide the numerical answer for b1. [Note: Don't normalise the transfer func on, i.e. b0 # 1). r98111acontentid1837836_1&step QUESTION 7 Windowing based FIR filter design techniques...
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...