Homework Answers
The characteristics of a bandstop filter are given below:
In order to determine the condition, we have to first look at the transfer functions of lowpass and highpass filters.
The circuit diagram and transfer function of lowpass filter is given below:
where wc1 is the cut-off frequency.
The circuit diagram and transfer function of highpass filter is given below:
where wc2 is the cut-off frequency.
The characteristics of the lowpass and highpass filters are given below:
As we can see, if we combine a lowpass filter with a highpass filter we would get a bandstop filter. The cut-off frequency of the lowpass filter should be less than the cut-off frequency of the highpass filter to obtain a bandstop filter.
Therefore the answer would be wc1 < wc2
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Question 29 (3 points) 1 wc2 A filter has the transfer function T(s) = 11 S...
A filter has the transfer function H(S) = s+2007 If the input to the filter is...
A filter has the transfer function H(S) = s+2007 If the input to the filter is v;(t) = 1 + 0.5sin(204t) + 0.1sin(2000xt) V, which of the following is the correct output? (if you see a "p", those should all be pi) All figures show vo(t) in V on the y-axis and t on the x-axis. Be careful, the figures have different scales for both the X- and y-axes. The figure numbers may not be real clear, but they are...
Question 11 1 pts The transfer function of a particular active low pass filter is G(s)...
Question 11 1 pts The transfer function of a particular active low pass filter is G(s) = 400/[s(1+0.8s)(1+0.15)). The phase shift in degrees through the filter at a frequency of 100 Hz is determined as nearest to which of the following answers:- -13 degrees 0 -63 degrees -123 degrees O 198 degrees O-269 degrees
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies Wej and Wc2, the bandwidth ß, and quality factor, Q. Co...
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies Wej and Wc2, the bandwidth ß, and quality factor, Q. Compute values for R and L to yield a bandpass filter with a center frequency of 5kHz and a bandwidth of 200Hz, using a 10nF capacitor. (25 points)
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies...
Question # 2 For the filter shown: a) Write an expression for the filter transfer function...
Question # 2 For the filter shown: a) Write an expression for the filter transfer function Vo(oVs() b) Determine the filter type. c) Based on the filter type, Calculate the filter cut off frequency or frequencies. 1.0 Vs(o) (* 1 10 Vo(t)
Consider the following transfer function of a bandpass filter: 20 1,500 T(S) = 2 1,500 +...
Consider the following transfer function of a bandpass filter: 20 1,500 T(S) = 2 1,500 + 1)(30.000 +1) a) Draw the Bode plot (magnitude and phase) of T(s). Label the slopes (dB/decade) b) Name the filter type. c) Determine the resonant frequency o d) Determine the gain in dB at the resonant frequency e) Determine bandwidth B, and the quality factor of the filter. Magnitude (dB) Phase (Deg)
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)
Question 2 (10 points) Show all your work) inear time-invariant filter has the following transfer function: 1-3z H(z) 221리> 1+z-z 2 a) Is this filter an IIR or FIR? Explain. b) (1 point) What is...
Question 2 (10 points) Show all your work) inear time-invariant filter has the following transfer function: 1-3z H(z) 221리> 1+z-z 2 a) Is this filter an IIR or FIR? Explain. b) (1 point) What is the order of this filter? (1 point) (1 point) 5 points) c) Is this filter stable? Explain. d) Determine the impulse response of the system. e) Determine the difference-equation description for the system. (2 points) nd order
Question 2 (10 points) Show all your work)...
a.b. c. d. An FIR filter has the transfer function: If the following input sequence is entered into this filter: This will result in the output y[n] In the blank space provided, enter the length of t...
a.b.
c.
d.
An FIR filter has the transfer function: If the following input sequence is entered into this filter: This will result in the output y[n] In the blank space provided, enter the length of the output sequence yin). Give a numerical answer for this. N, Determine the transfer function of the filter whose z-plane is given below. 0.5 -0.5 0.5 0.5 1.5 Real Part Enter the filter coefficient into the blank spaces below H(z) -2 An FIR filter...
Question #3 (25 points): A unity feedback system has the following forward transfer function: K(s+20)(s +30) G(S) =...
Question #3 (25 points): A unity feedback system has the following forward transfer function: K(s+20)(s +30) G(S) = s(s+25) (s + 35) Find using Matlab: a) The static error constants Kp, Kv and Ka if the inputs are 15u(t), 15tu(t), and 15t u(t). [15 pts b) The steady-state error for the following inputs: 15u(t), 15tu(t), and 15tu(t). [10 pts
Question #3 (25 points): A unity feedback system has the following forward transfer function: K(s+20)(s +30) G(S) = s(s+25) (s +...
Digital Signal Processing QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Der...
Digital Signal Processing
QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Derive an expression for the output sequence yin], in terms of the input b) sequence, xla], and delayed input and output sequences 10 151 e) Find the unit sample response for the filter (first three terms only)
QUESTION SIX A digital filter system has a transfer...
A filter has the transfer function H(S) = s+2007 If the input to the filter is v;(t) = 1 + 0.5sin(204t) + 0.1sin(2000xt) V, which of the following is the correct output? (if you see a "p", those should all be pi) All figures show vo(t) in V on the y-axis and t on the x-axis. Be careful, the figures have different scales for both the X- and y-axes. The figure numbers may not be real clear, but they are...
Question 11 1 pts The transfer function of a particular active low pass filter is G(s) = 400/[s(1+0.8s)(1+0.15)). The phase shift in degrees through the filter at a frequency of 100 Hz is determined as nearest to which of the following answers:- -13 degrees 0 -63 degrees -123 degrees O 198 degrees O-269 degrees
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies Wej and Wc2, the bandwidth ß, and quality factor, Q. Compute values for R and L to yield a bandpass filter with a center frequency of 5kHz and a bandwidth of 200Hz, using a 10nF capacitor. (25 points)
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies...
Question # 2 For the filter shown: a) Write an expression for the filter transfer function Vo(oVs() b) Determine the filter type. c) Based on the filter type, Calculate the filter cut off frequency or frequencies. 1.0 Vs(o) (* 1 10 Vo(t)
Consider the following transfer function of a bandpass filter: 20 1,500 T(S) = 2 1,500 + 1)(30.000 +1) a) Draw the Bode plot (magnitude and phase) of T(s). Label the slopes (dB/decade) b) Name the filter type. c) Determine the resonant frequency o d) Determine the gain in dB at the resonant frequency e) Determine bandwidth B, and the quality factor of the filter. Magnitude (dB) Phase (Deg)
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)
Question 2 (10 points) Show all your work) inear time-invariant filter has the following transfer function: 1-3z H(z) 221리> 1+z-z 2 a) Is this filter an IIR or FIR? Explain. b) (1 point) What is the order of this filter? (1 point) (1 point) 5 points) c) Is this filter stable? Explain. d) Determine the impulse response of the system. e) Determine the difference-equation description for the system. (2 points) nd order
Question 2 (10 points) Show all your work)...
a.b.
c.
d.
An FIR filter has the transfer function: If the following input sequence is entered into this filter: This will result in the output y[n] In the blank space provided, enter the length of the output sequence yin). Give a numerical answer for this. N, Determine the transfer function of the filter whose z-plane is given below. 0.5 -0.5 0.5 0.5 1.5 Real Part Enter the filter coefficient into the blank spaces below H(z) -2 An FIR filter...
Question #3 (25 points): A unity feedback system has the following forward transfer function: K(s+20)(s +30) G(S) = s(s+25) (s + 35) Find using Matlab: a) The static error constants Kp, Kv and Ka if the inputs are 15u(t), 15tu(t), and 15t u(t). [15 pts b) The steady-state error for the following inputs: 15u(t), 15tu(t), and 15tu(t). [10 pts
Question #3 (25 points): A unity feedback system has the following forward transfer function: K(s+20)(s +30) G(S) = s(s+25) (s +...
Digital Signal Processing
QUESTION SIX A digital filter system has a transfer function given by 1-0.4z-1 T(z) = 1 + 0.2z-2 a) Draw the z-domain version of the block diagram for the filter 110) Derive an expression for the output sequence yin], in terms of the input b) sequence, xla], and delayed input and output sequences 10 151 e) Find the unit sample response for the filter (first three terms only)
QUESTION SIX A digital filter system has a transfer...
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