![1. Consider a continuous-time ideal high-pass filter that removes all frequencies below a given cut-off frequency, and allows all frequencies at or above that cut-off frequency to pass through the system unchanged. That is, the filter will keep frequency w if w] 2we and remove frequency w if ww Let the cutoff frequency we have value 2π. (a) Sketch this filters frequency response H(ju). (b) Let x(t) 4-3 cos(3m) + 6eMt. Find ak, the Fourier series coefficients of x(t) (c) Now, let r(t) (defined as in part b) be the input to this high-pass filter. Let y(t) represent the filters output, and let bk represent the Fourier series coefficients of y(t) Write an expression for bk (d) Write an expression for y(t)](http://img.homeworklib.com/questions/82a18be0-7c5f-11eb-9c48-d56a931241d8.png?x-oss-process=image/resize,w_560)
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1. Consider a continuous-time ideal high-pass filter that removes all frequencies below a given cut-off frequency,...
Explain your process please 1. Design 6th order Butterworth band-pass filter with cut-off frequency is 4KHz...
Explain your process please
1. Design 6th order Butterworth band-pass filter with cut-off frequency is 4KHz and 7KHz and pass- band gain is 20dB Draw the circuit, write the transfer function of the filter, and sketch a frequency spectrum of the filter and show the cutoff frequencies on the spectrum Solution:
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass...
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass through an ideal lowpass filter with cut off frequency =102.5Hz. The resulting signal y, (t) is sampled periodically with T 0.005 sec determine the spectrum of the sequence y(n) = ya(nT)
Problem 2: (10 points) A high pass filter with a cut-off frequency of 1200Hz is desired...
Problem 2: (10 points) A high pass filter with a cut-off frequency of 1200Hz is desired for a data acquisition system. Design the filter and specify the components for the electrical circuit that can be built into the data acquisition system.
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%]...
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...
A) Design a low-pass filter using the given circuitry with a cut-off value of 1 kHz and plot the ...
a) Design a low-pass filter using the given circuitry with a cut-off value of 1 kHz and plot the frequency response curve on the given axes 1.0 0.7 0.5 in out 0.0 101 102 103 104 10s Hz b) Design a band-pass filter using the given circuitry with a bandwidth of 500 Hz and a lower cut-off value of 100 Hz, and draw the frequency response curve. Keep all resistors at the same value (i.e. Ri-R-R3-R4). 1.0 0.7 0.5 0.0...
2. By applying Bode plot approximations, sketch the response of each filter, and hence complete the Table below. Filter Type Order Cut-off Frequency High Passsecond 120kHz Low Pass fourth 2250Hz 400H...
2. By applying Bode plot approximations, sketch the response of each filter, and hence complete the Table below. Filter Type Order Cut-off Frequency High Passsecond 120kHz Low Pass fourth 2250Hz 400Hz Gain in Stop Band Pass-Band Gain OdB Gain at 15kHz Gain at 18kHz = ? Gain at 50Hz-18dB Gain at 15Hz = ? Gain at 64kHz ? Gain -60dB at 50kH:z 6dB OdB OdB High Pass Band Pass fourth 60Hz, 4kHz 12dB Low Pass sixth 1?
2. By applying...
Please answer in detail A) Assume that x(t) -2 sin (4 pi t)-2 input is applied to a high pass filter with the cut off frequency of 2 Hz. Explain in detail with appropriate justification and accuratel...
Please answer in detail
A) Assume that x(t) -2 sin (4 pi t)-2 input is applied to a high pass filter with the cut off frequency of 2 Hz. Explain in detail with appropriate justification and accurately sketch the output voltages that appears on the oscilloscope screen if 1 volt/div and 0.25 sec. time/div are set. + B) Assume that x(t) 4 cos (2 pi t)+4 input is applied to a low pass filter with the cut off frequency of...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.5...
Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.56 n -3]. i. Derive the filter's frequency response; 11. Roughly sketch the filter's magnitude response for 0 ii. Is it a low-pass or high-pass filter? Ω 2m; (b) A continuous-time signal se(t) is converted into a discrete-time signal as shown below. s(t) is a unit impulse train. s(t) x,) Conversion into x(1) __→ⓧ一ㄅㄧ-discrete-time sequence ー→ xu [n] The frequency spectrum of ap (t) is...
The following periodic signal is input to an ideal low pass filter of bandwidth 25 KHz. 1. x(t) 2...
The following periodic signal is input to an ideal low pass filter of bandwidth 25 KHz. 1. x(t) 2 a) Determine the average power of the signal x(t). b) If T 0.1 ms, give the output of the filter as a function of time, y(t) e) Determine the average power of the signal y(t) d) Determine the bandwidth of the signal y(), considered as a baseband signal. e) Now assume that the signal x() (with T-0.1 ms) is instead input...
Explain your process please
1. Design 6th order Butterworth band-pass filter with cut-off frequency is 4KHz and 7KHz and pass- band gain is 20dB Draw the circuit, write the transfer function of the filter, and sketch a frequency spectrum of the filter and show the cutoff frequencies on the spectrum Solution:
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass through an ideal lowpass filter with cut off frequency =102.5Hz. The resulting signal y, (t) is sampled periodically with T 0.005 sec determine the spectrum of the sequence y(n) = ya(nT)
Problem 2: (10 points) A high pass filter with a cut-off frequency of 1200Hz is desired for a data acquisition system. Design the filter and specify the components for the electrical circuit that can be built into the data acquisition system.
Question 2 (50 points]: Continuous-Time Signals Given the following continuous-time signal (t). (t) 5t (a) [4%] What is the fundamental period (i.e., T) and fundamental frequency (ie, wo) of (+)? (b) [8%] Calculate the time average, average power and total energy of x(t). Is x(t) an energy signal? Explain. (c) [8%] Calculate the Fourier series coefficients of (t), i.e., {x}. [Hint: You can make use of the result in Q1(a).] (d) [8%] What is the percentage of power loss if...
a) Design a low-pass filter using the given circuitry with a cut-off value of 1 kHz and plot the frequency response curve on the given axes 1.0 0.7 0.5 in out 0.0 101 102 103 104 10s Hz b) Design a band-pass filter using the given circuitry with a bandwidth of 500 Hz and a lower cut-off value of 100 Hz, and draw the frequency response curve. Keep all resistors at the same value (i.e. Ri-R-R3-R4). 1.0 0.7 0.5 0.0...
2. By applying Bode plot approximations, sketch the response of each filter, and hence complete the Table below. Filter Type Order Cut-off Frequency High Passsecond 120kHz Low Pass fourth 2250Hz 400Hz Gain in Stop Band Pass-Band Gain OdB Gain at 15kHz Gain at 18kHz = ? Gain at 50Hz-18dB Gain at 15Hz = ? Gain at 64kHz ? Gain -60dB at 50kH:z 6dB OdB OdB High Pass Band Pass fourth 60Hz, 4kHz 12dB Low Pass sixth 1?
2. By applying...
Please answer in detail
A) Assume that x(t) -2 sin (4 pi t)-2 input is applied to a high pass filter with the cut off frequency of 2 Hz. Explain in detail with appropriate justification and accurately sketch the output voltages that appears on the oscilloscope screen if 1 volt/div and 0.25 sec. time/div are set. + B) Assume that x(t) 4 cos (2 pi t)+4 input is applied to a low pass filter with the cut off frequency of...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
Question 5 (a) The impulse response of a discrete-time filter is given as, hin) 0.56n-1] +n-2)0.56 n -3]. i. Derive the filter's frequency response; 11. Roughly sketch the filter's magnitude response for 0 ii. Is it a low-pass or high-pass filter? Ω 2m; (b) A continuous-time signal se(t) is converted into a discrete-time signal as shown below. s(t) is a unit impulse train. s(t) x,) Conversion into x(1) __→ⓧ一ㄅㄧ-discrete-time sequence ー→ xu [n] The frequency spectrum of ap (t) is...
The following periodic signal is input to an ideal low pass filter of bandwidth 25 KHz. 1. x(t) 2 a) Determine the average power of the signal x(t). b) If T 0.1 ms, give the output of the filter as a function of time, y(t) e) Determine the average power of the signal y(t) d) Determine the bandwidth of the signal y(), considered as a baseband signal. e) Now assume that the signal x() (with T-0.1 ms) is instead input...
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