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P6.31. In steady-state operation, a first-order RC lowpass filter has the input signal Vin(t) = 5...
3. The input signal to a certain filter is given by Vin(t) = 2cos (10 state...
3. The input signal to a certain filter is given by Vin(t) = 2cos (10 state output is given by Vout(t) = cos(10000 t + 20°). Determine the filter this will include both a magnitude and phase angle). * 2cos (10000nt - 25%) and the steady- °). Determine the transfer function of
An input signal: vi (t)-5cos(100mt+20 ) + 5 cos(400π t + 60 ) [V] is applied...
An input signal: vi (t)-5cos(100mt+20 ) + 5 cos(400π t + 60 ) [V] is applied to a first order high pass RL filter with break frequecyf 100 [Hz/The filter contains one resistor and one inductor connected in series. The output signal will have the form Vout(t)-Vi cos( 100 π t + Φ) + V2 cos(400 π t + Φ) [vj a) Calculate values for the amplitudes and phase angles for each of the components of the output signal, and...
1. A continuous-time signal x(t) is obtained at the output of an ideal lowpass filter with...
1. A continuous-time signal x(t) is obtained at the output of an ideal lowpass filter with cutoff frequency wc = 10007. If impulse-train sampling is performed on x(t), which of the following sampling periods would guarantee that y(t) can be recovered from its sampled version using an appropriate lowpass filter? (a) T=0.5x10-3 (b) T=2x10-3 (c) T=10-4
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs =...
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs = 8000 Hz and produces at its output a sampled discrete-time signal x$(t) = x(nTs), where To = 1/fs is the sampling period. If the sampled signal is passed through a unity-gain lowpass filter with cutoff frequency of fs/2, sketch the magnitude spectrum of the resulting signal for the following input signals: (a) x(t) = cos(6000nt). (b) x(t) = cos(12000nt). (c) x(t) = cos(18000nt).
Problem 5) The approximate magnitude and phase values of a passive filter circuit is given in the...
Problem 5) The approximate magnitude and phase values of a passive filter circuit is given in the Table P5 Table P5 Frequency Magnitude Phase 0 rad/s 50 500 4500 10000 dB -40 -20 -3 0 90 90 45 a) Find an expression for the output signal Vo(t) when input signal is vs(t)-10 sin(4500t+10) b) Find a steady-state expression for Vo(t) when input signal is vs(t)-50 cos(50t-45°).u(t) c) Find a steady-state expression for vo(t) when input signal is vs(t)-15 sin(10000t+550).u(t) d)...
Aliasing occur? (Justify your answer.) 5.38. An ideal lowpass digital filter has the frequency fu...
5.38 a,b,c
aliasing occur? (Justify your answer.) 5.38. An ideal lowpass digital filter has the frequency function H(2) given by H(n) (a) Determine the unit pulse response h[n] of the filter. (b) Compute the output response yln] of the filter when the input [n] is given by (i) x[n] = cos(m/8), n = 0, ±1, ±2, . . . (ii) x[n] = cos(3rm4) + cos(πη/16), n = 0, ±1, ±2,… (iii) x[n]-sinc(n/2), n-0, ±1,±2 (iv) x[n] = sine(n/4), n =...
Question 7 The diagram depicts a digital filter that samples the continuous time input signal x(t)...
Question 7 The diagram depicts a digital filter that samples the continuous time input signal x(t) at 6 kHz. The digital is filter described by y(n) -x(n) + 0.8y(n -1) Find an expression for the steady state output if x(t) -3sin(2mft) with f 200 Hz? Hint: evaluate the filter's frequency response at the discrete time frequency corresponding to 200 Hz. (12 points) Anti-alias filter Sample A/D Digital Filter
Problem 18.2 For the following circuit, when input V(t)Acos(5000), we measure steady-state output...
Given Answers
Problem 18.2 For the following circuit, when input V(t)Acos(5000), we measure steady-state output ).3416cos(5000t +0), and when V (t)- Acos(8000r) we measure steady-state output r_(t)-1.1714cos(8000t +0,). If R-100Ω, find A, 9,4, and L. Vout Vin Fig 26.2: Passive RL circuit. A-1.5 V, L-10 mH,0,--0.46 rad, θ2-_0.67 rad Problem 18.2
Problem 18.2 For the following circuit, when input V(t)Acos(5000), we measure steady-state output ).3416cos(5000t +0), and when V (t)- Acos(8000r) we measure steady-state output r_(t)-1.1714cos(8000t +0,). If R-100Ω, find...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) |...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) | and phase θ(f) response given below H(f) 90 70 50 30 10 10 θ(f) 25 -50 70 05 35 -3-252 -15105 0 05 115 2 25 3 35 -35-3-25-2-15-1-05 0 0.5 15 2 25 35 frequency (kHz) frequency (kHz) a) For x,(t)-2cos(22500t) find output signal ya(t) b) For x,(t) 4cos(27750t) find output signal yb(t) c) For x,(t)=2cos(2π500t) +4cos(2π750t) find output signal ye(t) d) For...
3. The input signal to a certain filter is given by Vin(t) = 2cos (10 state output is given by Vout(t) = cos(10000 t + 20°). Determine the filter this will include both a magnitude and phase angle). * 2cos (10000nt - 25%) and the steady- °). Determine the transfer function of
An input signal: vi (t)-5cos(100mt+20 ) + 5 cos(400π t + 60 ) [V] is applied to a first order high pass RL filter with break frequecyf 100 [Hz/The filter contains one resistor and one inductor connected in series. The output signal will have the form Vout(t)-Vi cos( 100 π t + Φ) + V2 cos(400 π t + Φ) [vj a) Calculate values for the amplitudes and phase angles for each of the components of the output signal, and...
1. A continuous-time signal x(t) is obtained at the output of an ideal lowpass filter with cutoff frequency wc = 10007. If impulse-train sampling is performed on x(t), which of the following sampling periods would guarantee that y(t) can be recovered from its sampled version using an appropriate lowpass filter? (a) T=0.5x10-3 (b) T=2x10-3 (c) T=10-4
Consider a sampler which samples the continuous-time input signal x(t) at a sampling frequency fs = 8000 Hz and produces at its output a sampled discrete-time signal x$(t) = x(nTs), where To = 1/fs is the sampling period. If the sampled signal is passed through a unity-gain lowpass filter with cutoff frequency of fs/2, sketch the magnitude spectrum of the resulting signal for the following input signals: (a) x(t) = cos(6000nt). (b) x(t) = cos(12000nt). (c) x(t) = cos(18000nt).
Problem 5) The approximate magnitude and phase values of a passive filter circuit is given in the Table P5 Table P5 Frequency Magnitude Phase 0 rad/s 50 500 4500 10000 dB -40 -20 -3 0 90 90 45 a) Find an expression for the output signal Vo(t) when input signal is vs(t)-10 sin(4500t+10) b) Find a steady-state expression for Vo(t) when input signal is vs(t)-50 cos(50t-45°).u(t) c) Find a steady-state expression for vo(t) when input signal is vs(t)-15 sin(10000t+550).u(t) d)...
5.38 a,b,c
aliasing occur? (Justify your answer.) 5.38. An ideal lowpass digital filter has the frequency function H(2) given by H(n) (a) Determine the unit pulse response h[n] of the filter. (b) Compute the output response yln] of the filter when the input [n] is given by (i) x[n] = cos(m/8), n = 0, ±1, ±2, . . . (ii) x[n] = cos(3rm4) + cos(πη/16), n = 0, ±1, ±2,… (iii) x[n]-sinc(n/2), n-0, ±1,±2 (iv) x[n] = sine(n/4), n =...
Question 7 The diagram depicts a digital filter that samples the continuous time input signal x(t) at 6 kHz. The digital is filter described by y(n) -x(n) + 0.8y(n -1) Find an expression for the steady state output if x(t) -3sin(2mft) with f 200 Hz? Hint: evaluate the filter's frequency response at the discrete time frequency corresponding to 200 Hz. (12 points) Anti-alias filter Sample A/D Digital Filter
Given Answers
Problem 18.2 For the following circuit, when input V(t)Acos(5000), we measure steady-state output ).3416cos(5000t +0), and when V (t)- Acos(8000r) we measure steady-state output r_(t)-1.1714cos(8000t +0,). If R-100Ω, find A, 9,4, and L. Vout Vin Fig 26.2: Passive RL circuit. A-1.5 V, L-10 mH,0,--0.46 rad, θ2-_0.67 rad Problem 18.2
Problem 18.2 For the following circuit, when input V(t)Acos(5000), we measure steady-state output ).3416cos(5000t +0), and when V (t)- Acos(8000r) we measure steady-state output r_(t)-1.1714cos(8000t +0,). If R-100Ω, find...
10. An input signal x(t) is processed by a filter with an amplitude | H(f) | and phase θ(f) response given below H(f) 90 70 50 30 10 10 θ(f) 25 -50 70 05 35 -3-252 -15105 0 05 115 2 25 3 35 -35-3-25-2-15-1-05 0 0.5 15 2 25 35 frequency (kHz) frequency (kHz) a) For x,(t)-2cos(22500t) find output signal ya(t) b) For x,(t) 4cos(27750t) find output signal yb(t) c) For x,(t)=2cos(2π500t) +4cos(2π750t) find output signal ye(t) d) For...
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