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a) Two bandpass signals are added together. j2rfet j2Tfet y(t)-Re y(t)e v(t)-x(t) y(t) v(t) may be represented as, What...
2.45,2.48 explain clearly please Signals and Systems: A Primer with MATLAB 104 20 1H y(t) x(t)...
2.45,2.48 explain clearly please
Signals and Systems: A Primer with MATLAB 104 20 1H y(t) x(t) FIGURE 2.38 For Problem 2.48. 2.45 An accumulator has impulse response h[n] = u[n]. Check if an accumulator is BIBO stable 2.46 The input to the circuit discussed in Example 2.15 is v,) ut - )dt - 2) Use convolution to determine the output 2.47 Determine the output of the circuit discussed in Practice Problem 2.15 if v,) u() 2.48 If the filter in...
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are...
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t)...
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t –...
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier transform pair Pr(t) ←→ τ sine ( (b) An ideal bandpass filter has frequency response w) 0,...
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier transform pair Pr(t) ←→ τ sine ( (b) An ideal bandpass filter has frequency response w) 0, otherwise 2(t-1 Find the output response y(t) when the input is (t)-sinc 2
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier...
Problem 1 Let's consider an LTI system with intput and output relatex through the equation y(t)...
Problem 1 Let's consider an LTI system with intput and output relatex through the equation y(t) - --- (T 2) dr a) Find the impulse response h(t) for the given system (1). b) Is this system cansal or not? c) Determine the output of the system when the input x(t) is as shown below. Problem 2 Evaluate the following convolution where (t) and y(t) are plotted helow z(t) = z(t) * y(t) Hint. Expr the signals as a linear combination...
5) Consider the following second-order bandpass filter. As input voltage, apply V(t) 100Ω, C-4.7 μF. and L-10mH. sin(wt).R in Vout Fig 9: Second-order band-pass filter a) Determine the frequenc...
5) Consider the following second-order bandpass filter. As input voltage, apply V(t) 100Ω, C-4.7 μF. and L-10mH. sin(wt).R in Vout Fig 9: Second-order band-pass filter a) Determine the frequency response function H(ju) Ve-ju) / Vm(ju) and sketch the magnitude and phase characteristics versus w by calaulation. Calculate the theoretical cutoff frequency of the filter Using PSpice AC analysis, plot magnitude lHju)l and phase ф characteristics of the filter, between 1 Hz-100 KHz b) c)
5) Consider the following second-order bandpass...
1. For the function (t) below, T 2 and Vm-100 V. vt) 3 2 012 3...
1. For the function (t) below, T 2 and Vm-100 V. vt) 3 2 012 3 (a) Sketch v'(t) and derive the Fourier coefficients for '(t). (b) Use your results from part (a) to determine for Fourier coefficients for v(t). Express your solution in the complex form of the Fourier series, nugt and verify your solution by plotting your results using Matlab. 2. Assume that the signal above is the input to the bandpass filter shown below. y (t (a)...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
2.45,2.48 explain clearly please
Signals and Systems: A Primer with MATLAB 104 20 1H y(t) x(t) FIGURE 2.38 For Problem 2.48. 2.45 An accumulator has impulse response h[n] = u[n]. Check if an accumulator is BIBO stable 2.46 The input to the circuit discussed in Example 2.15 is v,) ut - )dt - 2) Use convolution to determine the output 2.47 Determine the output of the circuit discussed in Practice Problem 2.15 if v,) u() 2.48 If the filter in...
4 a. y(t)-x(t)cos(t/2 b. y(t)-x(t)cos(') x()cos(21) c. X (ju) 5. The signals y(t) in 4a-4e are passed through a filter with unit impulse response h(t) so that the output is z(t)-h(t)*y(t) . Ifthe frequency response of the filter is sketch by hand the Fourier transforms Z(j for 4a-4e Fromjust observing your sketches of Z (jo), which z(1) if any in a-e equal to the original
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
Problem 4: Evaluation of the convolution integral too y(t) = (f * h)(t) = f(t)h(t – 7)dt is greatly simplified when either the input f(t) or impulse response h(t) is the sum of weighted impulse functions. This fact will be used later in the semester when we study the operation of communication systems using Fourier analysis methods. a) Use the convolution integral to prove that f(t) *8(t – T) = f(t – T) and 8(t – T) *h(t) = h(t...
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier transform pair Pr(t) ←→ τ sine ( (b) An ideal bandpass filter has frequency response w) 0, otherwise 2(t-1 Find the output response y(t) when the input is (t)-sinc 2
(a) Show that for any B 〉 0 and any c E R. 3, sinc is a Fourier transform pair. You may assume the Fourier...
Problem 1 Let's consider an LTI system with intput and output relatex through the equation y(t) - --- (T 2) dr a) Find the impulse response h(t) for the given system (1). b) Is this system cansal or not? c) Determine the output of the system when the input x(t) is as shown below. Problem 2 Evaluate the following convolution where (t) and y(t) are plotted helow z(t) = z(t) * y(t) Hint. Expr the signals as a linear combination...
5) Consider the following second-order bandpass filter. As input voltage, apply V(t) 100Ω, C-4.7 μF. and L-10mH. sin(wt).R in Vout Fig 9: Second-order band-pass filter a) Determine the frequency response function H(ju) Ve-ju) / Vm(ju) and sketch the magnitude and phase characteristics versus w by calaulation. Calculate the theoretical cutoff frequency of the filter Using PSpice AC analysis, plot magnitude lHju)l and phase ф characteristics of the filter, between 1 Hz-100 KHz b) c)
5) Consider the following second-order bandpass...
1. For the function (t) below, T 2 and Vm-100 V. vt) 3 2 012 3 (a) Sketch v'(t) and derive the Fourier coefficients for '(t). (b) Use your results from part (a) to determine for Fourier coefficients for v(t). Express your solution in the complex form of the Fourier series, nugt and verify your solution by plotting your results using Matlab. 2. Assume that the signal above is the input to the bandpass filter shown below. y (t (a)...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
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