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4. Given the following signals, a) (6 pts). Find the signal energy in the voltage x(t)...
4. Given the following signals, a) (6 pts). Find the signal energy in the voltage x(t)...
4. Given the following signals, a) (6 pts). Find the signal energy in the voltage x(t) = 10rect b) (6 pts). Find the average signal power in the following periodic voltage, x(t). Express your answer in dBV 4AAK x(t) 9 10 11 12 Given the following amplifier 22 kn 56 kn o ww x(t) c) (6 pts). What is the loss in decibels? d) (7 pts). If the input to the amplifier is 3cos(2T300t+25°) V, what is the output in...
Let the signals x(t) and y(t) be the input and output signals to a differentiator, respectively....
Let the signals x(t) and y(t) be the input and output signals to a differentiator, respectively. x(t) do y(t) (a) Let the autocorrelation of the signal x(t) be R (T) and the autocorrelation of the signal y(t) be R (T). If y(t)= X, express R, (T) in terms of R. (T) dt (b) Assume R (T) = 5e and find the power in the output signal y(t). JA, \f}<B (c) Assume that the power spectral density (PSD) of x(t) is...
3. (45 pts) On signal energy and power. From the following signals, identify energy signals and...
3. (45 pts) On signal energy and power. From the following signals, identify energy signals and power signals. For energy signals, calculate their energy. For power signals, calculate their average signal power. (g) x(t)= rect(t)) (h) x(t) =Loo rect(A) (i) 2(t)=e(-1-j80%(t) (k) x(t) = e-M/2 (l) x[n] = e-jm/2
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to b...
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to be observed in this laboratory assignment are shown below. In all the examples A represents the amplitude of the signal and may be given as the measurement from 0 to the peak value A, Apk or can be given as the measurement between A and -A which defines a peak-to-peak...
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) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given bel...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
3. Sketch stuff (by hand or by computer) 3.1 Systems signals The signal x()-sin^t), for 0stsl;...
3. Sketch stuff (by hand or by computer) 3.1 Systems signals The signal x()-sin^t), for 0stsl; is applied to a circuit with an impulse response given by h(t)-2, for Osts1. Sketch these signals and the output of the circuit If the input signal is now set to x()-6(t-3), sketch the input and output signals. (3.2)
Q1) For the periodic signals x() and ) shown below: x(t) YCO y(t) a) Find the exponential Fourier...
Q1) For the periodic signals x() and ) shown below: x(t) YCO y(t) a) Find the exponential Fourier series for x(t) and y). b) Sketch the amplitude and phase spectra for signal x(). c) Use Parseval's theorem to approximate the power of the periodic signal x() by calculating the power of the first N harmonics, such that the strength of the Nth harmonic is 10% or more of the power of the DC component.
Q1) For the periodic signals x()...
Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t)...
Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t) (b) x(t) = Sin (t + /3). Cos(5t-5) (c) a periodic delta function (comb signal) is given x(t) = (-OS (t-n · T). Express x(t) in Fourier Series. (d) Find X(w) by taking Fourier Transform of the Fourier Series you found in (a). No credit will be given for nlugging into the formula in the formula sheet.
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the...
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the 'input' and the loop current y(t) as the 'output' (20 pts) L-11 R=3.22 yo 1) find its frequency response function H(w). (5 pts) 2) then, find its response to the following input signals, respectively 2-a) x(t)=8(t), (2 pts) 2-b) x(t)=u(t), (3 pts) 2-c) x(t)=sin(10t), (3 pts) 2-d) x(t)=2sin(10t)+cos(20t+1), (3 pts) 3) For the signals in 2), calculate the energy or the average power (whichever...
4. Given the following signals, a) (6 pts). Find the signal energy in the voltage x(t) = 10rect b) (6 pts). Find the average signal power in the following periodic voltage, x(t). Express your answer in dBV 4AAK x(t) 9 10 11 12 Given the following amplifier 22 kn 56 kn o ww x(t) c) (6 pts). What is the loss in decibels? d) (7 pts). If the input to the amplifier is 3cos(2T300t+25°) V, what is the output in...
Let the signals x(t) and y(t) be the input and output signals to a differentiator, respectively. x(t) do y(t) (a) Let the autocorrelation of the signal x(t) be R (T) and the autocorrelation of the signal y(t) be R (T). If y(t)= X, express R, (T) in terms of R. (T) dt (b) Assume R (T) = 5e and find the power in the output signal y(t). JA, \f}<B (c) Assume that the power spectral density (PSD) of x(t) is...
3. (45 pts) On signal energy and power. From the following signals, identify energy signals and power signals. For energy signals, calculate their energy. For power signals, calculate their average signal power. (g) x(t)= rect(t)) (h) x(t) =Loo rect(A) (i) 2(t)=e(-1-j80%(t) (k) x(t) = e-M/2 (l) x[n] = e-jm/2
One of the most important classes of time dependent signals are periodic signals. Periodic signals satisfy tho following signal equations, x(t) X(t) x(t+nt) for n 2,3. The periodic signals to be observed in this laboratory assignment are shown below. In all the examples A represents the amplitude of the signal and may be given as the measurement from 0 to the peak value A, Apk or can be given as the measurement between A and -A which defines a peak-to-peak...
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) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
3. Sketch stuff (by hand or by computer) 3.1 Systems signals The signal x()-sin^t), for 0stsl; is applied to a circuit with an impulse response given by h(t)-2, for Osts1. Sketch these signals and the output of the circuit If the input signal is now set to x()-6(t-3), sketch the input and output signals. (3.2)
Q1) For the periodic signals x() and ) shown below: x(t) YCO y(t) a) Find the exponential Fourier series for x(t) and y). b) Sketch the amplitude and phase spectra for signal x(). c) Use Parseval's theorem to approximate the power of the periodic signal x() by calculating the power of the first N harmonics, such that the strength of the Nth harmonic is 10% or more of the power of the DC component.
Q1) For the periodic signals x()...
Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t) (b) x(t) = Sin (t + /3). Cos(5t-5) (c) a periodic delta function (comb signal) is given x(t) = (-OS (t-n · T). Express x(t) in Fourier Series. (d) Find X(w) by taking Fourier Transform of the Fourier Series you found in (a). No credit will be given for nlugging into the formula in the formula sheet.
HW 2-1. For the RLC circuit in HW 1-2, with the voltage source x(t) as the 'input' and the loop current y(t) as the 'output' (20 pts) L-11 R=3.22 yo 1) find its frequency response function H(w). (5 pts) 2) then, find its response to the following input signals, respectively 2-a) x(t)=8(t), (2 pts) 2-b) x(t)=u(t), (3 pts) 2-c) x(t)=sin(10t), (3 pts) 2-d) x(t)=2sin(10t)+cos(20t+1), (3 pts) 3) For the signals in 2), calculate the energy or the average power (whichever...
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