![Power/energy objective] The following is a full-wave ueatified 5 sinusoid x(0) -6lcos(2r) C. 0 1.25 0.75 0.5 0.25 0.25 0.5 0.75 t [seconds] 12 The signal may be expressed in trigonometric Fourier series form as eUen 24(-1)k+1 x(t) = 12 t coS(k4Ttt k=1 Calculate the power of the signal using the time-domain integral. Calculate the power of the signal for all frequency components up to the 3rd harmonic. a. b. Ktl 2](http://img.homeworklib.com/questions/0efeb730-17c3-11ec-ac4e-afdc528bc36b.png?x-oss-process=image/resize,w_560)
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Power/energy objective] The following is a full-wave ueatified 5 sinusoid x(0) -6lcos(2r) C. 0 1.25 0.75...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396]...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
We may design a dc power supply by cascading a full-wave rectifier and an RC circuit....
We may design a dc power supply by cascading a full-wave rectifier and an RC circuit. The full wave rectifier output x(t) = |cos(120t)I is the input to the RC circuit whose frequency response is 4. a) Find the Fourier transform for the input signal x(t) b) Find the Fourier transform for the output signal y(t) c) Find the range for the RC such that magnitude of the first harmonic of the ripple in y(t) is less than 1% of...
Use MATLAB to solve this question: Lab Exercises: Fourier Series Coefficients 4 In this lab, the...
Use MATLAB to solve this question: Lab Exercises: Fourier Series Coefficients 4 In this lab, the objective is to create a set of functions that will enable us to do the following 1. Evaluate the Fourier Series coefficients for the following periodic signal which is defined over one period to be rt)240sin (100nt) for 0ts 1/100 (6) The period is 1/100 seconds. This signal is called a full-wave rectified sinusoid, because it contains only the positive lobe of the sinusoidal...
A device produces a square wave current waveform as depicted below i (mA) 10 5 t...
A device produces a square wave current waveform as depicted below i (mA) 10 5 t (sec) fur w It is desired to obtain the triangular voltage waveform shown below v (V) 12 < 1 1 1 3 4 t (sec) What device/element would you use and what are its characteristics including its initial state? Hint: one definition of the square wave is simply the sign function of a sinusoid: x(t) = sign(sin[2nft]) which will be 1 when the sinusoid...
)Consider the wave equation for a vibrating string of semi-infnite length with a fixed end at z = 0, t > 0 a(0,t) = 0, and initial conditions 0 < x < oo u(z,0) = 1-cos(nz), ut(x,0) = 0,...
)Consider the wave equation for a vibrating string of semi-infnite length with a fixed end at z = 0, t > 0 a(0,t) = 0, and initial conditions 0 < x < oo u(z,0) = 1-cos(nz), ut(x,0) = 0, Complete the table below with the values of u(0.5, t) at the specified time instants 0.5 0.5 x 0.5 0.5 0.5 2 0.5 0.75 t 0.25 u(x,t)
)Consider the wave equation for a vibrating string of semi-infnite length with a fixed...
ffset sawtooth wave x(t). 1-7 A binary signal x(t) = 0 for t <0. For posi-...
ffset sawtooth wave x(t). 1-7 A binary signal x(t) = 0 for t <0. For posi- tive time, x(t) toggles between one and zero as follows: one for 1 second, zero for 1 second, one for 1 second, zero for 2 seconds, one for 1 1-11 second, zero for 3 seconds, and so forth. That is, the "on" time is always one second but the “off” time successively increases by one sec- ond between each toggle. A portion of x(t)...
A transverse harmonic wave travels on a rope according to the following expression: y(x, t) =...
A transverse harmonic wave travels on a rope according to the
following expression:
y(x, t) = A cos(kx − ωt − φ)
The mass density of the rope is μ = 0.113 kg/m. x and y are
measured in meters and t in seconds. Using the graphs at of y vs t
at x=0 and y vs x at t=0 shown below, answer the following
questions:
(a) What is the value for the wave number, k, for the expression
y(x,t)?...
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...
(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...
I need help with number 2 . Please answer in MATLAB thank you! 1. In the lab we analyzed filtering 60 Hz power-line noi...
I need help with number 2 . Please answer in MATLAB thank
you!
1. In the lab we analyzed filtering 60 Hz power-line noise from ECG signal using a digital (signal processing) filter. Now let's try to an analog (circuit) filter approach to remove the 60 Hz line-noise. Following is an active twin-T notch filter with transfer function: (1+m)((2joRC? +1 Z(a) 2R 2R Here m is the ratio of the two feedback 2C R resistance which determines the gain and...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
We may design a dc power supply by cascading a full-wave rectifier and an RC circuit. The full wave rectifier output x(t) = |cos(120t)I is the input to the RC circuit whose frequency response is 4. a) Find the Fourier transform for the input signal x(t) b) Find the Fourier transform for the output signal y(t) c) Find the range for the RC such that magnitude of the first harmonic of the ripple in y(t) is less than 1% of...
Use MATLAB to solve this question: Lab Exercises: Fourier Series Coefficients 4 In this lab, the objective is to create a set of functions that will enable us to do the following 1. Evaluate the Fourier Series coefficients for the following periodic signal which is defined over one period to be rt)240sin (100nt) for 0ts 1/100 (6) The period is 1/100 seconds. This signal is called a full-wave rectified sinusoid, because it contains only the positive lobe of the sinusoidal...
A device produces a square wave current waveform as depicted below i (mA) 10 5 t (sec) fur w It is desired to obtain the triangular voltage waveform shown below v (V) 12 < 1 1 1 3 4 t (sec) What device/element would you use and what are its characteristics including its initial state? Hint: one definition of the square wave is simply the sign function of a sinusoid: x(t) = sign(sin[2nft]) which will be 1 when the sinusoid...
)Consider the wave equation for a vibrating string of semi-infnite length with a fixed end at z = 0, t > 0 a(0,t) = 0, and initial conditions 0 < x < oo u(z,0) = 1-cos(nz), ut(x,0) = 0, Complete the table below with the values of u(0.5, t) at the specified time instants 0.5 0.5 x 0.5 0.5 0.5 2 0.5 0.75 t 0.25 u(x,t)
)Consider the wave equation for a vibrating string of semi-infnite length with a fixed...
ffset sawtooth wave x(t). 1-7 A binary signal x(t) = 0 for t <0. For posi- tive time, x(t) toggles between one and zero as follows: one for 1 second, zero for 1 second, one for 1 second, zero for 2 seconds, one for 1 1-11 second, zero for 3 seconds, and so forth. That is, the "on" time is always one second but the “off” time successively increases by one sec- ond between each toggle. A portion of x(t)...
A transverse harmonic wave travels on a rope according to the
following expression:
y(x, t) = A cos(kx − ωt − φ)
The mass density of the rope is μ = 0.113 kg/m. x and y are
measured in meters and t in seconds. Using the graphs at of y vs t
at x=0 and y vs x at t=0 shown below, answer the following
questions:
(a) What is the value for the wave number, k, for the expression
y(x,t)?...
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...
(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...
I need help with number 2 . Please answer in MATLAB thank
you!
1. In the lab we analyzed filtering 60 Hz power-line noise from ECG signal using a digital (signal processing) filter. Now let's try to an analog (circuit) filter approach to remove the 60 Hz line-noise. Following is an active twin-T notch filter with transfer function: (1+m)((2joRC? +1 Z(a) 2R 2R Here m is the ratio of the two feedback 2C R resistance which determines the gain and...
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