We have seen that the Hilbert transform introduces a 90° phase shift in the compo-nents of a signal and the transfer function of a quadrature filter can be written aseH(f) = {0f >0f =0.We can generalize this concept to a new transform that introduces a phase shift of 0in the frequency components of a signal, by introducinge-je f > 0f = 0ejeHạ(f) = {0f < 0and denoting the result of this transform by xa(1), i.e., X4(f) = X(f)H9(f), whereXe(f) denotes the Fourier transform of xe (t). Throughout this problem, assume thatthe signal x (t) does not contain any DC components.1. Find hø (1), the impulse response of the filter representing this transform.2. Show that xe(t) is a linear combination of x(t) and its Hilbert transform.3. Show that if x(t) is an energy-type signal, xe(t) will also be an energy-typesignal and its energy content will be equal to the energy content of x(t).

According to the Hilbert transform, the transfer function of the quadrature filter is written as:…

Answered: We have seen that the Hilbert transform…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.16P

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A filter is given by:- fy(k+1)=Afy(k)+(1-A)fm(k) where fy filtered signal and fm input signal. write the transfer function in z-transform and impulse function.
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Problem 1. Which gives the inverse transforms of the given s-domain function? [(e^-5t)/72](24te^6t - 20e^6t + 27e^8t - 7) [(e^5t)/72](-24te^6t - 20e^6t + 27e^8t - 7) [(e^-5t)/72](-24te^6t + 20e^6t - 27e^8t - 7) [(e^-5t)/72](-24te^6t - 20e^6t + 27e^8t - 7)
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You have a following analog filter, which is realized using a discrete filter: Xa (t) -> A/D ->x(n) h(n) ->y(n) D/A ->ya (t) The sampling rate in the A/D and D/A is 120 samples/sec, and the impulse response is h(n)=(0.5)n u(n). what is the digital frequency in x(n) if xa (t)=3cos(20πt)? Find H(z), the z-transform of h(n). Find |H(Ω)|, the magnitude response of the filter, where Ω=2π F: digital frequency Draw the pole-zero plot of the filter. Hint: H(z)=N(z)/D(z), where N(z) and D(z) are the functions of z) Find the output Ya (t)=Xa (t)* h(n). (* : convolution, when Xa (t)=3u(t).) Find the steady-state output Yss (t) when Xa (t)=3u(t). To prevent aliasing, a prefilter would be required to process Xa (t) before it passes to the A/D converter. What type of filter should be used, and what would be the largest cutoff frequency that would work for the given configuration?

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