Physics

Physics, 10.07.2019 23:30, ligittiger12806

(a) use the fourier transform, and the inverse transform 1 e-i#f/rd3r 2th to prove the fourier integral theorem

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Physics, 05.07.2019 01:20, edailey7230

(a) use the fourier transform in 1-dimension, -) +00 1 (p)ep/h dp 27th and the inverse transform, +oo 1 (p) b(x)eipa/hdt 27th to prove the fourier integral theorem +o0 +oo 1 p(p')e(p-p)a/hdp'da 27th -oo (b) working in 1-dimension for simplicity, use (r) xp ()h x(x) to show that the position operator in momentum space is d

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Physics, 12.07.2019 18:20, catman7884

a few useful properties of fourier transforms a) proove parseval's theorem (10) for any regular function g(k) exp(ikr)dk with f(x) exp(-ikx)dr b) the convolution of two functions fi and f2 is defined as the integral show that if g(k) is the fourier transform of f(x) and gi(k) and g2(k) are the fourier transforms of fı(x) and f2(x) respectively, then

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Physics, 12.07.2019 23:20, Christyy9608

A) write a function that calculates the continuous time fourier transform of a periodic signal x (t). syntax: [w, x]- ctft(, x) the outputs to the function are: w = the frequencies in rad/s, and x = the continuous fourier transform of the signal the inputs to the function are: x- one period of the signal x(t), and t the time vector the continuous time fourier transform of a signal x(t) is given by: | x(t)e-jatdt x(a))= b) write a function that calculates the inverse continuous time fourier transform. the inverse continuous-time fourier transform is given by: 2π syntax: x ictft(t, w. x) the output to the function is: the signal x(t) the inputs to the function are: the time vector, w = the frequencies in rad/s, and x = the continuous fourier transform c) test both ofyour functions ctft and ictft with x(t) =sin(t) , where t =-50: 0.1 : 50, and use subplot to plot each of x(c), and the output of icft to verify its accuracy. label all plots and axes appropriately

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Engineering, 15.11.2019 23:31, paigefields2578

Lower side-band suppressed carrier (lsb-sc) modulation i: in lecture we studied how to modulate a (band-limited) signal x(t) such that we can remove the lsb from a signal r(t) and keep only the upper side-band (usb); we will assume that the bandwidth w of r(t) is less than the carrier frequency wc. note that for this we first produced the hilbert transform of the signal r(t), which we call (t), by passing it through an lti system with frf h(w) j sgn(w), where is the sign function. then we constructed yusb(t)t) cos(wct) - (t) sin(wct), which is the modulated signal with the lsb eschewed. answer the following with minimal calculations but using properties of fourier transforms (a) show that ylsb(t)-r(t) cos(wct) + (t) sin(wct) (b) show that you can decode using synchronous decoding just as with either the dsb or usb modulation schemes, i.e., by multiplying by cos(wct) and then using a (ideal) low-pass filter. hint: work exclusively in the fourier domain. determine the fourier transform of the hilbert transform x(t) using the fourier transform of x(t), then apply the consequences of modulation. use generic shapes for the fourier transform of x(t). the following trigonometric identities maybe useful too cos(a) cos(b) sin(a) cos(b) - sin( a) sin(b) cos(a+ b) +cos(a- b) sin(a + b) +sin(a - b) cos(a b) - cos(a b) 2

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