x(t) = (A+m(t)) cos(100πt) m(t) is a low-pass signal with B<<50. A=10. Write down Fourier transform of X(f) in terms of M(f) which is the Fourier transform of m(t).

The following are the Fourier transforms of discrete-time signals. Determine the signal corresponding to each transform. (a) X(e) = 1 + 3e-jw - 5e4jw (b) X(ejw) = 3e-jw _1 4-e-jw

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First Exercise   Calculate the Fourier Transform of the signal x(t) = cos(2*pi*t) + cos(5*pi*t)and draw the signal and its amplitude spectrum.

2. A function f(t) has Fourier transform, F(w) = we-w². What are the Fourier transforms of: (a) f(t-3) (b) f(1/2) (c) f(¹=³)

1. Find the Fourier transform for the following signals (a) e-3t e-³t (u(t+2) — u(t — 3)). (b) e-at cos(wot)u(t). (c) te-2t sin(4t)u(t). (d) sint + cos(2ñt +ñ/4).

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The signal continuous x(t) is given by the following equation: (image 001) The signal will be passed through a frequency shaping filter which has an impulse response: (image 002) a) With the help of the Fourier Transform table, determine the spectrum of x(t) and provide a plot for that spectrum (if needed you can provide a magnitude plot and a phase plot for the spectrum). b) With the help of the Fourier Transform table, determine the frequency response of the frequency shaping filter above and provide a plot for the frequency response (if needed you can provide a magnitude plot and a phase plot for the frequency response). c) If the output of the frequency shaping filter above is a signal y(t), then determine both y(t) and the representation of y(t) in the frequency region or spectrum of y(t). Provide a plot for the spectrum of y(t) (if needed you can provide a magnitude plot and a phase plot for the spectrum). Note: if necessary, use the help of the Fourier Transform Table

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