P-4.4 The spectrum diagram, which gives the frequency content of a continuous-time signal, helps in determining the

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P-4.4 The spectrum diagram, which gives the frequency content of a continuous-time signal, helps in determining the Nyquist rate for sampling that signal.
(a) Given the signal x(t) = cos(4000?t) cos(8000?t), draw a sketchof its spectrum.
Label the frequencies and complex amplitudes of each component spectral line.
(b) Determine the minimum sampling rate that can be used to sample (t) without
aliasing for any of its components.
(c) Given the signal r(t) = cos(3×106?t) sin(5×106?t) cos(7×106?t), determine the minimum sampling rate to avoid aliasing for any of its components.
(d) Given the signal v(t) = cos(3 × 106?t) + sin(5 × 106?t) + cos(7× 106?t), determine the minimum sampling rate to avoid aliasing for any of its components.