(Solved): Consider a continous-time bandlimited real-valued signal x with Fourier Transform X. The Nyquist f ...

Consider a continous-time bandlimited real-valued signal x with Fourier Transform X. The Nyquist frequency of the signal x is defined as the smallest value wnƒ € R+ such that X(w) = 0 for all w > Wnf. a) Consider the signal x given by x(t) = cos(10?t) sinc(2t) for all t € R. Plot its spectrum X(w)| as a function of w and then show via this plot that its Nyquist fre- quency equals 12?. b) Let the signal y be the product of two bandlimited signals y? and y2. Thus y(t) = y?(t)y2(t) for all t € R. Express the Nyquist frequency of the signal y in terms of the Nyquist frequency of y? and the Nyquist frequency of y2. Explain your answer.