Question

onsider the sampling and reconstruction system shown in the figure. x(t) IdealIdeal) D-to-C Converter Converter Assume that the sampling rates of the C-to-D and D-to-C converters are equal, and the input to the Ideal C-to-D converter is x(t) = 2 cos (2m(50)t +π) + cos(2π(150e) a. (5) If the output of the Ideal D-to-C converter is equal to the input x(t) i.e. ()2 cos (2m(50)t +7)+cos(2(150)) b. (5) If the sampling rate is fs = 250 samples/sec, determine the discrete-time signal x[n] and give c. (5) Plot the spectrum of the signal in part (b) over the range of frequencies-r ώ +1. Be sure d. (5) If the output of the ideal converter is What general statement can you make about the sampling frequency fs in this case? an expression for x[n] as a sum of cosines. Be sure the frequencies are within the Nyquist Interval. to label your frequencies and complex amplitudes of each component. y(t)-2 cos (2r(50)t ) + 1 determine the value of the sampling frequency fs Remember that the input x() is defined above. e. (5) Using the sampling rate given in part (b), is the output of the ideal D-to-C converter undersampled, oversampled or sampled at the Nyquist rate?

Answer 1