(a) A system samples a sinusoid of frequency 480 Hz at a rate of 100 Hz and writes the sampled signal to its output without further modification. Determine the frequency that the sampling system will generate in its output.
Hint: keep in mind that no discrete system can generate an output greater than fs/2 where fs is the sampling frequency. Also, the frequencies produced by sampling a sinusoid are given by \(fout =kfs \pm fin\) is the sampling frequency, fin is the input frequency and k, is any integer, positive or negative. However, the only frequency that will come out of the system will be the one that is between 0 and fs/2. So choose k, positive or negative, such that it yields a positive output frequency less than fs/2. Note that only one value of k will yield a positive frequency in the range 0 to fs/2.
(b) Find the output frequency when the input frequency is 425 Hz. Assume fs is unchanged at 100 Hz.