An analog electronic signal is composed of three sine waves: 1 kHz @ 1 volt amplitude, 3 kHz @ 2 volts amplitude, and 4 kHz @ 5 volts amplitude (all voltage readings are peak-to-peak). The signal is digitized with 12 bits, spread over the range of -5 volts to +5 volts. For each sampling rate below, describe the frequency components that exist in the digital signal.
Be sure to specify three things for each component: its digital frequency (a number between 0 and 0.5), its amplitude (in digital numbers, peak-to-peak), and its phase relative to the original analog signal (either 0 degrees or 180 degrees).
a. Sampling rate = 100 kHz.
b. Sampling rate = 10 kHz.
c. Sampling rate = 7.5 kHz.
d. Sampling rate = 5.5 kHz.
e. Sampling rate = 5 kHz.
f. Sampling rate = 1.7 kHz.