The correct answer is: A. Non-linear system
A Hilbert transformer is a non-linear system because it takes two inputs, a signal and its time derivative, and produces a single output, the Hilbert transform of the signal. This is in contrast to a linear system, which takes a single input and produces a single output.
A Hilbert transformer is also a time-varying system because its output depends on the time at which the input is applied. This is in contrast to a time-invariant system, whose output is independent of the time at which the input is applied.
A Hilbert transformer is not a low-pass system because it does not pass all frequencies equally. Instead, it passes high frequencies more strongly than low frequencies. This is because the Hilbert transform is a frequency-domain operation, and high frequencies have higher values in the frequency domain than low frequencies.
Here is a brief explanation of each option:
- A non-linear system is a system whose output is not proportional to its input. In other words, the output of a non-linear system depends on the input in a more complex way than just multiplying the input by a constant.
- A time-varying system is a system whose output depends on the time at which the input is applied. In other words, the output of a time-varying system is not the same for all inputs applied at different times.
- A low-pass system is a system that passes low frequencies more strongly than high frequencies. In other words, the output of a low-pass system is attenuated at high frequencies.