Question

If the signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt, -∞ < t < ∞ when excited by the input signal x(t) then such a filter is called as __________

(a) Analytic transformer

(b) Hilbert transformer

(c) Both Analytic & Hilbert transformer

(d) None of the mentioned

I had been asked this question in an online quiz.

This intriguing question originated from The Representation of Bandpass Signals topic in chapter Sampling and Reconstruction of Signals of Digital Signal Processing

Answer 1

The correct answer is (b) Hilbert transformer

Easy explanation: The signal ẋ(t) can be viewed as the output of the filter with impulse response h(t) = 1/πt,

 -∞ < t < ∞ when excited by the input signal x(t) then such a filter is called as Hilbert transformer.