Final answer:
The impulse response h[n] = [n] - [n - 1] does correspond to a linear phase discrete-time system, as it represents a first-order high-pass filter with symmetrical FIR filter coefficients.
Step-by-step explanation:
The student is asking if the impulse response function h[n] = [n] - [n - 1] indicates a linear phase system. In digital signal processing, an LTI (Linear Time-Invariant) system with a linear phase has the property that all frequency components of an input signal are shifted in time by the same constant amount, which corresponds to a straight line when phase is plotted against frequency.
To determine whether a system's impulse response corresponds to a linear phase system, one approach is to look at its frequency response, particularly the phase response. For the given impulse response, we can compute the frequency response through the Fourier transform. However, without performing the transformation, we can also analyze this system's impulse response based on its properties.
In this case, the impulse response represents a difference equation which corresponds to a first-order high-pass filter. This kind of system indeed has a linear phase characteristic because it is a simple FIR (Finite Impulse Response) filter where the coefficients are symmetrical. Therefore, we can confirm that h[n] corresponds to a linear phase discrete-time system.