This original signal is shown below (time domain):
It is a real signal. According to the signal processing theory, the form part of the angle is conjugate to that of the latter part. That is, $\sphericalangle X(e^{j\omega}) =\sphericalangle X^*(e^{-j\omega})$ when $x[n] \in \mathbb{R}$.
However, I implement X = angle(fft(x));
and plot(X)
in MATLAB. The figure is shown below:
The phase is continuous! Could anyone explain the reason? Thanks in advance!