Sampling: How should I sketch a signal spectrum? As revision, I am going through Signals and Systems, and in Section 7.1the authors are sketching representative spectra for x(t) and xp(t)as follows



However when I search for "How to draw a signal spectrum" I get results (here and here), where signal spectra are shown like this:



For example,how should I go about sketching the the spectrum of signal x(t), where x(t) = 4cos(8000πt)?

Here are my two answers:



Which one is the correct approach? Any suggestions would be appreciated.
Figure 7.4 just concerns itself with an example signal, which happens to have triangular spectrum.

your $x(t)=a\cos(2\pi f t)$ signal is just that: a single cosine tone, and thus has the "shape" of two dirac impulses with integral area $\frac a2$ each.