# 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)?

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.