What tools do you use to create signal processing plots?
Extending a bit on the answer of @Rob. If you are writing a paper in LaTeX (and friends), it is (imho) highly desirable to draw the diagrams also in a LaTeX related way. This comes with a number of advantages:


Direct and easy integration, using either \input or including as PDF using \includegraphics
The same fonts, font sizes, colors, etc. as in the rest of the document (main advantage in my opinion)
One workflow. You can put everything under the same version control (e.g. Git, Mercurial, ...) and do not require any other software: only a LaTeX installation - which is needed anyways.
No need to manually move stuff around using the arrow keys, no automatically changing grids, no vector-based programs which can't export eps, ... (yes, I'm looking at you, Visio!)


Now there are a number of LaTeX related tools for this. Rob mentioned TikZ in his answer. There are also Metapost and PSTricks which also have the capabilities to get the job done. If you want to stick closely to the LaTeX syntax you seem to already know, you might want to chose TikZ.

To do especially plots using TikZ, you might want to have a look at the PGFPlots package, which offers extensive plotting capabilities. All options are well described in the manual, and there is a huge example gallery. For example to get a plot as the first one in your diagram, all you need is

\documentclass{article}
\usepackage{pgfplots}
\begin{document}   
\begin{tikzpicture}
\begin{axis}[
        width = 8cm, height = 4cm,
        xlabel={$\omega$},ylabel={$X(\omega)$},
        xtick = {-1,1},
        xticklabels={-B,B},
        ytick = {0,1},
        axis lines=middle,
        xmin = -4, xmax = 4,
        ymin = 0, ymax = 1.2
    ]
        \addplot[] coordinates {(-1,0)(0,1)(1,0)};
\end{axis}
\end{tikzpicture}
\end{document}