With Digital Signal Processing, you can manipulate signals after they have been converted from analog voltages and currents into digital form -- i.e., as numbers.  Normal analog operations of filtering, mixing, and signal detection all have their parallels in the DSP world.  Because the cost of complex digital processing is very low, DSP is often the preferred way to build high-performance communications systems.

• Signals, Samples and Stuff: A DSP Tutorial - Part 1
  QEX, March 1998, pp. 3-16
  What's DSP all about?
• Signals, Samples and Stuff: A DSP Tutorial - Part 2
  QEX, May 1998, pp. 22-37
  Let's look inside an IF-DSP transceiver.
• Signals, Samples and Stuff: A DSP Tutorial - Part 3
  QEX, July 1998, pp. 13-27
  Advances DSP techniques.
• Signals, Samples and Stuff: A DSP Tutorial - Part 4
  QEX, September 1998, pp. 19-29
  Conclusion.
• Digital Signal Processing for the Experimenter
  QST November 1984, pp22-27
  Flash - A/D-igital data stream replaces an analog signal. DAC puts it back again!
• An Introduction to Digital Signal Processing
  QST July 1991, pp35-37
  DSP makes headlines even in an age where digital seems to be applied to just about everything electronic - and now it's part of Amateur Radio.
• Digital Signal Processing and GNU Radio Companion, QEX, July/August 2014, pp. 41-46
  
• Digital Signal Processing (DSP) Projects: Examples of GNU Radio and GRC Functionality, QEX, September/October 2014, pp. 25-30.
  

•  "The Scientist & Engineer's Guide to Digital Signal Processing", by Steven W. Smith. Download individual chapters or the entire book absolutely free!
• SM 5 BSZ - DSP radio for LINUX on Intel platformsLeif Åsbrink, SM5BSZ describes a Linux dsp radio in weak signal CW mode