Digital Signal Processing (DSP) is just one more step towards the world of discrete domains. We need to understand what discrete domain is and how it differs from continuous domain in order to understand the basics of digital signal processing. In the realm of mathematics, we have two types of objects: discrete and continuous. Examples of discrete objects are integers. Examples of continuous objects are real numbers. In other words, state of a continuous object varies smoothly in stark contrast to a discrete object which enumerates from one state to another. Keeping our focus on discrete domains, if you have a collection of integers ranging from 1-3, the first enumeration takes you to 1, the second enumeration takes you to 2 and the third enumeration takes you to 3. You are basically jumping from one discrete state to another. You are not capturing the states between 1 & 2 and 2 & 3. For example your digital clock displays 7:45 till it is time to jump to 7:46.
Once you understand discrete, you are able to tackle the digital world. In old days, our signal processing was done using Analog Signal Processing which was a continuous domain where the object transitioned from one state to another continuously (smoothly). In order to take advantage of modern digital algorithms, a signal must be converted from analog to digital. The process of converting analog signal to digital signal is called sampling which consists of two phases discretization and quantization. Discretization partitions an analog signal into multiple classes and quantization repalces the signal with the appropriate class. Once you have converted an analog signal to a digital signal, you can perform all sorts of compuational techniques on it which can improve functionality of your signal dependent device.
Thank you for your responses. They were informative. I don't have one of these but I do have a Tecsun PL-380 which is also a DSP. AM, FM (stereo on the headphones) and short wave. I use Koss KTXPRO1 Titanium Headphones and they really sound nice together.