One astute reader of a previous post observed that although I seemed to imply that only bitmaps can be digital images, there also exists such a thing as vector graphics which are also considered digital images. At the time, it was not clear in context what was meant in describing an image as digital. While I conflated digital images with bitmaps, which is inaccurate, I was only discussing bitmaps in that post, and the conclusions therein are still valid. ...

• photography
• dsp

The end of the fall semester is always a very special time of year. The hubbub of plans for winter break are omnipresent, festive lights illuminate themselves around campus, and most importantly of all, professors finally get around to assigning all their term projects with scarcely three weeks left with which to complete them. This isn’t news to my fellow upperclassmen, although the sophomores may only just begin to experience this for the first time. ...

• dsp
• programming

In a previous post, I discussed the physical interpretation of digital music (and all digital audio) as both a time-varying signal and a frequency-varying signal. This, of course, makes intuitive sense - as we spend three or four minutes listening to a song, we can hear the guitars and horns coming in and fading out, a singer intone the chorus of a song, etc. At the same time, we appreciate the frequencies changing as well — the singer hitting different notes, the instruments forming different chords. Understanding the time and frequency behavior of auditory information is fairly intuitive - in fact, one could even argue that visualizing the frequency-based content is more informative than visualizing the time-based content. ...

• photography
• dsp

The other day I was having a discussion with my roommate Mike about the physical intuition of digital photographs, and how performing even the most fundamental of operations (e.g. resizing) requires an appreciation of the underlying mathematics. We are both currently in image processing classes, but very different kinds. His course is in Computer Science, so his studies tend to be of the use Java; things happen; make apps variety, with only some slight motivation and understanding of what’s happening under the hood. My course, on the other hand, is in Electrical Engineering, which means it is of the here’s some math, and here’s how you do this math in Matlab variety. There’s advantages to both educational approaches, but debating the merits of theory- centric versus application-centric education styles is beyond the scope of this post. Instead I want to quickly motivate some of the fundamental theorems of Signal Processing and show how they are applied. In this post, I will cover the first, and most intuitive, of signals: audio. ...

• music
• dsp