I am now done with the convolution of my hypothalamus, cortex, cerebrum and hindbrain - if that means losing track of day and night, having an inclination towards obesity and/or bulimia and a lengthening of response times - a condition protracted when you cross the boundary of retardation. The last week of the semester gave me the opportunity to say phrases I never thought I’d say. Consider: “Ooooh! I see a birdie in my room…” or “Who cares! I will just marry a billionaire and settle in Hawaii” or screaming in the middle of the night “it’s a frigging Fourier series, why don’t you get it?” Ah well! All is well that ends well, isn’t it? Oh but wait, did it? Tough question. For all those who still have not recovered from ‘that’ phase and are unable to figure out the answer to this million-dollar question, please refer to the last ten lines.
In spite of all my complaints (force of habit), I can’t deny that Signals and Systems (for which I was expressing overflowing affection in MY way) gave me the real essence of Electrical Engineering. As a friend put it appropriately: “its just a bunch of incessant or disjunct thingies entering into this other box-like- thingy and/or thingies and voilà…you have a weirder thingy!”. It’s funny when I recall a similar description from another friend: “A system responds to applied input signals, and its response is described in terms of one or more output signals. The response of a system to an impulse which differs from zero for an infinitesimal time but whose integral over time is unity; this impulse may be represented mathematically by a Dirac delta function”. Yes I know, I like the first friend more too.
With a unifying view of signals and systems as functions with different domains and ranges, we dealt with a wide range of fundamental subjects, including linear time-invariant systems, filtering, and some more advanced materials such as Laplace and Z-transforms and feedback control, as well as modern topics such as image, video and audio signal processing, and system stabilization.
Focusing on image processing which interests me most, it was exciting to find how the simple formulae we found so hard to memorize can be applied in their entirety for X-ray or CT scanning.
Some types of signals used in image processing include:
1) Linear attenuation coefficient in X-Rays
2) Radioactivity in nuclear medicine
Considering the fact that most medical imaging systems are linear and shift-invariant systems, the impulse response of these systems is:
Figure 2(a) shows the original image A and (b) shows the image synthesized from the Fourier transform phase of (a) with unity magnitude.
An MRI uses similar techniques. Besides providing excellent discrimination between different types of soft tissue, MRI can provide information about physiology, such as blood flow through arteries. MRI relies totally on Digital Signal Processing techniques, and could not be implemented without them.
Many of the high-frequency structures are preserved in the phase-only image. Indeed, the transformation into a phase-only image can be approximately interpreted as a high pass filtering operation (a concept I will elaborate in some of my later posts). Therefore, all those signals which are distorted by noise can be recovered successfully considering the phase only while the magnitude can be adjusted accordingly. This is frequently the case with images taken from unmanned satellites and space exploration vehicles. No one is going to send a repairman to Mars just to tweak the knobs on a camera! DSP can improve the quality of images taken under extremely unfavorable conditions in several ways: brightness and contrast adjustment, edge detection, noise reduction, focus adjustment, motion blur reduction, etc.
Okay: so what if I messed up the final and the midterms and the countless quizzes and assignments? I dare say I learnt something. Indeed, the course was highly engrossing and intriguing but I honestly feel as if, at times, we were subjected to a policy similar to the one used by Adolf Hitler:
“Demoralize the enemy from within by surprise, terror, sabotage, assassination. This is the war of the future.”
I’ll let those who experienced it become nostalgic (unavoidably) and for those who didn’t: let your imagination go wild!
Perhaps I am exaggerating. Perhaps I am merely reaching out to the cries of many. But when the ‘final blow’ is dealt, I can only phrase my reaction in Shakespeare’s words:
"But, for my own part, it was Greek to me" – Julius Caesar (Act I, Scene II).
Note: For all those interested in an elaboration of some of the concepts I have mentioned, read an abstract on the importance of phase in signals, or about the Mystery Signals of the Short Wave, or even about the Euronumbers Mystery.