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This is a soft question. The frequency domain has made revolution in the field of Mathematics, Digital Signal and Image Processing etc. Some of concepts which are very difficult to analyse in spatial or time domain can be very easily understood in the frequency domain using theorems like Fourier transform & series, wavelets, Laplace transform, etc.

Well, I am doing under graduation in 4 years Electronics and Telecommunication Engineering. We have semester pattern system (2 semesters in 1 year). In the 3rd semester, we have subject named "Signals and Systems" under which the above topic is covered.

But my experience is that when it is being taught in the academic curriculum or course, it is not given as much importance as it has to be. Most of the teachers or professors don't know how teach this topic. They teach with the help of ready-made PowerPoint presentations (e.g. for Laplace transform, single PPT which is mostly downloaded from internet) and sometimes they take chalk in their hand. So the students like us get hardly any knowledge about the frequency domain in academic course compared to discussions in the forum like the very useful http://www.DSP.stackexchange.com and http://www.math.stackexchange.com.

So can anybody give explanation about how to effectively teach topic of frequency domain? You can also explain with the help of any subtopic like Fourier domain , Laplace or wavelets etc. So that all of us would study this difficult topic with interest.

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  • $\begingroup$ Many "scholars, eminent professors and researchers" have written whole books full of explanations designed to help students learn about the frequency domain. Many of these books even have a separate Instructor's Guide that is not available to students or to the public but only to faculty/instructors who have adopted the book. Some guides include Powerpoint slides that the instructor can use in the classroom, most have fully written out answers to all the questions at the end of the chapter which answers can copied by lazy instructors into the "homework solutions" handed to students. $\endgroup$
    – Dilip Sarwate
    Commented May 25, 2015 at 15:04
  • $\begingroup$ It seems you're not getting your money's worth, at least in that course. A solution is to learn on your own. Search on this website for book suggestions; many are free, and others available at most libraries (like R. Lyons'). Since you're electrical, I'll suggest an experiment which I found enlightening. I assume you have access to a spectrum analyzer. Set up a 555 timer to oscillate at 20 kHz. Look at its output in a scope and in the SA, and determine how the two are related by the Fourier series. Then bandpass filter one of the harmonics and confirm it's a sine with the expected frequency. $\endgroup$
    – MBaz
    Commented May 25, 2015 at 18:39

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In my personal opinion, it's best to study how the master teachers of the field have presented this information, and to the extent possible, copy their approaches and their style.

There are two teachers in the field who have more or less taught a generation of DSP engineers their craft, either by direct teaching, or by teaching teachers. They are Alan V. Oppenheim and Richard G. Lyons. In Oppenheim's case, the Signals and Systems courses that he taught are still available on MIT's web site for free viewing, and his Discrete-Time Signal Processing is still the bible for many engineers on the topic. Lyons still teaches and writes from Besser Associates, and his "Understanding Digital Signal Processing" book is simple and lucid.

You can't go too far wrong by copying the masters.

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Play sine waves, then composite sine waves, then white noise and eventually music visualizing the output via a real-time spectrum analyzer, or software EQ plugin with input monitoring.

For complete newbies, playing something (a guitar tone or a single sine-wave) and getting visual/intuitive feedback on the screen about what's going on is a powerful way to set the mental-framework for more complicated topics like filters, transforms, wavelets, etc. Plus there's plenty of material online/youtube/etc and everyone likes music. Best of luck!

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Even during my college days, I did not have lecturers who could teach this subject very well, however that did not stop me from learning and what I found was -->Check out http://ocw.mit.edu/resources/res-6-008-digital-signal-processing-spring-2011/, lectures and course materials by Prof. Alan V. Oppenheim. And also http://www.dspguide.com/pdfbook.htm by Steven W. Smith. These resources are great for self learning. For gaining further grasp of concepts clearly, I'd suggest you start off by implementing some DSP functions in C++ like Fourier transforms.

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