Having stated my abhorrence for the convenient short-cut, I cannot to this day fathom why the brain-warping tedium of time-domain Fourier Transforms continues to be an essential part of the EE curriculum in most universities, when all along, frequency-domain Laplace Transforms can be used to arrive at the same answers in a fraction of the time.

To this day, the mere mention of Fourier Transforms induces a migraine, and I would expunge the very name from all electronics engineering textbooks, if it were within my power to do so.

 

Well, the FFT is still alive and kicking. I think it's a necessary evil.

 

Having stated my abhorrence for the convenient short-cut, I cannot to this day fathom why the brain-warping tedium of time-domain Fourier Transforms continues to be an essential part of the EE curriculum in most universities, when all along, frequency-domain Laplace Transforms can be used to arrive at the same answers in a fraction of the time.

I don't understand your comment. We studied the Fourier Transform, which transformed a time-domain signal to the complex frequency, or 's' domain, and the inverse Fourier Transform, which changes it back. I don't know of another kind.

 

I was just poking fun at the extreme difficulty I remember having in understanding Fourier waveform analysis, Brownout.

Looking through the mists of time to my college years back when dinasaurs roamed the Earth, I still remember the class session during which our lecturer introduced the far less daunting Laplace Transform, and informed the class that in most instances Laplace methods could be utilized in place of Fourier analysis, with far less strenuous of a mathematical workout.

 

I almost forgot about Laplace. If memory serves, Laplace is a special case, while Fourier is completely general. Maybe it's time I dust off my old "Signals and Systems" textbook. My professor would be so disappointed in how much I've forgotten. Particularly since he is the book's author.

 

In my line of work, working with FFT is as common place as working with derivatives and integrals. It is not a necessary evil. It is essential.

 

If you hadn't mentioned your frequent use of the Fourier concept in your profession, Mr. Chips, I would have held on to my sour-grapes misconception that it was one of those esoteric mathematical concepts that all EE students endure as a rite of passage, but which has limited application in the real world.

Oh well, so much for my feeble attempt to denigrate that which I failed to understand during my years as a "Gentleman C" student.

 

Fourier transforms appear in a lot more everyday places than you may realize. All radio, TV, computer and internet communications rely on knowledge of FFT. Optical, audio, acoustics and medical instruments all use FFT in some form or another. Even the cochlea in your ear is a Fourier transformer.

 

The FFT is just another slick shortcut. It's an algorithm to compute the discreet version of the Fourier Transform for arbitrary signals that is suitable for digital processors. You don't need to know how to actually compute the Fourier Transform in order to use FFT, but it helps to know what the actual product of the transform is to understand what you have.

Oh well, so much for my feeble attempt to denigrate that which I failed to understand during my years as a "Gentleman C" student.

Oddly, perhaps, the rare occasion I've had to analyze a causal, dynamic circuit (outside of the acedemic setting), I've used the long method of writing the differential equations and using m-substitution method. Although I can get correct solutions using FT, I don't belive it gives me any insight in the interplay between curcuit elements. I can't "see" how the node voltage and mesh currents work.

 

#12 Here's a slide rule for you ... if you need to brush up.

http://www.antiquark.com/sliderule/sim/virtual-slide-rule.html

Wow! That's something to treasure

Ramesh

 

I was just poking fun at the extreme difficulty I remember having in understanding Fourier waveform analysis, Brownout.

Looking through the mists of time to my college years back when dinasaurs roamed the Earth, I still remember the class session during which our lecturer introduced the far less daunting Laplace Transform, and informed the class that in most instances Laplace methods could be utilized in place of Fourier analysis, with far less strenuous of a mathematical workout.

I almost forgot about Laplace. If memory serves, Laplace is a special case, while Fourier is completely general. Maybe it's time I dust off my old "Signals and Systems" textbook. My professor would be so disappointed in how much I've forgotten. Particularly since he is the book's author.

You guys have it backwards - the Fourier Transform is a special case of the more general Laplace Transform. The Fourier Transform basically deals with periodic signals while the Laplace Transform can deal with transient signals. Neither is "completely" general because both are limited to linear systems.

 

You guys have it backwards - the Fourier Transform is a special case of the more general Laplace Transform. The Fourier Transform basically deals with periodic signals while the Laplace Transform can deal with transient signals.

You're thinking of the Fourier Series. The Fourier Transform works for non-periodic signals.

http://en.wikipedia.org/wiki/Fourier_series

 

Yes, I stand corrected on that point. The Fourier Transform is the Fourier Series in the limit that the period extends to ±∞.

The Fourier Transform transforms a function into a space of frequency components while the Laplace transform transforms it into a space of moments.

But I stand by the statement that the Fourier Transform is a special case of the Laplace Transform. Specifically, when s=jω (instead of σ+jω).

 

Ah, I remember now. The Laplace transform is the general case. I had to travel back in time 20 years to snach that memory from its hiding place. I remember solving systems using Laplace until I was numb. It became muscle memory at some point.

 

You guys have it backwards - the Fourier Transform is a special case of the more general Laplace Transform. The Fourier Transform basically deals with periodic signals while the Laplace Transform can deal with transient signals. Neither is "completely" general because both are limited to linear systems.

This is the crucial distiction that had eluded me till you mentioned it, WBahn. I guess my vague recollection of Laplace Transforms having the flexibility to be utilized in place of Fourier analysis in all instances - i.e for the expression of both periodic and transient wave-forms as you have pointed out, was not too far off the mark.

Those Asiana pilots ought to be locked up in an isolation chamber as punishment for the crash at KSFO, and taught Fourier analysis till they either lose their minds, or repent their ways and pledge to learn how to hand-fly a Cessna 172, as a condition for being re-hired by the airline.

 

It's not the pilots, it's the system. In the U.S., because we have a vibrant civil aviation industry, the major airlines won't touch a pilot unless they have serious flight experience. Those that don't come from military aviation have to pay their dues in the civil world. Now, I'm recalling numbers from many years ago, so I don't know how much things have changed. But the rule of thumb I recall hearing alot was that the majors wouldn't consider you unless you had at least 2000hr of regional time. The regional airlines, in turn, wouldn't touch you unless you had at least 2000hr of charter time. The charter companies wouldn't touch you unless you had at least 2000hr of commercial time. To get the commercial time, you generally had to flight instruct and that was mostly for people gettng their private pilot's licence. So the whole system rests on having enough people that are wanting to get their private tickets and have the resources to pay for it. This allows the employers to require significant experience in the cockpit in order to even be considered -- experience that they don't have to pay for. This also results in the pay scale for flight instructors being extremely poor and it is a rare flight instructor that can live of their instructor's income.

But in countries that do not have vibrant and extensive aviation communities at each of these levels, the companies that hire pilots have to provide the instruction at their expense. Many airline pilots in these countries are hired by a major airline with absolutely zero flight experience. Not surprisingly, those companies are going to do the minimal amount possible to get those pilots into revenue producing cockpits, generally flying freight first and passengers second. But almost all of their training is in simulators and most of those airlines cannot afford anything resembling the simulators that U.S. and other first-world airlines can.

 

Until I read the above explantion, W. Bahn, I truly had no idea of how many thousands of hours of hands-on, real life yoke, rudder, VFR and IFR experience it actually takes before a new pilot, fresh out of flight school, can finally be entrusted with the lives of passengers aboard a North American flagged carrier.

I have a new and profound respect for the guys and gals that make the cut and earn their wings to occupy the flight deck with major carriers stateside, while on the other side of the coin, it is with even greater trepidation that I will board airliners flagged in nations where the pre-requisites for aviators are so much less exacting.

 

Less and less of that time is actually hand-on, in-the-air time and more and more of it is in the simulator. But this is not all bad. Modern simulators provide extremely realistic training experiences and you can actually give a pilot much more relevant experience per hour in a simulator because you control the environement. You make the "ho hum" portions of the flight much shorter, do a LOT more takeoffs and landings, a LOT more instrument time, a LOT more poor weather time, and LOT, LOT more time dealing with in-flight emergencies. What it all comes down to is the quality of the training syllabus. If I had to choose between flying with a pilot that had 10,000 hours and all of it hauling people or a pilot that had 8000 hours but with 7000 of it in a good simulator with a good training syllabus, I would opt for the latter (assuming all else was equal). I'm just not convinced that very many non-first-world airlines can claim they meet the "good simulator with a good training syllabus" criteria.

 

You're thinking of the Fourier Series. The Fourier Transform works for non-periodic signals.

http://en.wikipedia.org/wiki/Fourier_series

Ok, I am still trying to understand this 'off topic' category. I think I have it now, we start with, for example, " Korean Pilots' Inability to Hand-Fly" and try to veer 'off topic' !

 

Ok, I am still trying to understand this 'off topic' category. I think I have it now, we start with, for example, " Korean Pilots' Inability to Hand-Fly" and try to veer 'off topic' !

Yep, you're finally getting it! Some people are just slower to catch on than others, I guess.