Nathalie’s first bicycle ride

Posted on September 12, 2008 by cchang

It may be a father’s dream to catch his baby’s first step, that definitive moment, on a video.  But if you’ve ever tried, you know how hard it is.  The lone success I have ever seen is in the “Truman’s Show” movie.

Yet, the opportunity presented itself again on July 20, 2008, when I realized that Nathalie was close to riding a bike completely on her own.  This time, I caught it on the DV tape.  Check this out.

Filed under: Kids | Tagged: | Leave a comment »

Convolution and Multiplication

Posted on September 9, 2008 by cchang

When I first learned Fourier Transformation in signal processing, I was told that the convolution of two signals in time domain (or spatial domain) was equivalent to the multiplication of those two signals in frequency domain.  That was amazing, but I got no intuition about why it worked.

Then one day, it hit me that I had been doing convolution since I was a kid in elementary school.  Every time we multiply two decimal numbers, we are not really performing the multiplication.  We are actually computing the convolution of their digits.  For example, the reason why we know 22*33 is 726 is because we compute the convolution of the two signals (2,2) and (3,3), which gives us the signal (6, 2, 7).  (Note: I put the least significant digit to the left, so they look more like the signal in the “transformed” domain.)

Still didn’t get it?  Then think about this.  What is the meaning of the decimal number system that we have taken for granted?  Imagine the world 5,000 years ago.  How would a farmer count the number of plants in his land?  For example, if he has 22 rows of plants, and 33 plants in each row, how does he count the total number of plants?  Does he know the total is simply 22*33 if he doesn’t yet know the multiplication of two decimal numbers?

  • 22 and 33 are the results of projection to the tens and the singles digits of the decimal system.
  • 726 is the result of the convolution between (2,2) and (3,3).

Filed under: Technical Notes | Tagged: , | 6 Comments »

Advice for new graduate students in Taiwan

Posted on September 2, 2008 by cchang

Some hints for the transition from a undergraduate student to a graduate student:

First, you must get rid of some old habits that you may have acquired while preparing for the endless exams in your high school and college era.  For examples:

  1. Don’t fight a difficult problem alone in your research process.  Ask people if that helps you solve the problem quicker.  Remember, this is no longer an exam, and you are now allowed to ask for help.
  2. A commonly made mistake when a graduate student writes her/his first technical paper is to dump all her/his knowledge or whatever she or he has done so far to the paper writing.  Remember, the key point of a good paper is to convey a good idea to the readers, not to show off how knowledgeable you are.  Also, don’t give half-hearted effort in your paper writing.  You don’t get partial credit for dumping whatever you know to the paper.
  3. “Write something every day.”  This is the advice I learned from Prof. Fred Brooks at UNC.  In college entrance exams, your achievement was measured by the sum of your scores in various subjects, like Math, English, Physics, Chemistry, and Chinese.  A fallacy in that scheme is that you could improve your ranking by working on one subject alone.  However, in the graduate school (and beyond), you may find that your achievement is measured by a mysterious equation that is more like the product (i.e. multiplication) of your hard work in solving the problem (e.g. research and implementation) and your technical writing and presentation.  You get no credit if you have solved a extremely hard problem and tell no one.

Filed under: Research | Tagged: | Leave a comment »

  • Calendar

    • September 2008
      M T W T F S S
      1234567
      891011121314
      15161718192021
      22232425262728
      2930