Persistent Visions

Sampling Matters!

1) Take samples
2) Analyse Results
3) …
4) Profit!

Not so simple. Let’s talk about sampling. There are people who spend their careers on sampling issues and I’m not one of them. Here, I am just going to describe a simple and rather amusing thing that can go wrong with Plan to Profit.

Suppose you have a periodic signal, a diurnal cycle of some sort, which I simplify as a sinusoidal curve in black below.

You have, tragically, samples every quarter-cycle, or every 6 hours. A regular way to sample the cycle is at 0h, 6h, 12h, 18h, and then go back to 0h. The samples are marked in red circles. Now you take the samples and plot them out to get a not-very-sinusoidal but fair-enough representation of your signal:

Sometimes the sampling times can be offset. Instead of sampling at 0h, 6h, 12h, 18h, …, you may end up sampling at (0+T)h, (6+T)h, (12+T)h, (18+T)h, where T is some time offset. An example is marked in blue squares. Then you plot out your samples, and you get a saw-tooth pattern like below. This causes problems when calculating rate of change (gradient).

If you don’t even sample often enough, e.g. only sample at half cycle intervals of 0h, 12h, 0h, …, you might not even get anything! To capture a signal you must sample at at least twice its frequency. Think of it as you must see whatever you are measuring go up and down to realise that it is oscillating, so if you measure at twice it’s frequency and hit peak, trough, peak, trough, …, you recognise an oscillation. In this case (green below), I cheated and measured midpoint, midpoint, midpoint…

More realistically, there is sometimes a drift to the sample times. So the plan may be to measure at 0h, 6h, 12h, 18h, …,
but you end up measuring at, say, (0+t)h, (6+2t)h, (12+3t)h, (18+4t)h, where t is some small time drift. If so you can get something like below:

This hardly even resembles what we started out with. At this point, we can try to look for data with higher sampling frequency, or try to compile a profile over a long period of time. Or just give up, filter away the high frequencies and analyse lower frequency signals.

There’s also interpolating between the points but interpolation has its own set of problems.

(All this is just a long-winded way of saying whatever phenomena being studied has to be sampled adequately, which everyone knows already, but I thought the way the wave changed with the sampling was amusing enough to plot out…)

A Tropical Fruitstyle III

“…They were selling huge durians in my hometown. They were as big as this ” — my colleague gestured with his arms — “as long as my arm!”

I was stunned. I have never seen a durian that big, and I told him so.

“I think they were from Thailand. Are Thai durians all so big?” he replied.

“They are round…or long?” I asked.

“Long, not round.”

“Hmmmm…”

When I passed by the supermarket near my place, I took this photo and showed it to him:

“Are these the ‘durians’ you saw?” I asked.

“Yes! So you have such big durians here too.”

“They’re not durians. They’re jackfruits.”

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This is a durian:

The flesh of a durian is usually yellow, sometimes orange, and soft — from mushy-soft to firm-soft. The flesh of a jackfruit is also yellow/orange, but it is hard, shiny and not as complex tasting as that of a durian. In fact, I consider the taste of jackfruit mediocre. I don’t like jackfruits. Dried jackfruit chips are ok though.

I much prefer the cempedak, which many people mistake for the jackfruit. They look pretty much the same on the outside, but the flesh of the cempedak also yellow/orange) is soft and gooey. It tastes like a sweet durian, but is not as filling.

There are probably other variants, but I’ve never tried any of those, except the breadfruit, and only in the keripik version.

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There is something called an “ang moh durian” (红毛榴莲, or caucasian durian) here:

But that is just a soursop. It’s a “durian” with white flesh, so it’s a caucasian durian, get it?

A Tropical Fruitstyle II

[Disclaimer: All images shown here do not belong to me, they were googled from the web and belong to whoever they belong to -- click on the photos to visit the sites.]

My Indian colleague was making fun of my unsuccessful goatee, which looks to become a Fu Manchu thingy if I let it grow any longer. He would grow ten times more facial hair the moment he stopped shaving, he said.

Then your head would look like a rambutan, I quipped.

Blank stares.

What is a rambutan, he asked.

A rambutan is errr…a rambutan. You know, rambutan. The fruit?

Blank stares all around.

Ok, this is a rambutan:

No, it’s not a mutant golf-ball, but a real fruit that people eat. My grandmother used to have a rambutan tree in her garden. Rambutans are pretty annoying fruits to eat, because it’s difficult to open the tough shell to get at the fruit inside. People super-tough fingernails somehow manage to tear the casing open with their iron keratin daggers. I’d probably rip my nail clean of its bed if I tried. So I will grab the top and bottom of the oval fruit and twist one end clockwise and the other counter-clockwise. That would rip the shell open. Unfortunately, if I do it too hard, I end up ripping the inside into half. Also, your fingers start to ache after a while.

Rambutans look really gross on the outside. Unlike the specimen in the picture (which is probably grown in a farm where they marinate the trees in pesticides), pristine rambutans, such as picked from my grandmother’s garden, tend to have blackened, broken, half-rotten hairs on the outside. You have to remind yourself that once you get open the gross exterior, the inside fruit is nice and edible.

Sort of like some people.

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There’s another fruit that looks like a rambutan and tastes pretty much identical to a rambutan. I like to think of it as a shaven rambutan. The rambutan went to the hair-dresser and came out looking like this:

Apparently it’s called a “pulasan”. I prefer buah pulasan to rambutan any day. It’s juicier, I think, and definitely less hairy to deal with.

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While we’re on the subject of squishy white fruits inside red shells, why not show a picture of the lychee?

If the pulasan is a rambutan that went to the hair-dresser, the lychee is one who went bald. It’s also much easier to peel — the skin is like cardboard and easily broken…at which point all the juices of the fruit squirt out and hit your eye. The lychee tastes different from the rambutan and pulasan. The flavour is more intense.

According to my mother, one should only eat a few lychees at a time, because “one handful of lychees is three handfuls of fire”, i.e. too many lychees in one go will make one ill.

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Last, but not least, is the longan:

Poor longan, small and brown. It tastes sweet but is also a bit salty. It’s often dried and used in desserts or soups for cough.

A Tropical Fruitstyle

[Disclaimer: All images shown here do not belong to me, they were googled from the web and belong to whoever they belong to -- click on the photos to visit the sites.]

If you are a visitor to the Tropics, what should you experience, that will be unique to the Tropics?
No, it’s not the Sun and Rain (and more Rain).

It’s the Fruits. The sheer amount of fruits here that you will never find elsewhere.

Yesterday, my colleague brought back some fruits from Jakarta. They look like this:

I didn’t know what the real name of this thing is. I’ve always just known it as “the snake fruit”. After a search on the internet, it turns out that the thing is actually called Salak, and it comes from a palm. It’s unofficial name is indeed “snake fruit”, and the reason for that is obvious.

It’s pretty dry and crunchy. The colour and consistency of the fruit reminds me of hard cheese, but without the pungent aroma. The skins is fun to play with when you’ve finished the fruit.

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On the subject of bizarre looking fruits, one of my favorite fruits is what we call a “limkim”, which is this:

Inside is full of cloyingly sweet white flesh, which tastes like solidified sugar syrup mixed with flour. It is one of those fruits that taste so much like confectionery that you wonder if some baker had baked it and stuffed it into the shell of a fruit:

I’ve heard it labelled as “custard apple”, but it’s not a real custard apple. After some digging, I find that this thing is actually a “sugar apple”. It’s definitely sugary, but not very apple-like. We also call it a “shi jia” (释迦), after 释迦摩尼, and if you wonder why please direct your gaze towards the top of his head:

It’s kind of irreverent, but I’m sure buddha won’t be upset.

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The term apple seems more applicable to this fellow here, which we call “jambu”:

They look a lot more like red pears, but the skin is glassy and they are highly crunchy — they crunch louder than apples. The taste like bland, like slightly sweetened water.

Strangely enough, I’ve never seen a red d’Anjou pear, until my friend posted a picture of it on her blog last month.

The Power of Projection

My parents have bought a giant map of the world and it’s sitting on the living room table. I am glad to say that it is not a mercator map.

People of my age are brought up with the mercator map. It appeared everywhere. We saw it when learning country names in kindergarten. We saw it in our geography lessons in secondary school.

The more common form is one where Antartica has been snipped off, at 60S.

I love the mercator projection. It is easily one of my favorite projections, because angles are preserved in the projection. This means that if you are plotting winds they appear to be of the correct direction. Otherwise the wind angles would become more and more distorted further away from the equator.

The mercator projection distorts areas in higher latitudes. From the picture you would think that Greenland was the size of Africa, as is Europe. Generations of school children grew up with these impressions. Some children thought their country was big and important. Others thought theirs were small and insignificant.

Anyway, I’m glad that the giant map my parents bought appear to be of an area-preserving, or at least semi-area-preserving projection. Something like this:

As much as I like the mercator projection, I hope that the mercator map is removed forever from the realms of children’s education.

Also, click on the graphics to go to a site with a map projection tutorial. Very enlightening site.