Thursday, December 7, 2006

Filtering Out Noise In Life


Noise can mean much more than 'unwanted' audio signals. Noise can be defined as information that is not useful for your purpose at a certain point in time. It can be audio information, visual information or even olfactory [smell] or gustatory [taste] information. In this sense a frequent encounter with Noise is a part of daily Life. Here are some instances of Noise and how it is filtered:
1. When looking for a location or directions on a map, you have to choose the map with the appropriate scale. If you are traveling from Florida to New Jersey on a non-stop journey, a regional map showing the main highways is the one that is most useful. Detailed maps of each State are not necessary. The small county roads, the streets in each town are all Noise.
2. When getting familiar with a city, it pays to visualize the basic layout of it' s major streets first, and to ignore the rest temporarily. For example, anyone who wants to get to know Manhattan in New York City would first note that the Avenues in Manhattan are laid out from East to West, with 5th Avenue being the dividing point for prefixing an address with East or West. And that the Streets are laid out in a South to North direction. Then he/she would later be able to learn the details such as that after 3rd Avenue there is no 4th Avenue, but before 5th Avenue there is Park Avenue, Lexington and Madison too. And mid-town begins at14th street and ends at 59th before Central Park which goes on till 110th Stree. So this is an example of ignoring all the Noise first to concentrate on the big features. The subway map of New York City looking like chaotic spaghetti strands is also a good place to learn how to focus only on the main features first.
3. In financial markets, Noise exists at all scales but it means different things to different people. The Day Trader is concerned with minute by minute intra-day movements of prices. But to the short-term trader, this is Noise. All he needs is the Daily Close, High, Low and Open. For the long-term investors who are more concerned with fundamentals, even the Daily movements are too noisy. They will instead look at weekly, or even monthly price movements. The price of Oil may go up one day and down the next, but this is just Noise to long-term investors. More important are the fundamentals regarding the trend of the supply and demand for oil.
4. In Music, especially jazz, a score sheet may have many transitional chords or chords with complicated extensions at every bar. But to the jazz musician, more important is the main structure of the tune, and it's basic chord progression. For example, if he sees a progression in the key of C Major which goes: Fmaj7, Fm6, C69, A7b5b9, D7b9, G13, CMaj9. In his mind he can easily abstract it to F, Fm ,C, A7, D7, G7, C. and improvise within this main structure with embellishments over the transtional and extended chords as needed.
5. Digital image compression technology is able to compress big images into smaller files, by cutting out the noise. In this case, Noise means 'no change'. Thus a picture with a big expanse of sky will show pixels of blue over a wide area. The change from one pixel to the next is almost zero, and many pixels can be 'discarded', to plot only those where color change goes beyond a certain threshold. This can be visualized by thinking of a sparse matrix, with the empty squares deleted to be a smaller but filled matrix.
6. Why is a mother with a very young baby able to sleep and yet wake up at the slightest noise from her baby? It is because the mother's ear has learned to shut out all noise such as from a droning air-conditioner, noises from cars on the street, or even a TV that is still on. But when the baby cries, her noise filter lets it through. In the same way, in Penguin colonies, a mother Penguin is able to shut out the noise from the thousands of other Penguins and only listen to the 'voice' of her baby, when looking for it.
7. The wine taster also has to deal with noise. When tasting a wine, his tongue and nose is assaulted with a melange of taste and smell sensations. But he has to learn to isolate each sensation if he is to describe them. Although the wholeness of the wine depends on the combination of all the taste and smell information, to describe the wine requires him to focus one at a time on each 'quality' of the wine. While he is concentrating on one 'quality' whether acidity, bouquet or body of the wine, he has to temporarily shut out the other sensations.
The ability to filter out Noise is an extremely important component of human intelligence. Otherwise there would be information overload and we would not be able to function. Life is basically a process of sensing information and responding to it. But it's not only the ability to focus on the big things and main features that is important. More important is the ability to analyze the situation at different scales and to zoom in and out to the required scale of detail, refinement, texture or grain as the situation requires. This brings us to the subject of Wavelets, the successor to Fourier transforms in digital signal processing. While Fourier transforms only allow us to analyse signals in the Frequency dimension, Wavelets, allow us to analyze in both the Frequency and Time dimension, by having a Mother Wavelet which can have an infinite number of baby wavelets appropriate for different scales of analysis. More on Wavelets next time......

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