Anand CV Mallaya

Archive for February, 2010|Monthly archive page

The binary square wave transform

In math on February 2, 2010 at 9:49 am

You may have heard about Fourier Transform. It is a mathematical tool. It converts any wave form as a sum of sine waves with different amplitudes and frequencies. The reverse is also applicable. Any waveform can be made from sum of sine waves of different amplitude and frequencies. I was so much impressed by the idea that all the signals in the world, irrespective of random nature or periodic can be represented as the sum of periodic sine waves.

This love to the Fourier’s theorem guided me to think about an analogous principle related to the binary numbers. Binary numbers can be thought of as a stream of square waves(analogous to sine waves). So a stream of bits like a file, can be thought as an aperiodic signal. So if there exists a theorem that defines the relation between the binary bit sequence and square wave just like analog signals and sine waves, it will be interesting.

updates 5-october-2010

To get a small idea on what I am trying to do:

go to http://falstad.com/circuit/

wait for the java applet to load, and copy the following and click file->import and paste it, click import and watch the applet. Try clcking on different buttons and watch the out put changes.

$ 1 5.0E-6 10.20027730826997 50 5.0 50
R 192 128 144 128 0 2 25.0 5.0 0.0 0.0 0.5
R 192 176 144 176 0 2 50.0 5.0 0.0 0.0 0.5
R 192 224 144 224 0 2 40.0 100.0 0.0 0.0 0.5
R 192 272 144 272 0 2 200.0 5.0 0.0 0.0 0.5
R 192 320 144 320 0 2 400.0 5.0 0.0 0.0 0.5
152 304 224 416 224 0 5 5.0
w 304 128 304 192 0
w 256 176 256 208 0
w 256 208 304 208 0
w 256 272 256 240 0
w 256 240 304 240 0
w 304 256 272 256 0
w 272 256 272 320 0
M 416 224 512 224 0 2.5
s 192 128 304 128 0 0 false
s 192 176 256 176 0 1 false
s 192 224 304 224 0 0 false
s 192 272 256 272 0 0 false
s 192 320 272 320 0 1 false
o 13 64 0 34 5.0 9.765625E-5 0 -1

Recently I’ve collided with this Walsh functions , which is much like what I am intended to do.
Comment here your thoughts on it.
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