# Why sinusoidal signals?

1. Feb 22, 2014

### Bipolarity

It appears that sinusoidal signals are very useful in signal processing, communications, and information theory. I am curious to know very why. I understand that information can be transmitted via a sine wave, from the principle that sine waves of different frequencies are orthogonal.

But use sine waves to communicate information? Can't you use other functions? Isn't all digital data in 0s and 1s? Why even use the analog domain then?

These are rather general questions, so I expect no detailed answer in a post. However, I would be interested in a link or a recommendation to a text that explains this quite well, without being too dense in the details. My mathematical background is fairly strong, but I don't want the rigor of the mathematics to blind me from the actual ideas.

BiP

2. Feb 22, 2014

### Baluncore

Fundamentally, “simple harmonic motion” such as a string or a tuned circuit oscillate in a sinusoidal way. That makes transmission and reception of sinusoids natural.

A sinewave can be modulated to widen it's bandwidth in order to carry more information, but it can never be a square wave because the instant step change would be very wide band and so interfere with other signals.

3. Feb 23, 2014

### Devils

If you consider linear algebra and vector spaces, then sine waves form a basis, which as you allude to, orthogonal sine waves at different frequencies can be "added" to form an arbitrary waveform.

http://en.wikipedia.org/wiki/Trigonometric_functions
"Since the sine and cosine functions are linearly independent, together they form a basis of V."

Can you use other functions? Absolutely. As long as they are periodic & can form a basis. Trouble is, apart from sin/cos, there aren't too many other periodic functions.
http://en.wikipedia.org/wiki/List_of_periodic_functions

Another good choice is wavelets
http://en.wikipedia.org/wiki/Wavelet#As_a_representation_of_a_signal
http://en.wikipedia.org/wiki/Compressed_sensing
These are very active areas of math research at the moment, as they have numerous applications. They allow you to reconstruct MRI scans and even music with less information(bits) than was previously thought possible.

Last edited: Feb 23, 2014
4. Feb 23, 2014

### Staff: Mentor

When you pass a sinewave signal through a band-limited linear amplifier, filter, transformer, or transmision channel, the signal's amplitude may change but its shape will always remain a sinewave. All other waveshapes will have their shape changed to some extent, sometimes to the point of becoming unrecognizable.

5. Feb 23, 2014

### jim hardy

Who knows what the future will bring - there's been so much progress in applied math in my lifetime!

But to your question- i believe the choice of sinewave was the result of the sinewave's predominance in natural phenomena rather than the result of intelligent design.
At that time, they were developing radio transmission of voice to replace spark-gap.
Spark gap you might think of as primitive digital communication employing Morse code..

Tuned circuits and modulated carriers allowed voice(analog) which was a fantastic improvement over the digital of the day, Morse. They called it "Radio Telephony".
They used motor driven rotating alternators to produce their RF carriers, which were just a very few tens of kilohertz. Vacuum tubes were still a novelty.

As Baluncore pointed out, tuned circuits are harmonic motion and make sinewaves.

So, i'd say it's not so much a question "Why didn't we go there?" as "How did we get here?" .

When i read Devil's post it makes me think - "That's why we're alotted just threescore and ten. In that time the world changes more than we can absorb."

old jim (aka Analog on some other forums)