Frequencies on wires

[cjohnson]

I saw another thread about frequencies earlier today and it reminded me of a question I've had for a while. How/why do wires have frequencies? Like when people talk about DSL they talk about how the voice and data are on different frequencies... same thing for cable. Thanks.

 

[Shalmanese]

Each bit is a discrete packet of information. The frequency of a wire is how many discrete bits of information you can send down the wire in any one second.

 

[CTho9305]

If you take a sine wave, it has a frequency. You can add multiple waves together and get some really messy wave. Now, there is this thing called a Fourier Transform which you can do to a messy wave and it will tell you what sinusoidal components make it up - what frequencies are present (and in what amounts). If you wanted to send two messages at once, each 1 bit at a time, you could have two different frequency waves added up. If the wave is present at a given time, then that message is a 1, otherwise it is a 0. (I think that is kinda like how AM radio works - simplified though)

I still don't see how the fourier transform can possibly work even though I've had to learn and use it in two courses so far 😉.

 

[Special K]

I have a related question - Let's say you have a CD of an orchestra (or any music really, I just said an orchestra because I think it would have the greatest number of different sounds) and play it over FM radio at some specific frequency (say 100.4 Mhz). Now the sinusoid of the orchestra playing will contain the sum of the waves of all the individual instruments that are playing, which will be at different frequencies. (and you could use a Fourier transform to see the distribution of frequencies present in the whole sound wave). But then how is the entire sound broadcast on a single frequency (100.4 is the one I made up)? Or is the frequency of the sound itself and the radio frequency it is broadcast on two totally separate things?

 

[Mark R]

FM radio doesn't broadcast on one exact frequency - but a range of them.

At the transmitter, a sine wave generator which has an adjustable frequency is used. The sound waveform is used to control the frequency of the transmitter.

When there is silence, the sound waveform (and therefore electrical waveform) is flat at 'zero' - the transmitter will generate exactly 100.4 MHz in your example. When the sound waveform is 'positive', the freqency generated will be higher (up to a max of, say, 100.5 MHz). When 'negative' the frequency is reduced to a min of approx 100.3 MHz.

The principle works just as well for a simple sine-wave as it does for a complex sound like an orchestra

This link explains it with a picture:
http://www.howstuffworks.com/radio4.htm

 

[blahblah99]

I think what he meant was how can a single wire carry different data stream, ie, imposed on top of each other.

It works because the data stream is operating on a different frequency range.

For example, if you have an RCA cable, you can run an audio signal through it and a proprietary 900mhz signal through it because they are operating on a much different frequency range. Audio is 20Hz-20kHz, while the 900Mhz signal is well, 900Mhz.

On the receiving end of the RCA cable, the equipment "filters" out the unwanted frequencies. On the audio receiver, it has either passive or active filtering at the input stage which removes any frequencies above, lets say, 30khz. Hence, that 900Mhz signal will be attenuated so much that it'll be invisible to the amplifier.

On the 900Mhz receiver side, it has a sharp filter (high Q) to allow only the 900Mhz signal to pass while others are being attenuated.

DSL and regular phone lines work the same way, although I'm not sure at what frequency range the two operate at.

 

[blahblah99]

Originally posted by: SpecialK
I have a related question - Let's say you have a CD of an orchestra (or any music really, I just said an orchestra because I think it would have the greatest number of different sounds) and play it over FM radio at some specific frequency (say 100.4 Mhz). Now the sinusoid of the orchestra playing will contain the sum of the waves of all the individual instruments that are playing, which will be at different frequencies. (and you could use a Fourier transform to see the distribution of frequencies present in the whole sound wave). But then how is the entire sound broadcast on a single frequency (100.4 is the one I made up)? Or is the frequency of the sound itself and the radio frequency it is broadcast on two totally separate things?

That's the basis of FM (frequency modulation). Audio bandwidth is 20Khz, so if you modulate that with a 100Mhz signal, you will need, in the frequency spectrum, a bandwidth of 40Khz due to the sidebands generated by the modulation. Hence, the channel spacing on the FM spectrum is 200khz, or 0.2Mhz, to give each station some "gap" so that their signals will not be overlapped.

I may be wrong with the bandwidth requirements on this one, so correct me if I am. 🙂 It's been a while since I studied this.

 

[m0ti]

Originally posted by: CTho9305
If you take a sine wave, it has a frequency. You can add multiple waves together and get some really messy wave. Now, there is this thing called a Fourier Transform which you can do to a messy wave and it will tell you what sinusoidal components make it up - what frequencies are present (and in what amounts). If you wanted to send two messages at once, each 1 bit at a time, you could have two different frequency waves added up. If the wave is present at a given time, then that message is a 1, otherwise it is a 0. (I think that is kinda like how AM radio works - simplified though)

I still don't see how the fourier transform can possibly work even though I've had to learn and use it in two courses so far 😉.

It's cause they're all orthogonal to each other. And what you're talking about isn't the tranform, per se, rather a Fourier series (at least the first part about adding multiple waves together).

 

[CTho9305]

Originally posted by: m0ti

Originally posted by: CTho9305
If you take a sine wave, it has a frequency. You can add multiple waves together and get some really messy wave. Now, there is this thing called a Fourier Transform which you can do to a messy wave and it will tell you what sinusoidal components make it up - what frequencies are present (and in what amounts). If you wanted to send two messages at once, each 1 bit at a time, you could have two different frequency waves added up. If the wave is present at a given time, then that message is a 1, otherwise it is a 0. (I think that is kinda like how AM radio works - simplified though)

I still don't see how the fourier transform can possibly work even though I've had to learn and use it in two courses so far 😉.

It's cause they're all orthogonal to each other. And what you're talking about isn't the tranform, per se, rather a Fourier series (at least the first part about adding multiple waves together).

right, but to pull them back apart after adding them wouldn't you use a fourier transform?

 

[blahblah99]

The fourier transform only gives you the frequency content of a signal. To get time, frequency, and amplitude data, there's a more complex technique called Wavelet transforms.

 

[kylef]

right, but to pull them back apart after adding them wouldn't you use a fourier transform?

If you have added several signals together in a transport medium (be it wireless or some guided media) for some sort of communication mechanism, then to pull them apart again you would use a de-modulator. There are many types of demodulation, from simple AM sine wave "multiplication" to Direct Sequence Spread Spectrum pseudorandom correlation. You do not need a device that takes any sort of Fourier Transform to "get back" the original signal.

Fourier analysis is handy simply because it is an easier way to look at the same signal in a different manner (the frequency domain). It can also simplify calculations when manipulating signals in certain processes.

As for the original question, wires can carry many frequencies just like the air carries multiple radio stations. For the most part, they don't interfere with each other. Depending upon the linearity of the transmission media, you can modulate several signals onto different carrier frequencies (like AM radio) and insert them onto a transmission line at one end, and then at the other end, separate these carrier frequencies back into baseband signals.

 

[Howard]

On a related note, how can a speaker reproduce multiple sound waves at once? i.e anything other than a straight tone. And how do instruments sound the way they do? Additional waves?

 

[JonB]

The human ear, like any listening device, senses the instantaneous sum and or difference of the sound wave frequencies hitting the eardrum. If you sound a 800 hz tone at the same time as a 1300 hz tone, (and let's assume they are equal volume for now) the ear will hear a 500 hz difference tone, 800 hz, 1300 hz and 2100 hz. The sum and difference will be lower volume, but present and audible, sometimes called "beat frequencies." If you connected a microphone to an oscilliscope and looked at this resulting waveform, you would see only one waveform, but it would have irregularities all over it where the instantaneous sum and differences of the frequences created a lot of different amplitudes and the frequency would be changing constantly, ranging from 800 up to 2100.

Take the sound from an orchestra and look at it on that same oscilliscope; your waveform display will be MUCH more complex, but the human ear and brain can still discrimate between them all.

Sound recordings store that same sum and difference waveform. When you play it back through a speaker, there is only one waveform going to it. It tries its best to move in sync with the ups and downs and frequency changes, and if it does a good job, you will hear all the subtleties of the original. If the waveform is poorly recorded or poorly amplified or the speaker just can't keep up with the fast changes at high frequencies, then you would say it sounds "crappy" or "distorted" but you would still be able to distinguish the sounds.

While the human ear can hear up to 20,000 hz on a good day, us old farts don't hear quite that well, so we miss some of the subtle sum and difference frequencies. We make up for it with beer. 🙂