Understanding the Relationship Between Time and Frequency in Modulation?

[Tulio Cesar]

1) I understood how variations in the amplitude of modulating signals are represented in the carrier wave, but I didn't get how frequency variations of the modulating signal are represented, as both AM and FM modulations seem do not care about it. Ex: How to distinguish a high vocal range (high frequency) from a low vocal range (low frequency).

2) I didn't get the concept of bandwidth. Is the modulation bandwidth the same of computing bandwidth? And how the frequency of a carrier wave interfere the amount of information you can send for period of time? Why the higher frequency of a FM signal helps on increasing the quality of it in comparison with AM.

 

[tech99]

1) I understood how variations in the amplitude of modulating signals are represented in the carrier wave, but I didn't get how frequency variations of the modulating signal are represented, as both AM and FM modulations seem do not care about it. Ex: How to distinguish a high vocal range (high frequency) from a low vocal range (low frequency).

2) I didn't get the concept of bandwidth. Is the modulation bandwidth the same of computing bandwidth? And how the frequency of a carrier wave interfere the amount of information you can send for period of time? Why the higher frequency of a FM signal helps on increasing the quality of it in comparison with AM.

1) If you look at the output of a microphone on an oscilloscope, it is an electrical copy of the sound waves. The jagged, complex waveform we see contains many frequencies. When we amplitude modulate a carrier with it, we cause its amplitude to "slowly" increase and decrease in accordance with the instantaneous microphone output. So when we impress the jagged waveform on the carrier, we have placed all the sound frequencies on to it. Whereas the carrier might be 1 MHz, the modulating frequencies might be only hundreds of Hertz.
At the receiver, we can obtain the original electrical waveform as from the microphone. If you look at a carrier modulated with a high pitched sound, the envelope has many peaks across the CRO screen, but if we use a low pitched sound, the envelope has only a few peaks across the screen.
2) Bandwidth. We are talking here about using analogue signals; the term is not accurate in its popular usage for digital signals ("broadband" etc). For transmitting a 1 kHz analogue tone using AM, we require 2 kHz of radio spectrum. The carrier frequency does not make any difference provided it is itself higher than 2 kHz, so is not usually an issue. For FM, because the carrier frequency is swept up and down in accordance with the instantaneous voltage from the microphone, much more radio spectrum is needed. For this reason, to find sufficient spectrum for broadcasting in FM, the service was forced to start up using much higher carrier frequencies than previously, an expensive business. The higher quality from FM comes from the use of very high carrier frequencies, so there is spectrum available for the large bandwidth required by the transmission of high audio frequencies, and from its noise suppressing characteristic. Roughly speaking, FM will ignore AM interference such as from car ignition. So far as I know, FM is the only way in which hi fidelity broadcasting takes place, and is capable of near perfection (BBC Radio 3 in the UK for instance).

 

[meBigGuy]

I wonder how you got the idea that AM and FM "don't care about it".

The bandwidth is the frequency range required to enclose the carrier and all sidebands due to the modulation.

The frequency variations of an AM modulating signal cause the AM sidebands to move in frequency. In AM the bandwidth is a function of the modulating frequency. Essentially 2 times the modulating frequency (upper sideband and lower sideband)

FM gets more complex and can have infinite bandwith (read about bessel functions). Narrowband FM look much like AM, but wideband FM with high index of modulation gets very complex. (
From wikipedia https://en.wikipedia.org/wiki/Frequency_modulation :
A rule of thumb, Carson's rule states that nearly all (~98 percent) of the power of a frequency-modulated signal lies within a bandwidth

of:

 

[sophiecentaur]

Let's get the bandwidth that's used to describe digital data rate out of the way. The 'bandwidth' that you buy with your broadband service just tells you the number of data bits per second that you can get. How those bits get to you is an entirely different matter and it will depend upon how the data is coded and put onto some form of carrier. It's quite possible to transmit a 10Mb/s data stream over a 1MHz wide analogue channel, with the right coding and modulation system. (But don't go there till you've sorted out the basics first.)
Bandwidth, in the analogue sense, refers to the range of actual frequencies that encompass the energy of the signal that's being transmitted. For practical reasons, the stated 'bandwidth' is never exact and can be anything that the Engineers choose. Signals are always Filtered before being recorded or transmitted but you cannot manufacture filters with a completely 'rectangular' response; they will have 'rounded' ends. The width of that filter is often defined as the frequency range between the extreme frequencies that are transmitted at half power (where the rounded ends have dropped to half value).

AM is the only modulation system that can be explained and described with minimal Maths but it is as good example as any.
Take the spectrum of your audio signal and analysis it in terms of its frequency spectrum. Every frequency component of this 'base band' spectrum will appear as a pair of sidebands, (mirror images) on either side of the carrier this spectrum will change as the input audio changes and the various components will come and go with the programme sounds. The total occupied RF bandwidth for AM will be exactly twice the bandwidth of the base band signal and the Spectrum of each of the sidebands will be identical to the spectrum of the baseband signal if the modulator is 'ideal'.
Any real modulation / transmission system will distort the signal that it's carrying and it's just a matter of deciding how much distortion that you can accept. The theoretical spectrum of an FM signal is, as MBG (above) states, infinite but you can get a perfectly usable signal for speech communications through a bandwidth that's been limited to the same as you need for AM. That's referred to as Narrow Band FM and only one pair of sidebands is transmitted. It is more popular than AM, largely because the transmitter can be much more efficient and cheaper but it doesn't actually perform significantly differently. Using more Frequency Deviation (in wideband FM, the carrier frequency is swept over a big range by the audio signal) gives a massive signal to noise advantage (FM improvement) but uses progressively more and more RF bandwidth. A basic explanation for the improved performance of wideband FM is that the FM demodulator produces an output voltage that's proportional to the instantaneous frequency of the carrier. Double the frequency deviation and you get twice the voltage variation out - but the demodulated channel noise remains at the same level, so signal to noise ratio improves.

 

[Jeff Rosenbury]

This is a very difficult concept to grasp. It helps to understand the Fourier transform. Even then you will need to calculate a zillion of them to get a feel for them. A college course might be in order. Still, I'll try to get you started:

There is a relationship between time and frequency. Time is measured in seconds and frequency (in radians) is measured in one over the seconds (1/s or s^-1). You can convert between the two using some calculus like the Fourier transform. These are called the time domain (for s) and the frequency domain (for 1/s).

When you convert a function from one to the other, the waveform changes shape. A sin wave will turn into a spike (ray). A square wave turns into a sync pulse, etc. Here's some examples.

Once you get a feel for those, a more advanced course will demonstrate how varying the shape of the original waveform varies the transform. It will show (using math I long ago forgot) that the faster you vary a carrier wave, the broader the original spike becomes in the frequency domain. It turns out there's an absolute rule about how much information you can stick in a carrier. Information takes bandwidth. So if you want to catch those 20kHz high notes, you need 20kHz of bandwidth.

However that 20kHz can be shifted to some other frequency where there's more frequency to be had. So you can modulate a 1,000,000 Hz wave and it will hardly notice that 20,000 Hz.