Modulation is the conversion of a digital signal represented by binary bits (0 or 1) into an analog signal something like a sine wave. The modulated signal consists pure sine wave "carrier" signal which is modified to convey information. A pure carrier sine wave, unchanging in frequency and voltage, provides no flow of information at all (except that a carrier is present). To make it convey information we modify (or modulate) this carrier. There are 3 basic types of modulation: frequency, amplitude, and phase. They will be explained next.
The simplest modulation method is frequency modulation. Frequency is measured in cycles per second (of a sine wave). It's the count of the number of times the sine wave shape repeats itself in a second. This is the same as the number of times it reaches it peak value in a second. The word "Hertz" (abbreviated Hz) is used to mean "cycles per second".
A simple example of frequency modulation is where one frequency means a 0 and another means a 1. For example, for some obsolete 300 baud modems 1070 Hz meant a binary 0 while 1270 Hz meant a binary 1. This was called "frequency shift keying". Instead of just two possible frequencies, more could be used to allow more information to be transmitted. If we had 4 different frequencies (call them A, B, C, and D) then each frequency could stand for a pair of bits. For example, to send 00 one would use frequency A. To send 01, use frequency B; for 10 use C; for 11 use D. In like manner, by using 8 different frequencies we could send 3 bits with each shift in frequency. Each time we double the number of possible frequencies we increase the number of bits it can represent by 1.
Once one understands frequency modulation example above including the possibilities of representing a few bits by a single shift in frequency, it's easier to understand both amplitude modulation and phase modulation. For amplitude modulation, one just changes the height (voltage) of the sine wave analogous to changing the frequency of the sine wave. For a simple case there could only be 2 allowed amplitude levels, one representing a 0-bit and another representing a 1-bit. As explained for the case of frequency modulation, having more possible amplitudes will result in more information being transmitted.
To change the phase of a sine wave at a certain instant of time, we stop sending this old sine wave and immediately begin sending a new sine wave of the same frequency and amplitude. If we started sending the new sine wave at the same voltage level (and slope) as existed when we stopped sending the old sine wave, there would be no change in phase (and no detectable change at all). But suppose that we started up the new sine wave at a different point on the sine wave curve. Then there would likely be a sudden voltage jump at the point in time where the old sine wave stopped and the new sine wave began. This is a phase shift and it's measured in degrees (deg.) A 0 deg. (or a 360 deg.) phase shift means no change at all while a 180 deg. phase shift just reverses the voltage (and slope) of the sine wave. Put another way, a 180 deg. phase shift just skips over a half-period (180 deg.) at the point of transition. Of course we could just skip over say 90 deg. or 135 deg. etc. As in the example for frequency modulation, the more possible phase shifts, the more bits a single shift in phase can represent.
Instead of just selecting either frequency, amplitude, or phase modulation, we may chose to combine modulation methods. Suppose that we have 256 possible frequencies and thus can send a byte (8 bits) for each shift in frequency (since 2 to the 8 power is 256). Suppose also that we have another 256 different amplitudes so that each shift in amplitude represents a byte. Also suppose there are 256 possible phase shifts. Then a certain points in time we may make a shift in all 3 things: frequency, amplitude and phase. This would send out 3 bytes for each such transition.
No modulation method in use today actually does this. It's not practical due to the relatively long time it would take to detect all 3 types of changes. But what is quite common is the simultaneous change in both phase and amplitude. This is called phase-amplitude modulation (sometimes also called quadrature amplitude modulation = QAM). This method is used for the common modem speeds of 14.4k, 28.8k, and 33.6k. The only significant case where this modulation method is not used today is for 56k modems. But even 56k modems exclusively use QAM (phase-amplitude modulation) in the direction from your PC out the telephone line. Sometimes even the other direction will also fall back to QAM when line conditions are not good enough. Thus QAM (phase-amplitude modulation) still remains the most widely used method on ordinary telephone lines.
The modulation method used above 33.6k is entirely different than the common phase-amplitude modulation. The details of exactly how it works seem to be obscure and I couldn't find them on the Internet as of late 1998. But the basic idea behind it is easy to understand. Since ordinary telephone calls are converted to digital signals at the local offices of the telephone company, the fastest speed that you can send digital data by an ordinary telephone call is the same speed that the telephone company uses over its digital portion of the phone call transmission. What is this speed? Well, in the USA it's exactly 56k! In other countries it may be slightly higher.
Thus in the USA 56k is the absolute top speed possible for an ordinary telephone call using the digital portion of the circuit that was designed to send digital encodings of the human voice. In order to use 56k, the modem must know exactly how the telephone company is doing its digital encoding of the analog signals. This task is far too complicated if both sides of a telephone call have only an analog interface to the telephone company. But if one side has a digital interface, then it's possible (at least in one direction). Thus if your ISP has a digital interface to the phone company, the ISP may send out a certain digital signal over the phone lines toward your PC. The digital signal from the ISP gets converted to analog at the local telephone office near your PC's location (perhaps near your home). Then it's your modem's task to try to figure out exactly what that digital signal was. If it can do this then transmission at 56k (the speed of the telephone company's digital signal) is possible in this direction.
What method does the telephone company use to digitally encode analog signals? It uses a method of sampling the amplitude of the analog signal at a rate of 8000 samples per second. Each sample amplitude is encoded as a 7-bit (ASCII-like) byte. (Note: 7 x 8000 = 56k) This is called "Pulse Code Modulation" = PCM. These bytes are then sent digitally on the telephone company's digital circuits where many calls share a single circuit using a time-sharing scheme known as "time division multiplexing". Then finally at the local telephone office near your home, the digital signal is de-multiplexed resulting in the same digital signal as was originally created by PCM. This signal is then converted back to analog and sent to your home. Each 7-bit byte creates a certain amplitude of the analog signal. Your modem's task is to determine just what that PCM 7-bit byte was based on the amplitude it detects.
This is (sort of) "amplitude demodulation" but not really. It's not amplitude demodulation because there is no carrier. Actually, it's called "modulus conversion" which is the inverse of PCM. In order to determine the digital codes the telephone Co. used to create the analog signal, the modem must sample this analog signal amplitude at exactly the same points in time the phone Co. used when it created the analog signal. In order to get the modem to do this correctly the modem must go thru "training" periods where the ISP's modem sends out known digital signals and the modem trains itself to recognize those signals. (At least that's the way I think it works ??)
Note that the digital part of the telephone network is bi-directional. Two such circuits are used for a phone call, one in each direction. Also, while 7-bit bytes are used to encode the amplitude, the bytes sent are 8-bit ones with the extra bit used by the telephone company for its signalling purposes. The telephone users have no control over this extra bit. This means that while the digital signal is actually 64k bits/sec, only 56k can be controlled by the user.