Essential concepts that took me years to understand
Let's master some important electrical engineering ideas here. Powerpoint of some ideas.
As a signal travels down a cable the path is ideally a smooth one with minimal bumps. But when it gets to the load there's a chance that some of the energy will be reflected back down the path. This can happen if there is an abrupt change in the impedance. Changes in conductuctivity, capacitive, and inductive reactance can all contribute to a frequency dependent reflection of signal energy. This is desirable in some cases and not so much in others. See Max Power Transfer below for details.
In an electric circuit one can measure the impedence at any part. Between major components exist "transmission lines". If the impedance (relative to ground) on both conductors is the same all the way down the line, it is considered balanced. The benefit is that external noise is induced equally in both lines so common mode rejection is possible.
Signals are often transmitted over balanced connections using the differential mode, meaning the wires carry signals of opposite polarity to each other (for instance, in an XLR connector, pin 2 carries the signal with normal polarity, and pin 3 carries an inverted version of the same signal). Despite popular belief, this arrangement is not necessary for noise rejection. As long as the impedances are balanced, noise will couple equally into the two wires (and be rejected by a differential amplifier), regardless of the signal that is present on them. A simple method of driving a balanced line is to inject the signal into the "hot" wire through a known source impedance, and connect the "cold" wire to the signal's local ground reference through an identical impedance. Due to common misconceptions about differential signalling, this is often referred to as a quasi-balanced or impedance-balanced output, though it is, in fact, fully balanced and will reject common-mode interference. Most explanations of balanced lines assume symmetric (antiphase) signals but this is an unfortunate confusion - signal symmetry and balanced lines are quite independent of each other. Essential in a balanced line is matched impedances in the driver, line and receiver. These conditions ensure that external noise affects each leg of the differential line equally and thus appears as a common mode signal that is removed by the receiver. There are balanced drive circuits that have excellent common-mode impedance matching between "legs" but do not provide symmetric signals. Symmetric differential signals exist to prevent interference to other circuits - the electromagnetic fields are canceled out by the equal and opposite currents. But they are not necessary for interference rejection from other circuits. Lines carrying symmetric signals (those with equal but opposite voltages to ground on each leg) are often incorrectly referred to as "balanced", but this is actually differential signaling. Balanced lines and differential signaling are often used together, but they are not the same thing. Differential signalling does not make a line balanced, nor does noise rejection in balanced cables require differential signalling. Circuits driving balanced lines must themselves be balanced to maintain the benefits of balance. This may be achieved by transformer coupling or by merely balancing the impedance in each conductor. This advantage is not directly due to differential signaling itself, but to the common practice of transmitting differential signals on balanced lines. Single-ended signals are still resistant to interference if the lines are balanced and terminated by a differential amplifier.
In a transmission line there exist at least two conductors carrying a signal from the source to the load. When the signals are perfectly out-of-phase then the effective radiation at a distance is zero. This helps prevent the line from being the source of noise to other parts of the circuit. Single-ended signals by definition are not symmetric and can radiate!
Consider a complete circuit with a source and a load. We define this as a "network" and use network analyzers to measure important properties like impedence and bandwidth. A network analyzer typically has two ports S_1 and S_2. Sometimes you only need one port. For testing antenna bandwidth you would hook the antenna up to just S_1 and the analyzer tells you what frequencies are reflected across a band. Voltage standing waves...hmmmm I need to learn more about VSW ratios.
Max Power Transfer
For ideal load/source impedance ratios it depends on the application. Audio circuits contain wavelengths in the conductors that are huge compared to the circuit itself. This and the fact that modern amplifiers have super low output impedances makes efficiency an option. For audio it is usually desired that one "bridges" the source to the load. This puts a greater voltage drop across the load so more power is used by the load relative to the source. This of course means tons of energy reflected back to the source by the load but that's ok because it does not change the efficiency of the operation. RF circuits are different. RF wavelengths are about the size of the circuit and this makes it possible for tons of power to be wasted in reflection and standing waves. For radio circuits one ideally matches the source impedance to the load impedance such that no energy is reflected back. This is needed when noise is an issue.
In-Phase and Quadrature (analytic) signals
Sometimes it is important to know the instantaneous phase of a signal in real-time. Coherent systems by definition have well known phases along the transmission line. I-Q modulation is one way of doing this. With this modulation there are two signals, one "In-Phase" carries the raw signal of interest. The second carries the instantaneous phase of the raw signal. This is essentially two signals that are 90 degrees out of phase with eachother, hence quadrature because 360/4 = 90. Many times coherency through out the system is not needed untul post-processing. In this case a Hilbert transform takes any raw signal and generates a complex signal where the imaginary part is the instantaneous phase.
This is the idea that we tend to measure an unecessary amount of information when analyzing common natural systems. Intelligent systems are usually "sparse" in some domain. That domain unfortunately is a transform away from its natural state. However, upon transformation, this means that one can get a perfectly accurate sample of data with one-tenth the sampling rate for example. The trick is to find the domain in which it's sparse and transform the signal before or during the measurement!
For years Short-Time Fast-Fourier Transforms were the only way we analyzed the spectrum of signals in real-time.
That method of extracting signature signals out of noise?!?
To take advantage of a small voltage and control larger voltages both negative and positive one uses the H-bridge