Analog signal processing Totally Explained

Everything about Analog Signal Processing totally explained

Analog signal processing is any signal processing conducted on analog signals by analog means. "Analog" indicates something that's mathematically represented as a set of continuous values. This differs from "digital" which uses a series of discrete quantities to represent signal. Analog values are typically represented as a voltage, electric current, or electric charge around components in the electronic devices. An error or noise affecting such physical quantities will result in a corresponding error in the signals represented by such physical quantities. Examples of analog signal processing include crossover filters in loudspeakers, "bass", "treble" and "volume" controls on stereos, and "tint" controls on TVs. Common analog processing elements include capacitors, resistors, inductors and transistors.

Tools used in analog signal processing

A system's behavior can be mathematically modeled and is represented in the time domain as h(t) and in the frequency domain as H(s), where s is a complex number in the form of s=a+ib, or s=a+jb in electrical engineering terms (electrical engineers use j because current is represented by the variable i). Input signals are usually called x(t) or X(s) and output signals are usually called y(t) or Y(s).

Convolution

Convolution is the basic concept in signal processing that states an input signal can be combined with the system's function to find the output signal. The symbol for convolution is *. ť

y(t) = (x  * h )(t) = int_.

Impulse

An impulse (Dirac delta function) is defined as a signal that has an infinite magnitude and an infinitesimally narrow width with an area under it of one, centered at zero. An impulse can be represented as an infinite sum of sinusoids that includes all possible frequencies. This definition is really hard to use in real life, so most engineers conceptualize it to a signal that's one at zero and zero everywhere else. The symbol for an impulse is delta(t). If an impulse is used as an input to a system, the output is known as the impulse response. The impulse response defines the system because all possible frequencies are represented in the input.

Step

A step function is a signal that has a magnitude of zero before zero and a magnitude of one after zero. The symbol for a step is u(t). If a step is used as the input to a system, the output is called the step response. The step response shows how a system responds to a sudden input, similar to turning on a switch. The period before the output stabilizes is called the transient part of a signal. The step response can be multiplied with other signals to show how the system responds when an input is suddenly turned on.

Systems

Linear time-invariant (LTI)

Linearity means that if you've two inputs and two corresponding outputs, if you take a linear combination of those two inputs you'll get a linear combination of the outputs. An example of a linear system is a first order low-pass or high-pass filter. Linear systems are made out of analog devices that demonstrate linear properties. These devices don't have to be entirely linear, but must have a region of operation that's linear. An operational amplifier is a non-linear device, but has a region of operation that's linear, so it can be modeled as linear within that region of operation. Time-invariance means it doesn't matter when you start a system, the same output will result. For example, if you've a system and put an input into it today, you'd get the same output if you started the system tomorrow instead. There aren't any real systems that are LTI, but many systems can be modeled as LTI for simplicity in determining what their output will be. All systems have some dependence on things like temperature, signal level or other factors that cause them to be non-linear or non-time-invariant, but most are stable enough to model as LTI. Linearity and time-invariance are important because they're the only types of systems that can be easily solved using conventional analog signal processing methods. Once a system becomes non-linear or non-time-invariant, it becomes a non-linear differential equations problem, and there are very few of those that can actually be solved. (Haykin & Van Veen 2003)

Common systems

Some common systems used in everyday life are filters, AM/FM radio, electric guitars and musical instrument amplifiers. Filters are used in almost everything that has electronic circuitry. Radio and television are good examples of everyday uses of filters. When a channel is changed on an analog television set or radio, an analog filter is used to pick out the carrier frequency on the input signal. Once it's isolated, the television or radio information being broadcast is used to form the picture and/or sound. Another common analog system is an electric guitar and its amplifier. The guitar uses a magnet with a coil wrapped around it (inductor) to turn the vibration of the strings into a small electric current. The current is then filtered, amplified and sent to a speaker in the amplifier. Most amplifiers are analog because it's easier and cheaper than making a digital amplifier. There are also many analog guitar effects pedals, although a large number of pedals are now digital (they turn the input current into a digitized value, perform an operation on it, then convert it back into an analog signal).

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