Energy Signal

In signal processing, the energy E_s of a continuous-time signal x(t) is defined as

energy in this context is not, strictly speaking, the same as the conventional notion of energy in physics and the other sciences. The two concepts are, however, closely related, and it is possible to convert from one to the other:

where Z represents the magnitude, in appropriate units of measure, of the load driven by the signal.

For example, if x(t) represents the potential (in volts) of an electrical signal propagating across a transmission line, then Z would represent the characteristic impedance (in ohms) of the transmission line. The units of measure for the signal energy E_s would appear as volt²-seconds, which is not dimensionally correct for energy in the sense of the physical sciences. After dividing E_s by Z, however, the dimensions of E would become volt²-seconds per ohm, which is equivalent to joules, the SI unit for energy as defined in the physical sciences.

As the names suggest, this classification is determined by whether or not the time axis (x-axis) is discrete (countable) or continuous. A continuous-time signal will contain a value for all real numbers along the time axis. In contrast to this, a discrete-time signal is often created by using the sampling theorem to sample a continuous signal, so it will only have values at equally spaced intervals along the time axis.

Difference Between Analog Signal and Digital Signal

Analog signals are continuous where digital signals are discrete. Anolog signals are continuously varying where digital signals are based on 0's and 1's (or as often said------- on's and off's). As an analogy, consider a light switch that is either on or off (digital) and a dimmer switch (analog) that allows you to vary the light in different degrees of brightness. As another analogy, consider a clock in which the second hand smoothly circles the clock face (analog) versus another clock in which the second hand jumps as each second passes (digital). Digital computers work with a series of 0's and 1's to represent letters, symbols, and numbers. In addition, numbers are represented by using the binary code (where only 0's and 1's are used).

Number Binary equivalent
1----------------------------- -----------------1
2----------------------------- ----------------10
3----------------------------- ----------------11
4----------------------------- ---------------100
5----------------------------- ---------------101
6----------------------------- ---------------110
7----------------------------- ---------------111
8----------------------------- --------------1000

and so on. So each number (that we are accustomed to, such as 5) is represented by 0's and 1's. Morse code uses dits (or dots) and dashes. Digital signals are similar to Morse code. The signal is either a dit or a dash for Morse code and it is either a 0 or 1 for digital. A series of these dits and dashes might represent SOS to a navy radio man, and a series of 0's and 1's might represent the question mark to a computer.

When an e-mail is sent that says "Hello Joe", Hello Joe doesn't mysteriously appear on Joe's computer. What is sent through the phone line is a series of 0's and 1's and Joe's computer "interprets" these into the words Hello Joe. If you type the letter A into your computer, it converts this A into 01000001. This 01000001 goes to Joe's computer and his computer interprets it as A. Each 0 or 1 is "bit" and the series of eight 0's and 1's is a byte. Well, that is about as simple as it gets and about as simple as I can state it.

Digital Signal

The term digital signal is used to refer to more than one concept. It can refer to discrete-time signals that have a discrete number of levels, for example a sampled and quantified analog signal, or to the continuous-time waveform signals in a digital system, representing a bit-stream. In the first case, a signal that is generated by means of a digital modulation method which is considered as converted to an analog signal, while it is considered as a digital signal in the second case.

Analog Signal

An Analog or analogue signal is any continuous signal for which the time varying feature (variable) of the signal is a representation of some other time varying quantity, i.e analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are meaningful. Analog is usually thought of in an electrical context; however, mechanical, pneumatic, hydraulic, and other systems may also convey analog signals.

An analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. Electrically, the property most commonly used is voltage followed closely by frequency, current, and charge.

Any information may be conveyed by an analog signal; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure, and is achieved using a transducer.

For example, in sound recording, fluctuations in air pressure (that is to say, sound) strike the diaphragm of a microphone which induces corresponding fluctuations in the current produced by a coil in an electromagnetic microphone, or the voltage produced by a condensor microphone. The voltage or the current is said to be an "analog" of the sound.

An analog signal has a theoretically infinite resolution. In practice an analog signal is subject to noise and a finite slew rate. Therefore, both analog and digital systems are subject to limitations in resolution and bandwidth. As analog systems become more complex, effects such as non-linearity and noise ultimately degrade analog resolution to such an extent that the performance of digital systems may surpass it. Similarly, as digital systems become more complex, errors can occur in the digital data stream. A comparable performing digital system is more complex and requires more bandwidth than its analog counterpart. In analog systems, it is difficult to detect when such degradation occurs. However, in digital systems, degradation can not only be detected but corrected as well.

A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. In other words, it is a time series that is a function over a domain of discrete integers. Each value in the sequence is called a sample.

Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal. When a discrete-time signal is a sequence corresponding to uniformly spaced times, it has an associated sampling rate; the sampling rate is not apparent in the data sequence, so may be associated as a separate data item.

Continuos Time Signal

Continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum (e.g., a connected interval of the reals). That is, the function's domain is an uncountable set. The function itself need not be continuous. To contrast, a discrete time signal has a countable domain, like the natural numbers.

The signal is defined over a domain, which may or may not be finite, and there is a functional mapping from the domain to the value of the signal. The continuity of the time variable, in connection with the law of density of real numbers, means that the signal value can be found at any arbitrary point in time.

A typical example of an infinite duration signal is:

A finite duration counterpart of the above signal could be:

and f(t) = 0 otherwise.

The value of a finite (or infinite) duration signal may or may not be finite. For example,

and f(t) = 0 otherwise,

is a finite duration signal but it takes an infinite value for .

In many disciplines, the convention is that a continuous signal must always have a finite value, which makes more sense in the case of physical signals.

For some purposes, infinite singularities are acceptable as long as the signal is integrable over any finite interval (for example, the t ^{− 1} signal is not integrable, but t ^{− 2} is).

Any analogue signal is continuous by nature. Discrete signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals.

Continuous signal may also be defined over an independent variable other than time. Another very common independent variable is space and is particularly useful in image processing, where two space dimensions are used.