What are the four types of signals?

Deterministic and Non-deterministic Signals. Even and Odd Signals. Periodic and Aperiodic Signals. Energy and Power Signals.

tutorialspoint.com - Signals Classification - Tutorialspoint

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Signals Classification

Signals are classified into the following categories:

Continuous Time and Discrete Time Signals

Deterministic and Non-deterministic Signals

Even and Odd Signals

Periodic and Aperiodic Signals

Energy and Power Signals

Real and Imaginary Signals

Continuous Time and Discrete Time Signals

A signal is said to be continuous when it is defined for all instants of time. A signal is said to be discrete when it is defined at only discrete instants of time/

Deterministic and Non-deterministic Signals

A signal is said to be deterministic if there is no uncertainty with respect to its value at any instant of time. Or, signals which can be defined exactly by a mathematical formula are known as deterministic signals. A signal is said to be non-deterministic if there is uncertainty with respect to its value at some instant of time. Non-deterministic signals are random in nature hence they are called random signals. Random signals cannot be described by a mathematical equation. They are modelled in probabilistic terms.

Even and Odd Signals

A signal is said to be even when it satisfies the condition x(t) = x(-t)

Example 1: t2, t4… cost etc.

Let x(t) = t2 x(-t) = (-t)2 = t2 = x(t) $ herefore, $ t2 is even function Example 2: As shown in the following diagram, rectangle function x(t) = x(-t) so it is also even function. A signal is said to be odd when it satisfies the condition x(t) = -x(-t)

Example: t, t3 ... And sin t

Let x(t) = sin t x(-t) = sin(-t) = -sin t = -x(t) $ herefore, $ sin t is odd function. Any function (t) can be expressed as the sum of its even function e (t) and odd function o (t). (t ) = e (t ) + 0 (t ) where e (t ) = ½[(t ) +(-t )]

Periodic and Aperiodic Signals

A signal is said to be periodic if it satisfies the condition x(t) = x(t + T) or x(n) = x(n + N).

Where

T = fundamental time period, 1/T = f = fundamental frequency.

The above signal will repeat for every time interval T 0 hence it is periodic with period T 0 .

Energy and Power Signals

A signal is said to be energy signal when it has finite energy.

$$ ext{Energy}, E = int_{-infty}^{infty} x^2,(t)dt$$

A signal is said to be power signal when it has finite power.

$$ ext{Power}, P = lim_{T o infty},{1over2T},int_{-T}^{T},x^2(t)dt$$

NOTE:A signal cannot be both, energy and power simultaneously. Also, a signal may be neither energy nor power signal.

Power of energy signal = 0 Energy of power signal = ∞

Real and Imaginary Signals

A signal is said to be real when it satisfies the condition x(t) = x*(t) A signal is said to be odd when it satisfies the condition x(t) = -x*(t)

Example:

If x(t)= 3 then x*(t)=3*=3 here x(t) is a real signal. If x(t)= 3j then x*(t)=3j* = -3j = -x(t) hence x(t) is a odd signal. Note: For a real signal, imaginary part should be zero. Similarly for an imaginary signal, real part should be zero.

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What is 6 8 time called?

compound meter 6/8 is what's known as a compound meter. In a compound meter, we feel the pulse of the music in larger groupings of three notes, even though we count each of those notes as a beat. This means that we feel the pulse of 6/8 in two, with three beats filling in (or subdividing) the space between the pulses.

libertyparkmusic.com - What is 6/8 Time Signature? | Liberty Park Music

Time signatures like 4/4 and 3/4 are known as simple meters, meaning that they are counted and “felt” very simply, one pulse to one count. 6/8 is what’s known as a compound meter. In a compound meter, we feel the pulse of the music in larger groupings of three notes, even though we count each of those notes as a beat. This means that we feel the pulse of 6/8 in two, with three beats filling in (or subdividing) the space between the pulses. So what’s the difference between 3/4 and 6/8? Here are notated versions of 3/4 and 6/8 next to each other, with both their beats and pulse groupings labeled: As you can see, when in 3/4 we feel each of the beats as a pulse, but in 6/8 we only feel two pulses, each with three beats in between them. Because of this, 6/8 is usually used for slightly faster music, as it becomes easy to feel the pulse of slower tempos as 3/4.

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