Size Of Signal
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The document discusses different measures for quantifying the size of signals, including signal energy (Eg) which is defined as the integral of the signal amplitude squared and incorporates both amplitude and duration, and signal power (Pg) which is used for signals that do not approach zero at infinity and is defined as the time average of the signal amplitude squared. Examples are provided to illustrate calculating energy for a signal that approaches zero at infinity and power for a periodic signal whose power exists.
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![Size of Signal
Size- It is a quantity that indicates largeness or strength of any entity.
Signal-As the term implies, is a set of information or data.
Examples of signal include:
Electrical signals
– Voltages and currents in a circuit
Mechanical signals
– Velocity of a car over time
Video signals
– Intensity level of a pixel (camera, video) over time.
Mathematically, signals are represented as a function of one or more
independent variables.
For instance a black & white video signal intensity is dependent on x, y coordinates and time t
f(x,y,t)
Here, we shall be exclusively concerned with signals that are a function of a single variable: time.
4/14/2018
Lets begin
t
g(t)
Types:- (a) Continuous-time Signal
(b) Discrete-time Signal
How can a signal exists with certain time interval with
varing amplitude be measured by one number that will
x(t) x[n]
(a) (b)t n](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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The document discusses various properties of signals including:
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A signal can be defined as a pattern of variation that carries information over time. Signals can be continuous analog signals defined by mathematical functions, or discrete digital signals represented by discrete samples. Analog signals are more accurate but digital signals are easier to store and analyze. Conversion between analog and digital signals involves sampling the analog signal at discrete time intervals and quantizing the amplitude into discrete levels. Signals can be analyzed in the time domain, looking at amplitude variation over time, or the frequency domain, looking at how many times different events occur over the total observation period.
Signals
The signal encapsulates information about the behaviour of a physical phenomenon, for example, electrical current flowing through a resistor, sonar sound waves propagating under water, or earthquakes
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The signal encapsulates information about the behaviour of a physical phenomenon, for example, electrical current flowing through a resistor, sonar sound waves propagating under water, or earthquakes.
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Lecture No 5: https://youtu.be/pb7GdbcLnI0
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Size Of Signal
- 1. Nishant Kumar Regn No:-CSE/10114017 Indian Institute Of Information Technology,Kalyani Email:-nishantkr@iiitkalyani.ac.in Topic :- Size of Signal
- 2. Size of Signal Size- It is a quantity that indicates largeness or strength of any entity. Signal-As the term implies, is a set of information or data. Examples of signal include: Electrical signals – Voltages and currents in a circuit Mechanical signals – Velocity of a car over time Video signals – Intensity level of a pixel (camera, video) over time. Mathematically, signals are represented as a function of one or more independent variables. For instance a black & white video signal intensity is dependent on x, y coordinates and time t f(x,y,t) Here, we shall be exclusively concerned with signals that are a function of a single variable: time. 4/14/2018 Lets begin t g(t) Types:- (a) Continuous-time Signal (b) Discrete-time Signal How can a signal exists with certain time interval with varing amplitude be measured by one number that will x(t) x[n] (a) (b)t n
- 3. Signal Energy(Eg) Such a measure must consider not only signal amplitude but also ,its duration. We may consider ,the area under a signal g(t) as a possible measure of its size,because it includes both amplitude of direction. This will be defective measure because g(t) could be large signal,yet its +ve and –ve areas could cancel each other,indicating a signal of small size. This difficulty can be corrected by defining the signal size as the area g2(t),which is always +ve. We call this measure the signal energy Eg,defined (for real signals ) as For complex valued signal g(t), Eqn.1 Eqn.2 The signal energy must be finite for a meaningful measure of signal size, otherwise the integral in Eqn 1 will not converge.. Necessary condition for finite energy, Signal Amplitude→0,As |t|→∞ (Fig 1a)
- 5. Signal Power 4/14/2018 Assume condition,when amplitude of g(t) does not →0 as |t|→0 (Fig.1b),the signal energy is infinite. A more meaningful measure of signal size in such a case would be the time average of the energy(if it exists),which is the average power Pg defined (for real signal) by generalised defn. For complex signal g(t) as, Obserbe the signal power Pg is the time average(mean) of the signal amplitude squared,i.e mean-squared value of g(t). Indeed the square root of Pg will be the familier RMS value of g(t). Eqn.3 Eqn. 4
- 6. Example.1 4/14/2018 Determine the suitable measure of signals in figure given below. Fig. 2 (a) The signal in Fig 2(a)→0 as |t|→∞.so,suitable measure of this signal is Energy Eg given by, (b)The signal doesn’t →0 as |t|→∞.However it is periodic ,therefore its power exists. So from eqn.3,Power Pg, Signal power is square of its rms value .Therefore the rms value of the signal is 1/√3.