Signal Characteristics PDF

Part 3: Signal Characteristics  Signal Characteristics Need for Signals - Data are entities that convey meaning while signals are electric or electromagnetic representations of these data. - Signal is represented as a function of time. - The frequency domain representati...

Part 3: Signal Characteristics  Signal Characteristics Need for Signals - Data are entities that convey meaning while signals are electric or electromagnetic representations of these data. - Signal is represented as a function of time. - The frequency domain representation of the signal leads to the concepts of spectrum and bandwidth. - Its spectrum is the range of frequencies that it contains. - The bandwidth of a signal is the width of the spectrum.  Signal Characteristics Analog and Digital Concepts - Data can take either analog or digital form. - Analog refers to something that is continuous. - Digital refers to something that is discrete. - Like data, signals can be either analog or digital.  Signal Characteristics Periodic and Aperiodic Signals - Analog and digital signals can be periodic and aperiodic. - A periodic signal completes a pattern within a period. - It repeats that pattern over identical subsequent periods. x(t + T ) = x(t), - ¥  t  ¥ - The completion of one pattern is called a cycle. - A period is amount of time required to complete one cycle.  Signal Characteristics Periodic and Aperiodic Signals - An aperiodic, signal changes constantly without exhibiting a pattern (cycle) that repeats over time. - Any aperiodic signal can be decomposed into an infinite number of periodic signals.  Signal Characteristics Deterministic and random Signals - Deterministic signal has a regular pattern. - It can be modeled by an explicit mathematical expression. - The pattern of a random signal is quite irregular. - Example is noise.  Signal Characteristics Simple Analog Signals - Analog signals can be classified as simple or composite. - A simple analog signal, or a sine wave, cannot be decomposed into simpler signals. - A composite signal is composed of multiple sine waves. - A sine wave is denned by its amplitude, frequency, and phase. - The amplitude of a signal is the value of the signal at any time. - The period T is the time needed to complete one cycle.  Signal Characteristics Simple Vs Composite signals  Signal Characteristics 1. Simple Analog Signals - The frequency f is the number of periods in one second. - The wavelength λ is the distance traveled in one period.  Signal Characteristics 1. Simple Analog Signals The phase describes the position of the waveform relative to time zero.  Signal Characteristics 1. Simple (Time and frequency domains) - A signal is denned by its amplitude, frequency, and phase. - Time-domain shows changes in signal amplitude with time. - Frequency-domain plot shows the relationship between amplitude and frequency.  Signal Characteristics 2. Composite Signal - Many waveforms do not change in a single smooth curve. - For a signal to communicate data, it is usually a composite signal. - However, as long as any irregularities are consistent, cycle after cycle, a signal is still periodic. - Any periodic signal can be decomposed into a collection of sine waves. - This is the result of the work done by Fourier.  Signal Characteristics 2. Composite (Time and frequency domains) - Time-domain illustrates a composite signal as a single entity. - Frequency-domain shows it as a series of component frequency  Signal Characteristics Frequency Spectrum and Bandwidth - The frequency spectrum of a signal is the collection of all the frequency components it contains. - The bandwidth of a signal is the width of the frequency spectrum.  Signal Characteristics Digital Signals - Data can be represented by a digital signal. - Most digital signals are aperiodic. - The period or frequency is not appropriate to be used. - Two new terms, bit interval (instead of period) and bit rate (instead of frequency) are used to describe digital signals.  Signal Characteristics Digital Signals - Bit interval To is the time required to send one single bit. - Bit rate rs is the number of bit intervals per second. rs = 1/ To bps - For a digital signal with a bit rate of 5000 bps, the bit interval is 1/5000 bps - To send a digital signal, we are sending an infinite number of simple signals. - No practical medium can transfer the entire range of frequencies.  Signal Characteristics Digital Signals - Digital signal contains an infinite number of frequencies. - We can recreate it if we send only significant components. - This is the significant spectrum, and its bandwidth the significant or effective bandwidth.  Signal Characteristics Signal-to-noise ratio  Signal Characteristics Some Important Signals - Sine wave - Unit impulse. - Unit step. - Sampling function. - Gate function.  Signal Characteristics Sine Wave - It is the most fundamental in electrical communications. - The sin analysis of networks is simple and convenient. - The response of a sine wave to a linear time invariant system is also sinusoidal. - It changes in a smooth curve between a minimum and a maximum amplitude. - It is represented mathematically as x(t) = Asin(2pft)  Signal Characteristics Unit Impulse Function - It is also called Dirac delta function, d(t). - It has an infinite amplitude with zero width and unity weight ¥ òd (t)dt = 1 -¥ d (t) = 0 for t ¹ 0 ¥ ò x(t)d (t - to )dt = x(to ) -¥  Signal Characteristics Unit Step Function - It exists only in positive side and is zero in negative side. - It is discontinuous at t=0. - It may be expressed as 0 for t  0 u(t) = 1 for t0  Signal Characteristics Sampling Function - It is called interpolation function or the Sinc function. - It is defined as sinc (x) = sin(x) / 2 - Its maximum sinc(0) =1. - It is an even function of x. - It approaches 0 as x approaches. - It goes through 0 at x = ±1, ±2, …  Signal Characteristics Gate Function - It is a rectangular pulse with unity height and width t. - The gate pulse is represented mathematically as Thanks [email protected] Faris A. Almalki @EngFarisAlmalki