Signals and Systems Networks and Communication Department Chapter (1)

Lecture Contents What does a signal mean? Classifications of Signals Continuous-Time and Discrete-Time Signals Analog and Digital Signals Even and Odd Signals Periodic and Non-periodic signals Sinusoidal Signals Signals and Systems Analysis

1.1 What does a signal mean ? A signal is a function representing a physical quantity or variable, typically is contains information about the behavior or nature of the phenomenon. A system is viewed as transformation (mapping) of 𝑥 into 𝑦, to process input signals to produce output signals. Types of Signals in our lives and some examples: Electrical Signals: (e.g. voltage and current) Electromagnetic Signals: (e.g. radio, waves and light) Sound Signals: (e.g. human sounds and music) System Input signal 𝑥(𝑡) Output signal 𝑦(𝑡) Signals and Systems Analysis

1.1 What does a signal mean ? Data : Signals : Signaling : entities that convey information Signals : electric or electromagnetic representations of data Signaling : physically propagates along a medium Transmission : communication of data by propagation and processing of signals 7-Dec-18 Networks and Communication Department

1.2 Classifications of Signals Continuous-Time and Discrete-Time Signals (Basic types of Signals) Continuous-Time Signals: A signal 𝑥(𝑡) is continuous-time signal if the independent variable t is continuous. Discrete-Time Signals: A signal 𝑥(𝑡) is defined at discrete times, a discrete-time signal is often identified as a sequence of numbers, denoted by 𝑥 𝑛 . A very important class of discrete-time signals 𝑥 𝑛 is obtained by sampling a continuous-time signal 𝑥 𝑡 . Signals and Systems Analysis

Continuous-time Signals: A continuous-time signal is a signal that can be defined at every instant of time. A continuous-time signal contains values for all real numbers along the X-axis. It is denoted by x(t). Analog signals is a continuous-time signals. 7-Dec-18 Networks and Communication Department

Discrete-time Signals: Signals that can be defined at discrete instant of time is called discrete time signal. Basically discrete time signals can be obtained by sampling a continuous-time signal. It is denoted as x[n] Digital signals is Discrete-time signals. 7-Dec-18 Networks and Communication Department

1.2 Classifications of Signals (Cont.) Analog and Digital Signals Signals and Systems Analysis

1.2 Classifications of Signals (Cont.) Analog and Digital Signals Analog signals: If a continuous-time signal 𝑥(𝑡) can take on any value in the continuous interval (𝑎, b), where 𝑎 may be - and b may be +, then the continuous-time signal 𝑥(𝑡) is called an analog signal. Digital signals: It is a discrete or non-continuous 𝑥 𝑛 waveform, that could take only a finite number of values; with examples such as computer 1s and 0s. Signals and Systems Analysis

Analog and Digital data : Audio Video Text and Numbers. IRA (ASCII). 7-Dec-18 Networks and Communication Department

Analog Signals : Audio Signals Frequency range of typical speech is 100Hz-7kHz Easily converted into electromagnetic signals Varying volume converted to varying voltage Can limit frequency range for voice channel to 300-3400Hz 7-Dec-18 Networks and Communication Department

Analog Signals : Audio Signals 7-Dec-18 Networks and Communication Department

Analog Signals : Video Signals To produce a video signal a TV camera is used USA standard is 483 lines per frame, at a rate of 30 complete frames per second Actual standard is 525 lines but 42 lost during vertical retrace Horizontal scanning frequency is 525 lines x 30 scans = 15750 lines per second Max frequency if line alternates black and white Max frequency of 4.2MHz 7-Dec-18 Networks and Communication Department

Analog Signals : Video Signals 7-Dec-18 Networks and Communication Department

Analog signals : 7-Dec-18 Networks and Communication Department

Digital Signals: 7-Dec-18 Networks and Communication Department

Digital Signals : cheaper less susceptible to noise interference Advantages Disadvantages cheaper less susceptible to noise interference suffer more from attenuation 7-Dec-18 Networks and Communication Department

Digital Signals : 7-Dec-18 Networks and Communication Department

1.2 Classifications of Signals (Cont.) E. Even and Odd Signals A signal 𝑥(𝑡) or 𝑥 𝑛 is referred to as an even signal if 𝒙(−𝒕) = 𝒙(𝒕) 𝐱 −𝒏 = 𝐱 𝒏 Signals and Systems Analysis

1.2 Classifications of Signals (Cont.) E. Even and Odd Signals (Cont.) A signal 𝑥(𝑡) or 𝑥 𝑛 is referred to as an odd signal if 𝒙(−𝒕) = −𝒙(𝒕) 𝐱 −𝒏 = −𝐱 𝒏 Signals and Systems Analysis

Even and Odd signals: Even Odd An even signal is any signal 'x' such that x(t) = x(-t) Even signals are symmetric around vertical axis an odd signal is a signal 'x' for which x(t) = - x(-t) Odd signals are symmetric about origin 7-Dec-18 Networks and Communication Department

1.2 Classifications of Signals (Cont.) Periodic and Non-periodic signals: Periodic signal: Pattern repeated over time. Non-periodic signal(Aperiodic): Pattern not repeated over time.

1.2 Classifications of Signals (Cont.) Periodic and Non-periodic Signals: A continuous-time signal 𝒙(𝒕) is said to be periodic with period T if there is a positive nonzero value of T for which 𝒙(t + T) = 𝒙(𝒕) for all t In other words, a periodic signal has the property that it is unchanged by a time shift of T (called period T). An example of such a signal is shown below Signals and Systems Analysis

1.2 Classifications of Signals (Cont.) Periodic and Non-periodic Signals (Cont.): From this equation 𝒙(t + T) = 𝒙(𝒕) it follows that 𝒙(t + mT) = 𝒙(𝒕) for all t and any integer m. Note that this definition does not work for a constant signal 𝒙(𝒕). Any continuous-time signal which is not periodic is called a non- periodic (or aperiodic ) signal. Signals and Systems Analysis

1.2 Classifications of Signals (Cont.) Periodic and Non-periodic Signals (Cont.):   Signals and Systems Analysis

1.2 Classifications of Signals (Cont.) Periodic and Non-periodic Signals (Cont.):   Signals and Systems Analysis

Periodic and Aperiodic signals A signal is said to be periodic if it repeats itself after some amount of time x(t+T)=x(t), for some value of T. The period of the signal is the minimum value of time for which it exactly repeats itself. Signal which does not repeat itself after a certain period of time is called aperiodic signal. 7-Dec-18 Networks and Communication Department

Types of Signals and its Properties: Summary This module describes just some of the many ways in which signals can be classified. They can be continuous time or discrete time, analog or digital, periodic or aperiodic, odd or even. 7-Dec-18 Networks and Communication Department