Signals, Systems and Spectral Analysis (Week 3) PDF
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Cavite State University
Nemilyn A. Fadchar, ECE
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This document is a set of lecture notes on signals and systems analysis. It covers the classification of signals and systems, basic operations on signals, and various types of signals and systems. It provides an overview of the fundamental principles in communication systems.
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TOPIC 2: Signals, Systems and Spectral Analysis (WEEK 3) NEMILYN A. FADCHAR, ECE FIRST SEMESTER, 2024-2025 Learning Objectives Classify signals from different perspectives. Evaluate the energy and power of a signal. Discuss the classification of systems from different...
TOPIC 2: Signals, Systems and Spectral Analysis (WEEK 3) NEMILYN A. FADCHAR, ECE FIRST SEMESTER, 2024-2025 Learning Objectives Classify signals from different perspectives. Evaluate the energy and power of a signal. Discuss the classification of systems from different perspectives. BASIC OPERATIONS ON SIGNALS In communications, any time-varying physical phenomenon that conveys information is referred to as a signal. Examples include signals with useful information, such as human voices, MP3 music, JPEG images, seismic signals, CT scans, ECG signals, and MPEG videos, or signals that are considered useless and unwanted, such as noise and interference. BASIC OPERATIONS ON SIGNALS The basic operations on signals are divided into two distinct categories: i) operations performed on the dependent variable g(t) or g(n), and ii) operations performed on the independent variable t or n. In addition, a mixed set of operations from both categories can be simultaneously applied to signals. Operations Performed on Dependent Variables Amplitude Scaling Multiplication Addition Operations Operations 𝑦 𝑡 = Operations 𝑦(𝑡) = 𝑦(𝑡) = 𝑔! 𝑡 + 𝑔" 𝑡 𝑘𝑔(𝑡) 𝑔! 𝑡 𝑔" 𝑡 Integration Differentiation Operation Operations # Differentiation 𝑦 𝑡 = 𝑔 𝑡 = 𝑔′(𝑡) Operation #$ 𝑦 𝑡 = ∫ 𝑔(𝑡) 𝑑𝑡 Operations Performed on Independent Variables Time-shifting Time-reversal Operations Time- Operations reversal Operations 𝑦 𝑡 = 𝑔(−𝑡) 𝑦 𝑡 = 𝑔(𝑡 − 𝜏) Time-scaling Operations 𝑦 𝑡 = 𝑔(𝛽𝑡) CLASSIFICATION OF SIGNALS Representation and processing of a signal highly depends on the type of signal being considered. Signals can be broadly classified into a number of different ways. Continuous-Value and Discrete- Value Signals CONTINUOUS-VALUE SIGNAL DISCRETE-VALUE SIGNAL A continuous-value signal is one A discrete-value signal can only that may have any value within a have values taken from a discrete continuum of allowed values; the set consisting of a finite number of continuum on the vertical axis values. A discrete-value signal can be finite or infinite. An analog may be derived from a speech transmitted over a continuous-value signal when the twisted-pair telephone line can signal value is quantized be categorized as a continuous- (rounded). value signal, as the signal level over time can continuously range from a quiet whisper to a deafening scream. Continuous-time and Discrete-time Signals CONTINUOUS-TIME SIGNAL DISCRETE-TIME SIGNAL A signal is said to be a continuous- A signal is said to be a discrete-time time signal if it is defined for all time t, signal if it is defined only at discrete a real number. Continuous-time instants of time n. In other words, the signals arise naturally when a physical independent variable on the signal, such as a light wave, is horizontal axis has discrete values only converted by a transducer, such as a (i.e., it takes its value in the set of photoelectric cell, into an electrical integers). Note that it does not mean a signal. A continuous-time signal can discrete-time signal has zero value at have zero value at certain instants of nondiscrete (noninteger) instants of time or for some intervals of time. time, it simply implies we do not have (or probably we do not care to have) the values at noninteger instants of time. A discrete-time signal g(n) is often derived from a continuous-time signal g(t) by the sampling process. Analog and Digital Signals The terms analog and digital describe the nature of the signal amplitude on the vertical axis, as analog and digital signals are both continuous-time signals defined for all time t. ANALOG SIGNAL DIGITAL SIGNAL For an analog signal, the dependent For a digital signal, on the other hand, variable on the vertical axis can be over any finite interval of time, also any real number (- ∞, ∞). Humans known as a bit or symbol duration, produce and perceive audio and the continuous-time waveform visual signals in an analog form. belongs to a finite set of possible Examples of analog signals include waveforms. This is in contrast to signals representing light and sound analog communications where the intensity and multidimensional continuous waveform can assume an position. Analog signals arise when a infinite number of possible physical signal is converted by a waveforms. A good example of transducer, such as the conversion of digital signals is touch-tone signaling, an acoustic wave by a microphone in which a touch-tone telephone into an electrical signal. The variation simultaneously transmits down the of the analog signal with time is subscriber line a certain pair of analogous (proportional) to some audible sinusoidal frequencies for physical phenomenon, such as voice. each of the 12 possible keys. Deterministic and Random Signals DETERMINISTIC SIGNAL RANDOM SIGNAL A deterministic signal is a fully-defined In digital communications, a random (completely-specified) function of the signal may belong to a group of independent variable time. A signals, with each signal in the group deterministic signal is a signal about having a different waveform as well which there is no uncertainty with as having a certain probability of respect to its value, and we can thus occurrence. The ensemble of signals determine the exact value of the is referred to as a random (stochastic) signal at any given time. Signals process. Message signals, characterizing linear distortions in interference at all levels, and noise of communication channels or all types are considered as random sinusoidal signals used as local signals. oscillators in transmitters are all deterministic. Real and Complex Signals In both real and complex signals, the independent variable is real-valued. REAL SIGNAL COMPLEX SIGNAL A real signal at any given time takes A complex signal takes its value in the its value in the set of real numbers. set of complex numbers. Signals that we observe physically A complex signal can in turn be (using voltmeters, ammeters, represented by two real signals, such oscilloscopes, etc.) are all real signals. as the real and imaginary parts or equivalently magnitude (amplitude) and phase values. Periodic and Nonperiodic Signals PERIODIC SIGNAL NON-PERIODIC SIGNAL A periodic signal repeats itself in time. A signal that does not repeat itself A periodic continuous-time signal g(t) over time and have an unpredictable is a function of time that satisfies the or random pattern. periodicity condition. For a discrete-time signal to be periodic, the period must be a positive integer; otherwise, it is called nonperiodic. Even and Odd Signals EVEN SIGNAL ODD SIGNAL A signal is even if it is symmetric A signal is odd if it has rotational around the vertical axis. symmetry around the origin. Causal and Noncausal Signals CAUSAL SIGNAL NON-CAUSAL SIGNAL A signal that is zero for all negative A signal that has non-zero values for time.(i.e. t