Digital Signal Processing: Signal Fundamentals

• Digital Signal Processing is introduced by Engr. Julian Clement C. Villanueva.

Signal Fundamentals

• Signal refers to any physical quantity that varies with time, space, temperature, pressure, or any other independent variable.
• Mathematically, it is expressed as a function of one or more independent variables.
• Examples of signals include single-variable functions like s(t) = 2t² + 3t - 2 and multi-variable functions like u(x, y) = x²y – 3x + 2y.
• Some signals, such as speech signals, cannot be easily represented by functions; complex signals may be represented as a sum of sinusoids with varying amplitudes and frequencies.
• Signal generation is associated with a system responding to a stimulus or force.
• In speech signals, the system involves the vocal cords and vocal tract, known as the vocal cavity.
• The stimulus combined with the system forms a signal source, leading to various types of signal sources like speech and images.
• A system is a physical device or software that performs an operation on a signal.
• Filters are used to reduce noise or interference in information-bearing signals.
• Signal processing is a method of extracting information from a signal, based on its type and the nature of the information.
• It involves representing signals mathematically and extracting information through algorithmic operations.

Analog vs Digital Signal Processing

• In analog signal processing, most signals in science and engineering are processed directly in their analog form
• Digital signal processing uses an analog-to-digital (A/D) converter to interface between analog signals and digital processors.
• When the output is used in analog form, a digital-to-analog (D/A) converter is used.
• Advantages of digital signal processing over analog include:
• Digital circuits are less sensitive to component value changes, temperature variations, aging, and external parameters
• Flexibility is improved through digital programmable systems
• Digital signals are easily stored and transported for offline processing
• Better control of accuracy and potential cost effectiveness.
• Limitations of Digital Signal Processing (DSP) include the speed of analog-to-digital converters (ADCs) and digital signal processors, problems with handling signals with extremely wide bandwidths due to fast-sampling rate requirements, frequency limitations, and the higher energy consumption of active devices in digital systems compared to passive ones in analog systems..

Signal Classifications

• Signals are classified into multichannel and multidimensional signals, continuous-time versus discrete-time signals, continuous-valued versus discrete-valued signals, and deterministic versus random signals.

Multichannel and Multidimensional Signals

• Multichannel signals are generated by multiple sources or sensors and can be represented in vector form.
• Ground acceleration from earthquakes, which includes primary (P) waves, secondary (S) waves, and surface waves, provides an example of multichannel signals.
• Multidimensional signals are signals defined by a single or multiple independent variables.
• Signals that are functions of a single independent variable are one-dimensional, while those dependent on M independent variables are M-dimensional.
• A black and white TV picture can be represented as a three-dimensional signal whereas a color TV picture which can be described by three intensity functions relating to the brightness of the three principal colors is an example of a three-channel, three dimensional signal.

Continuous-Time vs Discrete-Time Signals

• Continuous-time signals are defined for every value of time within a continuous interval and are described by functions of a continuous variable.
• Discrete-time signals arise by selecting values of an analog signal at discrete-time instants through sampling or by accumulating a variable over time.

Continuous-valued vs Discrete-valued Signals

• Continuous-valued signals take on all possible values on a finite or infinite range.
• Discrete-valued signals take on values from a finite set of possible values that are usually equidistant and can be expressed as an integer multiple between values. A discrete-time signal having a set of discrete values is called a digital signal.

Deterministic vs Random Signals

• Deterministic signals can be uniquely described by an explicit mathematical expression, a table of data, or a well-defined rule, with all values known precisely without any uncertainty.
• Random signals cannot be accurately described by mathematical formulas and evolve in an unpredictable manner, with the output of a noise generator used as an example,