dsp suryakanta of digital signal processing.pdf
- 1. COOCHBEHARGOVERNMENTENGINEERINGCOLLEGE o NAME: SURYAKANTA KUMBHAKAR o ROLL NO.: 34901623066 o SUBJECT: DIGITAL SIGNAL PROCESSING o SUBJECTCODE: OE-EE-601A o DEPARTMENT: ELECTRICAL ENGINEERING o CA-1, 6TH SEMESTER, 3RD YEAR Presented on Signals & Systems
- 2. AGENDA Introduction to Signals & Systems Types of Signals Operations on Signals Types of Systems Signal Transformations Characteristics of Signals and Systems Applications of Signals & Systems Conclusion
- 3. Introduction to Signals & Systems What are signals? In electrical engineering, the fundamental quantity of representing some information is called a signal. It does not matter what the information is i-e: Analog or digital information. In mathematics, a signal is a function that conveys some information. In fact any quantity measurable through time over space or any higher dimension can be taken as a signal. A signal could be of any dimension and could be of any form. What are Systems? A system is a defined by the type of input and output it deals with. Since we are dealing with signals, so in our case, our system would be a mathematical model, a piece of code/software, or a physical device, or a black box whose input is a signal and it performs some processing on that signal, and the output is a signal. The input is known as excitation and the output is known as response. Importance of Signals and Systems Understanding signals and systems is fundamental to fields like electrical engineering, communications, control systems, and audio/video processing. This knowledge helps in designing and analyzing systems that process signals efficiently, whether it’s transmitting data, filtering noise, or processing sound.
- 4. Types of Signals • Analog signals: Analog signals are continuous time signals and they are used to represent data over a range of values. These are used to represent analogous values that vary with the continuous value of input for example the audio signals vary continuously with pressure change • Human voice: This signal is produced by the larynx present in the throat of human beings. The vibration of vocal cords due to the passage of air results in the audio signal. The frequency of human sound is 350 Hz to 17KHz for women and 100Hz to 8KHz for men. • Digital signals: Contrary to analog signals, digital signals are discrete in nature therefore, they are used to represent values that vary discretely with time. There are discontinuities in the digital signals, some examples of digital signals are signals in smartwatches and phones. • Continuous-time vs. Discrete-time: A continuous-time signal is defined at all time instants and can take on any value within a continuous range, whereas a discrete-time signal is defined only at specific time instants and can only take on distinct, separate values. • Analog vs. Digital: An analog signal is a continuous-time signal that can take on any value within a continuous range, whereas a digital signal is a discrete-time signal that can only take on distinct, separate values represented by binary digits (0s and 1s). • Periodic vs. Aperiodic: A periodic signal is a signal that repeats its values at regular intervals, whereas an aperiodic signal is a signal that does not repeat its values at regular intervals and has a unique pattern.
- 5. Operations on Signals • Time shifting, scaling, and reversal: Time shifting involves delaying or advancing a signal, time scaling involves compressing or expanding a signal, and time reversal involves flipping a signal around the time axis, effectively playing it backwards. • Even & Odd signals: An even signal is symmetric around the y-axis, satisfying x(t) = x(-t), whereas an odd signal is antisymmetric around the y-axis, satisfying x(t) = -x(-t). • Energy vs. Power signals: A signal is said to have finite energy if the integral of its squared magnitude over all time is finite, whereas a signal is said to have finite power if the average value of its squared magnitude over time is finite.
- 6. Types of Systems Casual & Anticasual • Casual: A system is said to be casual if the present value of the output signal depends on the present and/or past values of the input signal • Anticasual: A system is said to be anticasual if the present value of the output signal depends only on the future values of the input signal. Linear & Non Linear Systems • A system is said to be linear if it satisfies the principle of superposition • For checking the linearity of the given system, firstly we check the response due to linear combination of inputs • Then we combine the two outputs linearly in the same manner as the inputs are combined and again total response is checked • If response in step 2 and 3 are the same, the system is linear othewise it is non linear. Time Invariant and Time Variant Systems • A system is said to be time invariant if a time delay or time advance of the input signal leads to a identical time shift in the output signal. Stable & Unstable Systems • A system is said to be bounded-input bounded-output stable (BIBO stable) if every bounded input results in a bounded output. Static & Dynamic Systems • A static system is memoryless system • It has no storage devices • its output signal depends on present values of the input signal Invertible & Inverse Systems • If a system is invertible it has an Inverse system
- 7. Signal Transformations Fourier Series • A Fourier series represents a periodic signal in the frequency domain by expressing it as a sum of sinusoids with discrete frequencies, where each frequency component is represented by a complex coefficient known as the Fourier coefficient, effectively showing the amplitude and phase of each harmonic present in the signal; this representation is considered the "frequency-domain representation" of the Fourier series. Fourier Transform • The Fourier transform is a mathematical operation that converts time-domain data into frequency-domain data. It's used to analyse the frequency components of a signal. Laplace and Z-Transform basics • In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex valued frequency-domain (the z- domain or z-plane) representation . It can be considered a discrete-time equivalent of the Laplace transform (the s-domain or s-plane).
- 8. Characteristics of Signals and Systems • Causality: Signals and systems can have a causal system where the current output of the system depends on the present and past input values and is independent of future values. Causality is a requirement of some real-world systems. • Time Invariant: Time Invariant system can be defined as a system where If an input signal is shifted by some period then the response is that the system is also shifted by the same period. This ensures that the system doesn't change with time. • Linearity: Linear systems are defined by their property of superposition. It can be understood as the system response of the sum of two inputs is equal to the sum of the output response of individual input values. • Stability: Stability is necessary to ensure that the system doesn't grow uncontrollably, therefore stable systems are the ones that generate bounded output for a bounded input. • Convolution: Convolution is often used for calculating the output of the system by convoluting the input signal with the transfer function of the system.
- 9. Applications of Signals & Systems • Signals and systems are taught as a primary course in professional institutions to develop the basics of electronics engineering. • Signals and systems are used in fields like multimedia processing for efficient transfer of image and video data with minimal loss. • Sensing methods located in satellites and navigation ships like SONAR, RADARS, and LiDAR work on the principles of signal processing to analyze the received signals. • Principles of signals and systems are applied in the study of earthquakes I.e. in seismology to study the vibrations that result as a consequence of collision of plates. • Signals and systems are also used in the telecommunication industry to compress the signal like audio signals therefore efficiently managing the resources available for data transfer.
- 10. Conclusion • We have seen that signals and systems form an integral part of electronics and communication. It is necessary to define these terms to establish a basic understanding of the topic. The circuits are installed in various daily life appliances where they are used for signal processing. The advantages of the signals and systems are evident from their use in different applications. Despite the various features offered, there are some limitations of the system that have been discussed in the article. THANK YOU