Signals And Systems Schaum
Marilina Crawn
Develops the basic theory of continuous and discrete systems, with emphasis on linear time-invariant
systems. Discusses the representation of signals and systems in both the time and frequency domain.
Topics include linearity, time-invariance, causality, stability, convolution, system interconnection, and
sinusoidal response. The Fourier and Laplace transforms are developed for the discussion of frequencydomain
applications. Sampling and quantization of continuous waveforms (A/D and D/A conversion) are
analyzed, leading to the discussion of discrete-time FIR and IIR systems, recursive analysis, and
realization. The Z-transform and the discrete-time Fourier transform are developed, and applied to the
analysis of discrete-time signals and systems.
Topics Covered:
1. Basic signals and systems
a. Continuous and discrete time signals
b. Signal manipulation
c. Basic system properties
2. Linear time invariant (LTI) systems
a. Discrete time convolution
b. Continuous time convolution
c. Relationship of generic system properties to the impulse response for an LTI system
d. Use of differential and difference equations as models for LTI systems
3. Continuous time Fourier transform (CTFT)
a. Definition and derivation of the CTFT
b. Fourier transform representation of periodic signals using the CTFT
c. Properties of the CTFT
d. Convolution-multiplication duality and the CTFT
4. Discrete time Fourier transform (DTFT)
a. Definition and derivation of the DTFT
b. Fourier transform representation of periodic signals using the DTFT
c. Properties of the DTFT
d. Convolution-multiplication duality and the DTFT
5. Sampling
a. Derivation and application of the Sampling Theorem for bandlimited signals
b. Derivation and application of bandlimited (sinc) interpolation
c. Aliasing
6. The Laplace transform
a. Definition and relationship of Laplace transform to CTFT
b. Region of convergence
c. Inverse Laplace transform via partial fraction expansion method
d. Geometry evaluation of the CTFT via the pole zero plot.
e. Properties of the Laplace transform
f. Relationship of causality and stability to structure in the Laplace s plane
7. Z transform
a. Derivation of Z transform from Laplace assuming ideal, delta function sampling
b. Relationship of Z transform to DTFT
c. Region of convergence
d. Inverse Z transform via partial fraction expansion method
e. Geometry evaluation of the DTFT via the pole zero plot.
f. Properties of the Z transform
g. Relationship of causality and stability to structure in the Z transform z plane
Course Outcomes:
Students should:
1. Demonstrate the ability to recognize, analyze, and manipulate basic continuous time (CT) and
discrete time (DT) signals and to classify continuous and discrete time systems as to their linearity,
time invariance, causality, and stability.
2. Analyze both continuous and discrete linear time invariant (LTI) systems in the time domain
including leveraging the use of the impulse response, setting up and carrying out convolution
integrals and sums, using mathematical properties of the convolution operator to manipulate,
combine, and decompose systems and sub-systems, determine stability and causality from the
impulse response, and use linear constant coefficient differential / difference equations (LCCDEs) as
models for LTI systems.
3. Analyze both CT and DT LTI signals and systems in the frequency domain by using the appropriate
Fourier representation, including calculation of forward and inverse Fourier representation,
determining outputs using the frequency response, characterizing systems based on their frequency
response characteristics, and applying relevant properties of these representations.
4. Apply the Shannon sampling theorem and the sinc interpolation formula and quantify the effects of
aliasing.
5. Analyze CT and DT systems using the bilateral Laplace and Z transforms, including calculating
regions of convergence (ROCs) and interpreting the implications of those regions for the forms of
time domain behavior, determining specific time signals from their transform and ROCs using partial
fraction expansion, relating LCCDEs to the corresponding transform and vice-versa, determining
causality and stability from ROCs, and interpreting the relationship between pole / zero locations and
system frequency response.
Contribution of course to meeting
Signal refers to both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology.
In signal processing, a signal is a function that conveys information about a phenomenon.[1] Any quantity that can vary over space or time can be used as a signal to share messages between observers.[2] The IEEE Transactions on Signal Processing includes audio, video, speech, image, sonar, and radar as examples of signals.[3] A signal may also be defined as any observable change in a quantity over space or time (a time series), even if it does not carry information.[a]
In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with cell signaling. Signaling theory, in evolutionary biology, proposes that a substantial driver for evolution is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typically provided by a sensor, and often the original form of a signal is converted to another form of energy using a transducer. For example, a microphone converts an acoustic signal to a voltage waveform, and a speaker does the reverse.[1]
Another important property of a signal is its entropy or information content. Information theory serves as the formal study of signals and their content. The information of a signal is often accompanied by noise, which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals (crosstalk). The reduction of noise is covered in part under the heading of signal integrity. The separation of desired signals from background noise is the field of signal recovery,[5] one branch of which is estimation theory, a probabilistic approach to suppressing random disturbances.
Signals can be categorized in various ways. The most common[verification needed] distinction is between discrete and continuous spaces that the functions are defined over, for example, discrete and continuous-time domains. Discrete-time signals are often referred to as time series in other fields. Continuous-time signals are often referred to as continuous signals.
A second important distinction is between discrete-valued and continuous-valued. Particularly in digital signal processing, a digital signal may be defined as a sequence of discrete values, typically associated with an underlying continuous-valued physical process. In digital electronics, digital signals are the continuous-time waveform signals in a digital system, representing a bit-stream.
In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified into analog signals and digital signals; according to the determinacy of signals, classified into deterministic signals and random signals; according to the strength of signals, classified into energy signals and power signals.
Two main types of signals encountered in practice are analog and digital. The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants. Digital signals are quantized, while analog signals are continuous.
An analog signal is any continuous signal for which the time-varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the sound pressure. It differs from a digital signal, in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values.[6][7]
The term analog signal usually refers to electrical signals; however, analog signals may use other mediums such as mechanical, pneumatic or hydraulic. An analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. In an electrical signal, the voltage, current, or frequency of the signal may be varied to represent the information.
Any information may be conveyed by an analog signal; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure. The physical variable is converted to an analog signal by a transducer. For example, in sound recording, fluctuations in air pressure (that is to say, sound) strike the diaphragm of a microphone which induces corresponding electrical fluctuations. The voltage or the current is said to be an analog of the sound.
A digital signal is a signal that is constructed from a discrete set of waveforms of a physical quantity so as to represent a sequence of discrete values.[8][9][10] A logic signal is a digital signal with only two possible values,[11][12] and describes an arbitrary bit stream. Other types of digital signals can represent three-valued logic or higher valued logics.
c80f0f1006