1) What is the difference between a continuous spectrum and a line spectrum? 2)
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Question
1) What is the difference between a continuous spectrum and a line spectrum?
2) What is the fundamental difference between a continuous signal and a discrete signal?
3) Why are linear time invariant (LTI) systems so important in engineering and engineering analysis?
4)When solving a second-order differential equation of the form shown below, what effect can changing the coefficients a, b, and c have on the waveform of the solution of the differential equation (i.e., waveform of i as a function of time)?
a d^2x/dt^2 + b dx/dt + cx = k, when a,b,c and k are constant
5) What is meant by the frequency response of a system? '
7)What is meant by the steady state and transient response of a system? Which of the two is controlled by the input applied to the system, and what factors control the other response?
Explanation / Answer
1.)Continous spectra is the rainbow effect that you see when white light passes through a prism. It includes all of the visible light wavelengths, from about 380 nm to 780 or so.
Bright line spectra show only those colors that are emitted from a substance. Rather than seeing all of the wavelengths, you would see only those associated with that material; i.e. you might see a line at 450 nm, another at 610, and that could be it.
In a bright line spectra, you will see large areas of black broken up by the bright lines of color that identify the emitter. Each compound has it's own spectra, akin to a fingerprint. This is how we know what compounds are in the sun, stars, etc. We also use this to identify unknown compounds in the lab.
2.)A continuous signal is one that is measured over a time axis and has a value defined at every instance. The real world is continuous (ie. analog). A discrete signal is one that is defined at integers, and thus is undefined in between samples (digital is an example of a discrete signal, but discrete does not have to imply digital). Instead of a time axis, a discrete signal is gathered over a sampling axis. Discrete signals are usually denoted by x[k] or x[n], a continuous signal is x(t) for example. Laplace transforms are used for continuous analysis, Z-transforms are used for discrete analysis. Fourier transforms can be used for either.
3.)It is often useful (or necessary) to break up a system into smaller pieces for analysis. Therefore, we can regard a SIMO system as multiple SISO systems (one for each output), and similarly for a MIMO system. By far, the greatest amount of work in system analysis has been with SISO systems, although many parts inside SISO systems have multiple inputs
4.)the change in coefficients may lead to change in properties of wave that is its direction,probability etc.
5.)Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. In simplest terms, if a sine wave is injected into a system at a given frequency, a linear system will respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Also for a linear system, doubling the amplitude of the input will double the amplitude of the output. In addition, if the system is time-invariant, then the frequency response also will not vary with time.
7.)A control system is a device, or set of devices, that manages, commands, directs or regulates the behavior of other device(s) or system(s). Industrial control systems are used in industrial production.
There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls. There is also fuzzy logic, which attempts to combine some of the design simplicity of logic with the utility of linear control. Some devices or systems are inherently not controllable.
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