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Quartz? sorry if im wrong
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Overflow and underflow are both errors resulting from a shortage of space. On the most basic level, they manifest in data types like integers and floating points. Unlike the physical world, the number stored in a computer exists in a discrete number of digits.
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Use the convolution integral to determine the output of an LTI system with impulse response h(t) to input x(t) specified below.
h(t) = 4e^-6t-1 u(t+1) x(t)=2u(t – 2)
Explanation:
y(t)=∫0th(t−λ)f(λ)dλ
Start with a linear time-invariant (LTI) system (in box). There is an input to the system, x(t), and an output from the system, y(t).
Now consider the same system with the input as an impulse, δ(t). The output is then, by definition, the impulse response, h(t).
If we use a delayed impulse into the system, the output is just the impulse response with the same delay.
Because of linearity, if we scale the input by any factor, the output will be scaled by the same factor. In particular, we can scale the input (and hence the output) by the factor x(λ)dλ.
If we integrate the input, the output is also integrated. In this case we'll take the upper limit of the integration to be t+; but it could just as well have been positive infinity. We could also take the lower lower limit to be negative infinity.
By the sifting property of the impulse function we know that (if λ>0, t>0):
∫0tδ(t−λ)x(λ)dλ=x(t)
Therefore the input to the system is x(t)
If the input is x(t), then the output must be y(t) (by definition, from the first diagram).
Equating the outputs of the last two diagrams leads directly to the convolution theorem:
y(t)=∫0th(t−λ)f(λ)dλ
You will get the answer for your question in this text so first read it and then you will get the answer
“ Earliest records show a spoon shaped compass made of lodestone or magnetite ore, referred to as a "South-pointer" dating back to sometime during the Han Dynasty (2nd century BCE to 2nd century CE). The spoon-shaped instrument was placed on a cast bronze plate called a "heaven-plate" or diviner's board that had the eight trigrams (Pa Gua) of the I Ching, as well as the 24 directions (based on the constellations), and the 28 lunar mansions (based on the constellations dividing the Equator) . Often, the Big Dipper (Great Bear) was drawn within the center disc. The square symbolized earth and the circular disc symbolized heaven. Upon these were inscribed the azimuthal points relating to the constellations. Its primary use was that of geomancy (prognostication) to determine the best location and time for such things as burials. In a culture that placed extreme importance on reverence for ancestors, this remained an important tool well into the 19th century. Even in modern times there are those who use this divination concepts of Feng Shui (literally, of wind and water) for locating buildings or fortuitous times and locations for almost any enterprise. There is a story that the first Chin emperor used the divining board and compass in court to affirm his right to the throne. Primarily, the compass was used for geomancy for a long time before it was used for navigation
Ancient Chinese alchemists realized that the magnetite ore would point towards a magnetic north. Their understanding was not total, since they thought that there were north pointers and south pointers. "The lodestone follows a maternal principle. The needle is struck out from the iron (originally a stone) and the nature of mother and son is that each influences the other, and they communicate together. The nature of the needle is to return to its original completeness. As its body is very light and straight, it must indicate straight lines. It responds to the chhi by orientation, being central to the earth and deviating in various directions. To the south it points to the Hsuan-Yuan constellation, hence to the hsiu Hsing and therefore to the hsiu Hsu in the north, along the axis Ting-Kuei. The yearly differences follow the elliptic, and all such phenomena can be understood." (from Master Kuan's Geomantic Instructor), 8th century CE
By the time of the T'ang dynasty (7-8th century CE) , Chinese scholars had devised a way to magnetize iron needles, by rubbing them with magnetite, and then suspending them in water (early 11th century). They also had observed that needles cooled from red heat and held in the north-south orientation (the earth's axis) would become magnetic. These more refined needle compasses could then be floated in water (wet compass), placed upon a pointed shaft (dry compass) or suspended from a silk thread. Consequently, they were much more useful for navigation purposes since they were now much more portable (and smaller). During the Sung dynasty (1000 CE) many trading ships were then able to sail as far as Saudi Arabia without getting lost. The plate was converted to a bowl, and retained the markings of the heaven's plate around its circumference, in a simplified form. The inner circle had the eight trigrams and the outer circle the 24 directions (based on azimuth points).”