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Fourier analysis is used in many places. Three examples are digital filtering, where a signal is converted to frequency domain, certain bands are removed or processed, and then converted back to time domain; your cell phone or its headset, if it has advanced noise cancellation technology; and the telephone system itself, where digital filtering is used to minimize bandwidth demands.
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In Mathematics what is meant by the Fourier series?
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
How does the graph of Fourier Series differ to the graph of Fourier Transform?
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.
Are proportions used in real life?
Proportions are used in real life to determine prices of things.
Why fourier transform is used in digital communication why not laplace or z transform?
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How are opposites and reciprocals used in real life situations?
Believe it or not, school is a real life situation. If you are using it in school it real life for you.
Can a discontinuous function be developed in a Fourier series?
Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
In Mathematics what is meant by the Fourier series?
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
In Fourier transformation and Fourier series which one follows periodic nature?
The Fourier series can be used to represent any periodic signal using a summation of sines and cosines of different frequencies and amplitudes. Since sines and cosines are periodic, they must form another periodic signal. Thus, the Fourier series is period in nature. The Fourier series is expanded then, to the complex plane, and can be applied to non-periodic signals. This gave rise to the Fourier transform, which represents a signal in the frequency-domain. See links.
How does the graph of Fourier Series differ to the graph of Fourier Transform?
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.
What are the applicaton of fourier series?
It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.
What is relation between laplace transform and fourier transform?
The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.
When are Sin Cos and Tan used in life?
A huge practical application of trig is Fourier series. Fourier series says you can represent any periodic function as a sum of infinite sines and cosines. By constructively/destructively overlapping different frequencies with specific amplitudes, you can mimic a function, or signal, or different types of boundary conditions. With more terms, aka more frequencies, you get closer and closer to the actual function. Fourier series is the only way to solve some types of differential equations. In digital signal processing, fourier series is extremely important because it gives the option of changing a time domain signal into a frequency domain signal. This allows you to manipulate signals in ways one couldn't imagine. Its used in filters, compression, data transmission, etc. The end results affect cell phones, televisions, any kind of digital filter, etc...
What is the fourier series?
It's an infinite sum of sines and cosines that can be used to represent any analytic (well-behaved, like without kinks in it) function.
Where is the Discrete Fourier Transform used?
The Discrete Fourier Transform is used with digitized signals. This would be used if one was an engineer as they would use this to calculate measurements required.
What is the real ship used on the tv show suite life on deck?
it's not a real ship, it's a set, just like the hotel in the original series.
Difference between fourier series and z-transform?
Laplace = analogue signal Fourier = digital signal Notes on comparisons between Fourier and Laplace transforms: The Laplace transform of a function is just like the Fourier transform of the same function, except for two things. The term in the exponential of a Laplace transform is a complex number instead of just an imaginary number and the lower limit of integration doesn't need to start at -∞. The exponential factor has the effect of forcing the signals to converge. That is why the Laplace transform can be applied to a broader class of signals than the Fourier transform, including exponentially growing signals. In a Fourier transform, both the signal in time domain and its spectrum in frequency domain are a one-dimensional, complex function. However, the Laplace transform of the 1D signal is a complex function defined over a two-dimensional complex plane, called the s-plane, spanned by two variables, one for the horizontal real axis and one for the vertical imaginary axis. If this 2D function is evaluated along the imaginary axis, the Laplace transform simply becomes the Fourier transform.
Are proportions used in real life?
Proportions are used in real life to determine prices of things.
