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In Technology

The Fourier series is an expression of a pattern (such as an electrical waveform or signal) in terms of a group of sine or cosine waves of different frequencies and amplitude.… This is the frequency domain. The Fourier transform is the process or function used to convert from time domain (example: voltage samples over time, as you see on an oscilloscope) to the frequency domain, which you see on a graphic equalizer or spectrum analyzer. The inverse Fourier transform converts the frequency domain results back to time domain. The use of transforms is not limited to voltages. (MORE)

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A fast Fourier transform is an efficient algorithm for working out the discrete Fourier transform - which itself is a Fourier transform on 'discrete' data, such as might be he…ld on a computer. Contrast this to a 'continuous Fourier transform' on, say, a curve. One would need an infinite amount of data points to truly represent a curve, something that cannot be done with a computer. Check out: The Scientist And Engineer's Guide To Digital Signal Processing. It is a free, downloadable book that deals, inter alia, with Fourier transforms; chapters 8-12 are germane to your question. This is a highly practical, roll-yer-sleeves-up book for, as the title says, scientists and engineers, but Smith describes the underlying theory well. The sample code supplied with the book is in BASIC and FORTRAN, of all things; the author does this for didactic purposes to make the examples easy to understand rather than efficient. (MORE)

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Fourier transform. It is a calculation by which a periodic function is split up into sine waves.

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the main application of fourier transform is the changing a function from frequency domain to time domain, laplaxe transform is the general form of fourier transform .

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The Fourier transform is a mathematical transformation used to transform signals between time or spatial domain and frequency domain. It is reversible. It refers to both t…he transform operation and to the function it produces. (MORE)

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In Science

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 correspo…nding 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. (MORE)

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The fast fourier transform, which was invented by Tukey, significantly improves the speed of computation of discrete fourier transform.

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As it has been already hinted, Fourier Series is used for periodic signals. It represents the signal by the discrete-time sequence of basis functions with finite and concrete …amplitude and phase shift. The basis functions, according to the theory, are harmonics with the frequencies, divisible by the frequency of the signal (which coincides with the frequency of the 1st main harmonic). All the harmonics with the number>1 are called higher harmonics, whereas the 1st one is called - the main harmonic. After reminding the mathematical properties of the signal we can maintain, that sometimes harmonics with even or odd numbers are absent at all. There phases are sometimes always equal to 0 and 180 degrees or to 90 and -90 degrees. Fourier series are known to exist in sinus-cosinus form, sinus form, cosinus form, complex form. The choice depends on the problem solved and must be convenient for further analysis. Fourier tranform is invented and adjusted for aperiodic signals with integrated absolute value and satisfaction of Diricle conditions. It's worth saying, that Dirichle conditions is the necessary requirement for Fourier series too. Fourier representation of aperiodic signals is not discrete, but continious and the amplitudes are infinitely small. They play the role of the proportional coefficients. there are links between Fourier series of periodic signal and Fourier transform. These links may be easily found in almost all the books on classical Fourier analysis of signals. For example, see Oppenheim, Djervis and others. (MORE)

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20c + 5 = 5c + 65 Divide through by 5: 4c + 1 = c + 13 Subtract c from both sides: 3c + 1 = 13 Subtract 1 from both sides: 3c = 12 Divide both sides by 3: c = 4 20c + 5 = 5c …+65 20c - 5c= 65 - 5.
15c = 60.
15c/15 = 60/15.
c = 4 (alternative method). (MORE)

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In Science

tanx = 2*(sin2x - sin4x + sin6x - ... ) However, be warned that this series is very slow to converge.