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.
In electrical engineering, the Fourier series is used to analyse signal waveforms to find their frequency contest. This is needed to design communication systems that will deliver the signal to the receiver in good shape. If you go on to study the next step, the Fourier Transform, that is really interesting for electrical engineering because a signal can be a function of time and it can also be a function of frequency. These two representations of the same signal form a Fourier-Transform pair. So the spectrum is the FT of the waveform, while the waveform is reverse-FT of the spectrum. Fourier series are also good because they are the simplest example of the whole new subject of orthogonal polynomials, and these are also important in engineering because they are used to find solutions of the differential equations that are thrown up by physical systems. So, while a violin string can be analysed by a Fourier series which explains the harmonics that give a violin its distinctive sound, something more complex like a drum-skin can also be analysed, but the answer comes out in terms of another type of orthogonal function, the Bessel functions, instead of circular functions (sines and cosines). This explains why you get a note from a drum but it's less well defined, because the upper modes are not harmonically related to the fundamental.
Explain the difference between series and parallel connections.
in parallel the voltage stays the same in parallell the current is shared in series the voltage is shared in series the current stays the same the main similarity between parallel and series circuits is when voltage increases, current increases.
Basically Pi 3.14.... Etc. is the number that is used for circles. Should you want to build a building with a cirlce roof you'll need to find the circumference. Basically you multiply pi with the diameter and you get the circumference. There is a lot more to it than that; pi turns up in many contexts which aren't about circles. One is Fourier series, used in problems ranging from the distribution of heat in physics to acoustics, image analysis, and in filters in circuits in electrical and computer engineering. The formulas for Fourier series involve pi. I think you will find that pi turns up in every branch of engineering.
if resonant ckts r connected serially, it is called serial resonant ckt.. if resonant ckts r connected parallely, it is called parallel resonant ckt..
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.
Fourier series and the Fourier transform
z transform is related to discrete time signal while fourier series is related to continuous time signal. z transform=sigmalm -infinty to +infinity x(n)z-n
what are the limitations of forier series over 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.
A Fourier series is a series of sine and cosine harmonics of a particular frequency. For example sinf+icosf + 3 sin2f+ 5icos2f... where the successive terms are multiples of the fundamental frequency f. It is typical ( but as far as I know not required) that complex numbers are used. A Fourier transform converts a time domain wave form (like a sound wave) into the coefficients of the corresponding Fourier series. A DFT is a digital approximation to a Fourier transform, usually using something like the Cooley-Tuckey Fast Fourier Transform (FFT) for efficiency. The underlying Fourier theorem is something like: Every bounded periodic continuous (needed to avoid Gibbs) function , or wave form, can be written as the sum of its Fourier series. i.e. It is a sum of sines and cosines In otherwords, you take a wave form in the time domain like a sound wave and break it into its components (various frequencies) by the Fourier Transform. The results of the Transform are the coefficients of the Fourier series. The wave form of a voice converted to components (and perhaps a little more) is a voiceprint.
Joseph Fourier was the French mathematician and physicist after whom Fourier Series, Fourier's Law, and the Fourier Transform were named. He is commonly credited with discovering the greenhouse effect.
Spectral analysis of a repetitive waveform into a harmonic series can be done by Fourier analyis. This idea is generalised in the Fourier transform which converts any function of time expressed as a into a transform function of frequency. The time function is generally real while the transform function, also known as a the spectrum, is generally complex. A function and its Fourier transform are known as a Fourier transform pair, and the original function is the inverse transform of the spectrum.
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.
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.