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The Fast Fourier Transform is an implementation of the Discrete Fourier Transform. The DFT is a method of processing a time-sampled signal (eg, an audio wave) into a series of sines and cosines. As such, it is not a sorting algorithm, so this question does not make any sense.
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.
The fractiona lFourier transform (FRFT) is a potent tool to analyze the chirp signal. However,it failsin locating the fractional Fourier domain (FRFD)-frequency contents which is requiredin some applications. The short-time fractional Fourier transform (STFRFT) is proposed to solve this problem
The fourier transform is used in analog signal processing in order to convert from time domain to frequency domain and back. By doing this, it is easier to implement filters, shifters, compression, etc.
we use fourier transform to convert our signal form time domain to frequency domain. This tells us how much a certain frequency is involve in our signal. It also gives us many information that we cannot get from time domain. And we can easily compare signals in frequency domain.
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 .
The Fast Fourier Transform is an implementation of the Discrete Fourier Transform. The DFT is a method of processing a time-sampled signal (eg, an audio wave) into a series of sines and cosines. As such, it is not a sorting algorithm, so this question does not make any sense.
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.
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 the transform operation and to the function it produces.
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 fractiona lFourier transform (FRFT) is a potent tool to analyze the chirp signal. However,it failsin locating the fractional Fourier domain (FRFD)-frequency contents which is requiredin some applications. The short-time fractional Fourier transform (STFRFT) is proposed to solve this problem
A fast fourier transform is an algorithm that converts time or space to frequency, or vice versa. They are mainly used in engineering, math and sciences.
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.
K space refers to a space where things are in terms of momentum and frequency instead of position and time and the way you convert between real space and k-space (or Fourier space) is a mathematical transformation called the Fourier transform (and Inverse Fourier transform). This K-space also exists in classical physics. In quantum mechanics the space is made up of discrete values of K, whereas in classical physics K can take on a continuum of values.
A Z-transform is a mathematical transform which converts a discrete time-domain signal into a complex frequency-domain representation.
The fourier transform is used in analog signal processing in order to convert from time domain to frequency domain and back. By doing this, it is easier to implement filters, shifters, compression, etc.
it is used for linear time invariant systems