discrete fourier transformer uses digital signals whereas the fast fourier transform uses both analog and digital.
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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 held 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 8-12are 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.
The fundamental components of digital image processing are computer-based algorithms. Digital image processing allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and signal distortion during processing.
there are two types of image processing. 1.analog 2.digital.
discrete fourier transformer uses digital signals whereas the fast fourier transform uses both analog and digital.
digital fourier analyzer analyses the signals in the form of fast fourier transform.
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A Discrete Fourier Transform is simply the name given to the Fourier Transform when it is applied to digital (discrete) rather than an analog (continuous) signal. An FFT (Fast Fourier Transform) is a faster version of the DFT that can be applied when the number of samples in the signal is a power of two. An FFT computation takes approximately N * log2(N) operations, whereas a DFT takes approximately N^2 operations, so the FFT is significantly faster simple answer is FFT = Fast DFT
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 held 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 8-12are 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.
Laplace Transforms are used primarily in continuous signal studies, more so in realizing the analog circuit equivalent and is widely used in the study of transient behaviors of systems. The Z transform is the digital equivalent of a Laplace transform and is used for steady state analysis and is used to realize the digital circuits for digital systems. The Fourier transform is a particular case of z-transform, i.e z-transform evaluated on a unit circle and is also used in digital signals and is more so used to in spectrum analysis and calculating the energy density as Fourier transforms always result in even signals and are used for calculating the energy of the signal.
Albert A. Gerlach has written: 'Role of the sectionalized Fourier transform in high-speed coherence processing' -- subject(s): Digital techniques, Fourier transform spectroscopy, Signal processing 'Theory and applications of statistical wave-period processing' -- subject(s): Radar, Random noise theory, Signal theory (Telecommunication), Sonar
The use of the Laplace transform in industry:The Laplace transform is one of the most important equations in digital signal processing and electronics. The other major technique used is Fourier Analysis. Further electronic designs will most likely require improved methods of these techniques.
Jim B. Breckinridge has written: 'Basic optics for the astronomical sciences' -- subject(s): Astronomical instruments, Optics, Mathematics, Fourier transform optics, Image processing, MATLAB, Digital techniques
z transform perhaps? It's basically a laplace transform for discrete values rather than continuous (although this probably makes no sense to you if you're in algebra. This is stuff used in digital signal processing for Electrical Engineering).
The z-transform is commonly used in digital signal processing to analyze and manipulate discrete-time signals and systems. It allows for the representation of sequences in the complex frequency domain, facilitating the analysis of system behavior and the design of filters and controllers for digital systems.
Nadder A. Hamdy has written: 'Applied signal processing' -- subject(s): Digital Electric filters, Digital techniques, Electric filters, Electric filters, Digital, Equipment and supplies, Fourier transformations, Signal processing