why do we use discrete wavelet transform?
81441
Two reasons:\n1. Because it results in a finite spectrum result for a signal. Fourier Transform typically results in infinite spectrum result for a function (e.g if the function has C1 or C0 discontinuities e.g. square wave, triangular wave, ramp, sawtooth)\n\n2. FT assumes that signals are "stationary" and that their frequency-domain can be computed over infinite-time window and will not change. This is unrealistic - most real-world signals are not stationary in a window >10ms (e.g. speech, telecomms, EKG). WT computes its transform based on both a time- and frequency-window.\n\nAs to why you compute DWT rather than the direct Continuous (integral formulation) WT, it's for the same simple reason you generally use DFT instead of CFT - because it's mathematically tractable and lends itself to efficient digital computation (order(NlogN) time); also this formulation can be very efficiently parallelised whether in hardware or software esp. if N is a power of 2 e.g. 64,256,512,1024,... and people have developed these implementations very far (they're a standard toolbox feature or hardware IP).\n\nI don't know the theoretical links offhand but they should be trivial to find.
194578
Yes, it is  equivalent to upsampling by the factor.\nOf course the next question then is, 'why upsample more than you need to?' (especially as it requires a lot more processing power/silicon die area/cost). That could be for a variety or reasons, including needing to transmit the signal over a physical channel before the final downsample eg. audio separates with S/PDIF connection between them.
84915
The Fourier transform is used throughout physics. All the Fourier representation is, is an expansion of some variable, function or data in terms of sines and cosines.\n\nThis is valuable because:\n1. Simple harmonic oscillators are a very valuable model in physics (in mechanics, quantum mechanics, electromagnetism, etc), and the solutions of the simple harmonic equation are sines and cosines. Therefore sines and cosines are a natural basis to use in physics. \n2. The eigenfunctions of the infinitesimal generator of translations are complex exponentials, which can be expanded easily in the sum of a sine and a cosine by Euler's formula. \n\nTherefore, an expansion in sines and cosines is very valuable, because they can be used as a parsimonius representation of many phenomena in physics. In otherwords, it is a compact way to describe many physical processes. \n\nAnother reason that the Fourier transform is important in physics is that it is very useful for solving equations in physics like the heat equation, Maxwell's equations, fluid mechanics equations, the wave equation, etc. \n\nAnother reason that the Fourier transform is useful in physics is that many important physical properties are captured in things like dispersion relations. This even lead to Schrodinger's equation. Fourier transform pair uncertainty principles are reflected in the Heisenberg uncertainty principle. \n\nHow does the Fourier transform show up in nature? All over the place, such as in the spectra of gases, stars, etc. Rainbows are a visual example of a Fourier transform in nature.
935998
Just add them together sample by sample. Squaring them is destroying the negative values. (Just think of a sine wave.) \n The distortion must be terrible!\n\n Note however if when you add them the sum exceeds a certain value you will get some overload. If the sample values are modest to start with this will not happen.
654455
Two tutorials:\n\nhttp://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html\nhttp://perso.wanadoo.fr/polyvalens/clemens/wavelets/wavelets.html\n\nAnd a list of  Internet Sources:\nhttp://www.cosy.sbg.ac.at/~uhl/wav.html
562495
Well the Discrete Cosine Transform compacts a lot of energy into low frequencies, so the jist of compressing using it is to drop off the high frequency image components until the desired compression is reached.  The reason this works is because broad regions of color and shape are preserved (they are low frequency), so the image is still recognizable.\n\nWith matlab you will probably need the signal processing toolkit (they might include it these days), and you will just use the function dct(x).\n\nhttp://www-ccs.ucsd.edu/matlab/toolbox/signal/dct.html\n\nIf you look at the code sample, you can use that to find the DCT coefficients that have the most energy and drop the rest.  In the example it shows 99% as the threshold, but you can use less if you want more compression.  Then you will run an IDCT to reconstruct the image.  One last thing... before you do all this you need to make sure the input image has been imported into a matlab friendly matrix format.
112415
MatLab is a very powerfull program for signal processing and reserch for this particular reason this program is not free. there are a variaty of ILEGAL's ways to get it and that can cause you a lot of troubles (thrust me... it's scary) \n\nyou will find programs like e-donkey or i-mesh where you can do that kind of ilegal download.\n\nones again, I highly recomend not to use this way and make an effort to buy this program since you will be able to use a wide variaty of tools and support that you will not be able to use in the pirate one.\n\nhope this helps.\n\nLG2
387983
A digital signal is composed only of electrical pulses representing either zero or one. Because digital signals are made up only of binary streams, less information is needed to transmit a message. Digital encoding therefore increases the capacity of a given radio frequency. Furthermore, only digitized information can be transported through a noisy channel without degradation\n\nSignals that are recorded in analogue format are modulated, ie their information is contained in amplitude or amount of signal. Digital, conversely, is either on or off, and amplitude is identified in a different way
57773
What kind of enhancement?  Just how much work do you expect us to do?  Also, I'm assuming DCT is equivalent to DFT and you're just asking what to do with the signal's spectrum.
155410
Do a Google search for "Fourier Transform."  I'm sure that someone has a proof on the web.
1802
I haven't tried it, but check out MatPy (linked below).  Another possibility is Numerical Python (also linked below).
297836
Not much.  A while ago, it was unclear which representations would be most useful.  Binary is still useful for bit-operations and bit-math (shift, XOR, etc), hex is useful for viewing stack and/or program data.  Octal... not so useful anymore.
1148068
IFT means Inverse Fourier Transform\nDFT means Discrete Fourier Transform
973309
Im not sure what a Cb Cr is.\n\nDownsampling is "reducing the sampling rate".\nI would use the interp1 inter2 or interpn functions.  \n\nIf you use interp1 you can use pchip which has great data "fidelity".  You could also use nearest neighbor which is really fast, but a little junky.
1031386
Do you mean Fourier transform? \n\nIt's based on the idea that all signals are composed of simple sinusoidal signals at different frequencies.  The fourier transform converts a signal from time-domain, to frequency-domain. So when you go to graph the signal, instead of seeing the strength of the signal vs. time (time domain), you see it in terms of frequency (frequency domain). The Fourier transform provides an easy way to convert a time-domain signal into frequency domain, and vice-versa.\n\nThis is really nice when you want to see what parts of a signal will pass through a filter, or seeing what happens to your signal after a frequency shift, or checking sampling rates, etc.,etc.
73968
I have never used them, but I have heard they have uses in certain kinds of electrical engineering.  I think it involves phase shifts of period functions like sine waves.  Also, there are occasional problems where you start in the real numbers and end in the real numbers, but by doing the problem in the complex domain, certain difficult problems become solvable.  I think Cauchy integrals are used for this purpose.
468151
to convert an analog to digital.. you have to quantify the signal next you have to sampling.\n\nmeans that you have to divide the amplitudes to discret values. and the frequencies to discret.\n\nat the end you can encode the signal and compress it.\n\nyou run in the oposite way to convert an analog to digital signal.\n\nhope this can help