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Questions tagged [dct]

The Discrete Cosine Transform expresses a sequence of finitely many data points in terms of a sum of cosine functions oscillating at different frequencies.

DCTs are important to numerous applications in science and engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sine functions is critical in these applications: for compression, it turns out that cosine functions are much more efficient (as described below, fewer are needed to approximate a typical signal), whereas for differential equations the cosines express a particular choice of boundary conditions.

Source: wikipedia

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Fast DCT implementation

I'm having trouble figuring out how to follow the fast 8x8 DCT algorithm diagrams found in the following two papers: (1) A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al. and (2) Practical Fast 1-D DCT Algorithms With…
Mokosha
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Why zig zag manner scan is used in DCT for image compression?

I am not sure why zig zag manner scan is used in DCT. I can guess that might because it moves from low frequency component to high frequency component and as most of the energy is stored in low frequency component that's why this way of scan is…
Lakshmi
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Why are there only a few high frequency components in the Discrete Cosine Transform?

I am learning about the Discrete Cosine Transform (DCT) and I read somewhere that, in general, images have very few high frequency components. Can someone give me an intuitive explanation for why this is so? Is this assumption violated in any…
Joebevo
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FFTW: Logical array size in r2r transform?

I'm taking a multidimensional discrete cosine transform (FFTW_REDFT11) in FFTW, and am unsure how to compute the scaling factor. According to the documentation, taking the forward and reverse transforms results in the original image multiplied by a…
sudo make install
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DCT of 4x4 checkerboard matrix - what's the correct result?

I'm trying to work out what the correct solution is for a DCT of a 4x4 checkerboard matrix (let's call it A) and for a matrix of ones (let's call it B). So A is: 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 And B is: 1 1…
Johnny
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Understanding the DCT even symmetry

I wanted to prove to myself why the DCT is better than the DFT and heres a brief of what I understand so far. The DTFT works with a finite sampled input signal, but the frequency response obtained is continuous and periodic. The DFT samples the DTFT…
Bonavia
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What is the DCT used for in Computer Vision?

DCT, what is the benefit of using it for image processing? I noticed that it is used in JPEG compression. Can i use it for something else? Is it useful for motion detection? Is it useful for compressing further? If I convert an image to its DCT I…
Andrew Simpson
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Discrete Cosine Transform (DCT)

I need your help. My lecturer told me to do a study to finish the task that she gave us yesterday but the thing is there is no specific explaination on how to solve the question. Through the task, she gave us only this information. I went through…
NURA
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Do DCT each output coefficients have to be orthogonal?

I have a question: Do DCT each output coefficients have to be orthogonal? Here DCT is DCT-II type. It is used by the jpeg compression algorithm.
Carter
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Why do we quantize high frequencies coarsely, shouldn't it be the opposite?

Also, in Huffman Coding, why do we use fewer bits for high frequency data. I don't get the intuition. Shouldn't it be the opposite or does this have to do something with the psychoacoustic model of the human hearing which says that our cochlea is…
Ali Gajani
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«Energy compaction» justification

DCT, KLT and PCA is often said to be preferred due to their «energy compaction» properties, where an N-element vector can be expressed as K
Knut Inge
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Combine two 1D 16 band DCTs to one 32 band without converting to time-domain

Imagine someone had a signal of 32 samples. They cut it to two 16 sample pieces, converted to DCT frequencies, using DCT4. What I get is these two arrays. My goal is to get a x2 higher freq resolution DCT, x2 less time resolution. Of course, I can…
shal
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Notation in two-dimensional DCT

In this DCT video isn't $X^c$ the input image and what does the superscript $c$ signify? Why do they call $X^c$ "DCT coefficients " although it's the input image?
Suvi
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What frequency does each bin of a Discrete Cosine Transform represent?

I have applied a DCT (type 2) to a vector of values acquired from a sensor, of length $N = 8$. I received a vector of DCT coefficients. How can I find out the frequency of each bin in Hz? The sampling frequency of initial values is 10000 Hz.
Azazel
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Solve for minimum and maximum value of dct coefficient

Solve for minimum and maximum value of dct coefficient
Ashley
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