# 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.

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### What is the difference between a Fourier transform and a cosine transform?

In speech recognition, the front end generally does signal processing to allow feature extraction from the audio stream. A discrete Fourier transform (DFT) is applied twice in this process. The first ...
18k views

### Fast Cosine Transform via FFT

I want to implement the Fast Cosine Transform. I read on wikipedia, that there is a fast version of the DCT which is similarly computed to the FFT. I tried to read the cited Makhoul* paper, for the ...
2k views

### Could a DCT be used for an audio magnitude spectrum rather than DFT?

From what I understand, the DCT has half the bin size as a DFT of the same size N. The DFT also includes phase information, but often this is not needed when only the magnitude spectrum is desired. ...
4k views

### Relationship between DCT and PCA

I have a basic implementation knowledge of the 2D 8x8 DCT used in image & video compression. Whilst reading about Principle Component Analysis, I can see a lot of similarity, albeit PCA is clearly ...
8k views

### Is this a correct interpretation of the DCT step in MFCC calculation?

This is a continuation of the discussion here. I would comment there, but I don't have 50 rep so I'm asking a new question. Here's how I understand the DCT step in the MFCC calculation process: The ...
361 views

### JPEG steganography

Aside from Jsteg of Derek Upham, Outguess of Neils Provos, and F5 (improvement of F3 and F4) of Pfitzmann and Westfeld, What other methods can you use in information hiding in JPEG images? The ...
898 views

### DCT and Hard Thresholding

If I have an Image and i find the DCT and then apply hard thresholding on the coefficients and then IDCT then I have attenuated the noise. Can someone please explain in detail or point me to the ...
1k views

### 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....
449 views

### Non-orthogonal basis which offers better energy compaction in image compression

I am aware of image-independent basis, i.e. DCT, and image-dependent basis, i.e. Karhunen–Loève, which are used in compacting energies for image compression. These bases are orthorgonal. Are there ...
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### Need help implementing DCT Type 4 algorithm

I'm trying to implement Algorithm 2 from this paper: Xuancheng Shao and Steven G. Johnson: Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations, https://arxiv.org/...
2k views

### How to find first 25 coefficients of DCT in Matlab?

I need first $25 \times 25$ coefficients of DCT to encrypt an image in Matlab. How do I obtain them ? I used this code to compute DCT of an image : ...
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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 ...
1k views

### Why would you use DCT as oppose to DFT for detecting oscillation in a signal?

For my project, I needed to detect the primary oscillation frequency in a signal data. As I googled around, it turns out that DCT is the best tool to find this (http://www.mech.pku.edu.cn/robot/...
162 views

### Is discrete cosine transform differentiable?

Is DCT differentiable? I.e. is $\frac{\mathrm{d}\mathrm{DCT}(x)}{\mathrm{d} x}$ defined? I've seen a few implementations in automatic differentiation software packages, so I suppose the answer is ...
132 views

### Which of DFT, DCT and DWT transforms is more robust to noise and geometric transformations in image processing [closed]

I am currently studying about image watermarking and I have been testing these 3 domains to embed the watermark at. My question is, how do these domains hold up to noise addition or geometric ...
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### How to zoom an image using DCT transform

I am familiar with zoom using fourrier transform on an Image. I am also aware that DCT is used mainly to compress images. Meanwhile, how can someone use this transform to zoom an image?
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### In 1D DCT, why is the input a vector?

The question is specific to this document: Image Compression. It is chapter 6 from book "A First Course in Applied Mathematics" by Jorge Rebaza. It is, a to the point explaination of DCT that is ...
330 views

### Is there a way to evaluate block size when doing image processing or video processing

I am currently doing foreground segmentation in image sequences. A DCT 8 by 8 feature is extracted for each pixel. Now i want to explore dynamic block size for different scenes. Is there any rules ...
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### How to iplement fast DCT-III (for inverse of DCT-II) using FFT or iFFT

I have to implement DCT-II and its inverse which is equivalently given by a forward DCT-III. All from real to real. I have been checking some paper where it is specified how to do it. However, I ...
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### Why discrete cosine transform may not maintain locality

In paper Convolutional neural network for speech recognition, they say I didn't understand the highlighted sentence.
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### validation of a pseudo jpeg compression

I've done something which is not exactly the jpeg algorithm. What I've done is that given an image $I$ of $N\times N$ size, I have computed the DCT of individual $8\times 8$ blocks. Once this has ...
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### Why Wavelet based Transform Is More Suitable for Image Compression Compared to DCT?

Everyone knows that JPEG2000 can obtain much better compression result than JPEG. The fundamental transform behind JPEG2000 is wavelet while the basic transform in JPEG is DCT. So my question is why ...
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### How does using DCT help in image compression

I once learnt that the Huffman Encoding is used to rid of redundant information, thus reducing file size. I am not sure how using a DCT, or FFT on an image can help in reducing file size. It does not ...