# Tagged Questions

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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### 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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### How to get dct coefficients in libav

I want to implement an LSB-steganography algorithm for h264-encoded video. According to this paper, I need to modify the quantized coefficients in encoder, and translate video (via vlc-media player). ...
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### Decompose an N x N 2D DCT into 4 N/2 DCT's

I have a fast implementation of a 16x16 DCT and IDCT in c++, I would like to know how to partition a 32 x 32 array of values and scale factors to implement a 32 x 32 DCT, and IDCT respectively. A ...
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### Basis functions in DCT

I'm new to Discrete Cosine Transform (DCT) and I have a question relating to basis functions. In DCT, basis functions are defined by: \alpha_p\alpha_q\cos\frac{\pi \left(2m+1\right)p}{2M}\cos\frac{\...
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### What's the benefit of decorrelation when it comes to image splicing detection?

I've already known that DCT has the property of decorrelation, and computing the diffrence 2-D array of an image also makes the image decorrelated. But I really can't understand the meaning of ...
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### Real DFT Using DCT

In one of my projects I need to do a large number of real FFTs, so I'm looking for the most efficient algorithm. Is it possible to pre/process the N DCT in N operations to produce the real FFT - ...
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### Why is the DFT used for spectrograms rather than the DCT?

Related to Could a DCT be used for an audio magnitude spectrum rather than DFT?, but more on the (audio) spectrogram side of things I've been reading about the DCT (such as from here) and it ...
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### Extracting DCT coefficients from H.264/AVC bitstream

Is it possible to extract DCT coefficients from H.264/AVC bitstream without doing a full-decoding of the video? There are a lot of papers on compressed domain video processing which are based on the ...
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### Implementation of DCT for MFCC

I am in the process of implementing MFCC and I'm unsure about the DCT part. This is how I implemented it (using DCT II). ...
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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....
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### Is DCT (Discrete Cosine Transform) of Type-2 lossless or lossy?

As I know, in general, the DCT is lossless. But I'm not exactly sure about Type-2 of DCT. Is it lossless or lossy?
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### Before making BDCT on an image,should I make the pixel value in [-128,127] instead of the original range [0,255]?

I want to extract features of some images in the DCT domain.I wonder if it is necessary to change the range of pixel value into [-128,127] which is original in a range of [0,255]? Are there some ...
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### Multiplier in digital signal processing?

whenever we start working on Discrete Cosine Transform(DCT), Loeffler algorithm a key role. Furthur if we approach hardware implementation of this algorithm, we find methods based on Distributed ...
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### How to get cofficients in DFT?

In my recent study of signal processing I came to know that we can compress images/signal using DFT/DCT. If we consider the lossy compression of audio or any image then it follows the same steps: ...
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### Mask shape in image DCT transform

I've been studying image compression using the FFT and DCT transforms. When using the FFT transform, it is customary to perform a frequency shift (fftshift) so that ...
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### what is the differnence between 8x8 dct coefficients and 25 x 25 dct coefficients?

As I knkw the DCT is discrete cosine transform that mostly used in time domain analysis to frequency domain. Also 8x8 is used in nomaly in img processing. I don't know why that is defined by 8x8 ....
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### How to use wavelet decomposition for feature extraction (of fMRI images)?

I have a dataset consisting of fMRI images (from mice) which are divided into 4 groups (different drug dose levels applied). Each fMRI image is 4D, that means each voxel is a time series. For each ...
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### 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 ...
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### Is DCT basicly a filter?

I am reading about audio processing for my university project and I found out that DCT basicly filters out some frequencies. I wanted to use for example high-pass filter and then DCT for compression, ...
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### Illustration of timed domain aliasing cancellation (TDAC, MDCT, lapped transform)

Can someone find or make a visual illustration of how time domain aliasing cancellation works in lapped transforms such as the MDCT? I think a graphic would make it a lot easier to understand, and I ...
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### Working with the DCT

I am having a very hard time to implement the DCT algorithm. I have quite a few requirements like it has to work with NxN matrix or at least power of 2, it has to be 2D, it has to produce same output ...
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### Why doesn't JPEG use 1D DCT for image compression?

I know that JPEG uses 2D dct and splits the images in 8x8 blocks. Why doesn't it simply split the image in one-dimensional vectors in $\mathbb{R}^{64}$? Wouldn't it simplify the math? My guess is that ...
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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 ...
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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.
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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 ...
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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, ...
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### High energy coefficients in 1d DCT for audio

I've been reading a little bit about how DCT works in image compression using the 2D transform, however I don't know how this applies to audio using a 1D transform. Suppose I have an audio segment, I ...
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### 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 ...
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### 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/...
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### How to undo the quantization step in DCT?

How can I do point by point multiplication of the quantized DCT coefficients with the quantization matrix before computing the inverse DCT for each block? I want to modify the reconstruction algorithm ...
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### How is compression ratio related to number of dct coefficients

Lets say we have a picture with 6bits/pixel and we use discrete cosine transform with 8x8 blocks of pixels and each coefficient is 8 bits. We can use 2 8x8 masks, a zonal mask A and a zonal bit ...
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### NxM DCT matrix generation

How can I generate an NxM DCT matrix? In Matlab dctmtx function generates only square matrix (NxN).
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### 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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### 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 ...
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### What does the negative sign mean in the image frequency domain?

When I transform an image from the spatial domain to the frequency domain, some frequencies are negative. What is the meaning of the negative sign? For example:
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### DFT Vs DCT - spectrum differences

When you are transforming a signal in to a frequency domain using both DFT and DCT, say for a function sin(x), how the spectrum will be? will both frequency values (of DCT and DFT) same? Can anyone ...
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### DCT step suppress high frequencies in MFCC extraction process

I'm trying to get MFCC from speech audio data. I'm using 26 Mel Filter on 0-24kHz spectrum. My MFCCs doesn't look correct to me, cause always first bins have high values and values getting smaller ...
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### Conversion between DCT to DFT frequency domains

It is well known that the DFT can be interpreted as a filter bank. The same can be done for the DCT, for instance Fig. 3.29, pag. 129 in [1] shows a plot of the frequency response of a DCT filter bank....
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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 ...
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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: ...
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### Can the Walsh Hadamard transform be computed for non power of 2 sizes?

Can the walsh hadamard transform be calculated for odd image block sizes such as 5x5 or 7x7? Most of the examples I've seen are for 4x4 and 8x8? I fear it probably can't from the description I read ...
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### 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 ...
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### 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 ...
8k 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 ...
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### Why motion cannot be estimated in DCT domain using block match?

In all video coding standards, motion estimation is always done in pixel domain using block matching. I wonder why it cannot be estimated in DCT(Discrete cosine transform) domain using block matching ...
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### DCT Steganograhy

I'm trying to implement a simple steganography algorithm (similar to JSteg algorithm) for hiding data in LSB of DCT coefficients in Matlab, and I ran into a problem. a. I apply DCT. b. modify LSB ...
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### Determining the resulting pixel value before creating a compressed JPEG image

Is it possible to determine the resulting pixel values and modify them before the compressed jpeg image is actually created? For example, I'm at the stage where I already have the quantized DCT ...
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### 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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### 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 ...