# 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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### When to apply circular convolution formulas?

Context I am studying the family of Discrete Trignometric Transforms (DTT): Discrete Cosine Transforms (DCT) and Discrete Sine Transforms (DST). And trying to understanding more their properties, I ...
76 views

### DC Coefficient of JPEG Block

Suppose I take a grayscale image and break it into 8x8 pixel blocks, then take the DCT of those blocks. What is the DC coefficient of the block in relation to the whole image? To simplify I'm ...
114 views

### DCT - Coefficients and Basis Function

I am trying to understand how the Discrete Cosine Transformation works but I am not sure if I am at the right road. Assuming that I have an 8x8 pixels image and I am applying the DCT to this sample. ...
52 views

### DFT and integer valued basis functions'sf requencies

In Matlab the function W=dftmtx(N) gives the DFT matrix of size N. Each row is computed for an integer frequency k. $W_{k,n} = e^{-i2\pi kn/N}$, k-th frequency, ...
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### How to use a size N complex DFT to compute a size N/2 real DCT? [duplicate]

Can someone (maybe @hotpaw?) Explain How to use a size N complex DFT to compute a size N/2 real DCT? Also, I noticed that the DCT matrix (which can be obtained in Matlab by dctmtx(n)) contains dct ...
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### DCT vs DFT why do we need/want phase?

Why do we use complex exponentials in the Fourier transform, why do we want the phase part? As opposed to in DCT where there is no phase and only magnitude? Moreover, what does this phase concretely ...
164 views

### Why is the Fourier (or cosine) transform decorrelating?

The discrete Fourier transform (DFT) and the discrete cosine transform (DCT) both decompose a signal into its frequency-domain spectrum. One property that I have seen praised across various domains ...
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### What are the cosine functions in JPEG's DCTII table?

As I understand it from this video, in a JPEG image an 8x8-pixel block is made up of weighted cosine waves, calculated using DCTII. There are lots of visualizations of these waves, such as this one ...
156 views

### Low-pass filtering with DCT produces blocky, high-frequency results?

I have a grayscale image, available at https://pasteboard.co/IdX7NfA.png. Now I want to low-pass filter this image in the Discrete Cosine Transform (DCT) spectrum. Specifically, I centered the image ...
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### What are the variances of dct coefficients in the 2d dct of a 8x8 patch of an image?

Is it possible to calculate the variances of individual coefficients in the 2d-DCT of an 8x8 patch if a natural image? Can it be computed in closed form or can we only estimate it by calculating it on ...
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### What frequency each bin of a Discrete Cosine Transform represents?

A practical example: I perform a DCT on a time series of discrete values that are spaced in time by 1/30 of a second. What frequencies each bin of this DCT represents? What is the formula to find that?...
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### How do I find the frequency of a particular bin in a cosine transform, and two other questions

I have a discrete series of values and I have applied a Discrete Cosine Transform to it, obtaining values like: ...
77 views

### How to get a heartbeat signal from this data?

I am giving my first steps in data analysis, gathering/cleaning. To learn, I am trying to create a simple code that can detect heartbeats from color variations from the image coming from the camera ...
26 views

### DCT Based modelling

I have been reading this paper on MRI and I only do have novice level signal processing insight. I could not understand the following model: The displacement field (i.e. d) is modelled as a linear ...
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### Do I need equally paced values to do a Fourier Cosine Transform?

I am gathering data from a sensor, but the data gathering depends on a code running, so the timing is not precise to make it equally paced. What I mean is this, the time it takes to do measurement #1 ...
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### How to keep low frequencies in DCT

How can I keep a percentage r of the low frequencies of a Nx1 signal x using the Discrete Cosine Transform of it? Is it simply zeroing all but the first rN elements of DCT(x)?
158 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 ...
271 views

### How to determine a quantization table for image compression with DCT?

The quantization table is given on the JPEG Wiki page. How was this table derived? I'm currently doing a project where I have to come up with custom quantization table for an image, but I don't know ...
994 views

### Computation of the Inverse DCT (IDCT) Using DCT Or IFFT

Is there a way to compute the inverse discrete cosine transform (type-2) by leveraging either a DCT, FFT, or IFFT algorithm? I have seen ways to compute the DCT using FFTs, and I've seen ways to ...
60 views

### What is wrong with my 3D DCT quantization?

I'm implementing 3D DCT quantization as in Quantization of 3D-DCT Coefficients and Scan Order for Video Compression (sorry about the paywall). They propose the following equation for generating the ...
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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 ...
1k views

### DCT vs DST for image compression

I am doing a research project for DST (Discrete Sine Transform) versus DCT (Discrete Cosine Transform) image compression and for my conclusion, my supervisor told me to discuss why the differences ...
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### taking FFT from DCT

There is a speech signal, $y[n]$, in the time-domain. To take it to the frequency-domain, DCT has been got from $y[n]$ (w = dct(y) in MATLAB). After it, I applied ...
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### number of cosine waves in DCT

Why is it $N\cdot N$ a sufficient number of cosine waves equal to the size of the image or to a portion of it to describe it (or a portion of it) completely without losing information applying the DCT....
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### 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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### Zero Frequency Basis Equation for Discrete Sine Transform

So, I'm evaluating the Discrete Sine transform Basis functions and I found on the internet the following picture: So, I may be getting the point wrong, but, if the 2D DCT equation is: Then the ...
185 views

### Image not divisable by 8? (JPEG Compression)

I have learned that an image is to be divided by 8*8 blocks, and the 2D DCT is then applied to these blocks. My question is, what if the image is not divisible by 8? What should I do in this case?
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### Recursive DCT implementation

I am trying to understand the recursive implementation of the DCT on the input signal (used for LMS filtering) according to the pictures below. The pictures and formulas are taken from the paper: "...
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### Data representation of largest DCT coefficients

In many examples of data compression, we take the S largest coefficients of a signal in a sparse basis (eg. 1% of largest DCT coefficients) and set the rest to zero. How do we practically represent ...
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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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### Understanding the DCT

I have been trying to understand the definition of the DCT and found a really good website describing its definition. Here is the link DCT. What I don't understand is the part of the DFT. Why is the ...
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### What is the maximum value that can result from a 2D DCT?

Assuming that I have an 8x8 matrix of 8 bit unsigned values and carry out a 2D DCT on them, what is the biggest value that can result from it? This will help be decide how many bits to use. I am aware ...
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### Compute hilbert transform from DCT- FFTW3 REDFT00

My problem is similar to this but not the same. Edit: Here is a description of Neumann boundary conditions for differential equations: Neumann-type boundary conditions means derivatives are ...
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### discrete cosine transformation (dct-II) own implementation with loops

I want to implement the DCT-2, the dctmtx: $$X[k] = \sum_\limits{n=0}^{N-1} x[n] \,\cos \left(\frac{\pi}{N} \left(n+\tfrac12 \right)k \right) ~~~,~~ \;k=0,1, \dots N-1$$ ...
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### Do DCT results contain phase spectrum?

I've been working much with numpy.fft lately where just like the documentation says: When the input a is a time-domain signal and ...
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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 ...
253 views

### 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/...
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### Difference between compressive sensing and DCT-based compression?

I am working on transmitting EEG signals over wireless body area network. I have applied two different compression techniques: DCT-based and compressive sensing (CS-based) approach. I noticed that the ...
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### How to discard coefficients in the frequency domain without losing too much quality?

I was reading a text that shows that one can throw away 66% of the coefficients and gets an image that is still acceptable. I tried to replicate it using python (last example) and selectively ...
1k views

### Recovering an image using IDCT through DCT coefficients

I have computed the discrete cosine transform (DCT) of an image in MATLAB. I got a matrix of discrete cosine transform coefficients in the workspace. How can I recover the original image from its ...
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### How to get a real signal from complex ifft values?

I am trying to understand the difference between DCT and FFT in the context of compression. There is a nice practical example given here. (near the end of the page) When I try it in matlab I am ...
1k views

### Online DFT Algorithm

I have a discrete audio stream $x$ that needs to be processed in real-time. Specifically, as the each new sample is received, I would like to compute a Fourier transform of the last $n$ samples of the ...
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### DCT: Alternatives to quantization

When using the discrete cosine transform are there commonly used alternatives to quantization to decide which dct components to keep/are important? If not, how do people come up with quantization ...
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### Why do we use scaling factors in DCT? Are they important?

I don't understand the use of scale factors, why do we need them? Can we not use them or are they essential? The wikipedia page on DCT II shows this: https://en.wikipedia.org/wiki/...
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### How do I sum the discrete cosine transform cosine waves?

Sorry if this sounds like a stupid question, I'm new to DCT. I've implemented various types of DCT (like IV and II) and they all give vastly different coefficients. From what I've read, the DCT ...
487 views

### DCT and mean difference of an image

If we subtract the mean of image from the DCT coefficients of an image what does it signifies? and what type of distribution does it follow? Example in MATLAB: ...
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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 ...
338 views

### The magnitude of taking discrete cosine transform of an image two times is similar to the original

Consider the following: ...
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 ...