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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Fast standardised DCT algorithms

I'm wondering if the industry has converged on a standard approach to implement fast, efficient DCT ? Seems like there are many algorithms out there, e.g.: 1 A Fast Computational Algorithm for the ...
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Using DCT to create real-time "levels" animation from microphone input

For context: I'm trying to create a simple "level monitor" animation of audio data streaming from a microphone. I'm running this code on an iOS device and leaning heavily on the Accelerate ...
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Calculation of Compression Ratio after DCT

I am seeking information about the compression ratios achieved at each stage of DCT-based compression processes. Specifically, I'm interested in understanding the compression ratio immediately after ...
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Is there mathematical relationship between the FFT and DCT transforms

I need to model the relationship between the DCT and DFT transforms (If it exists). I mean real signal $x \to y = \textrm{DCT}(x) \to z = \textrm{DFT}(y)$, so I need to get the relationship between ...
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1 vote
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How can extract the cosine transform formula used for 2D by scipy.fft.dct

For the 1D cosine transform the documentation is clear in here, and I can reproduce it easily: The formula is: $$y_k= 2 \sum_{n=0}^{N-1}x_n \cos \left( \frac{\pi k(2n + 1)}{2N}\right)$$ and here it is ...
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Retrieve DFT coefficients from DCT coefficients

A vector a is transformed via a discrete cosine transform (DCT) to give vector b. For example in Matlab ...
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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 ...
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Phase shift of discrete cosine transform (DCT)

The most common type of discrete cosine transform (DCT-II) is defined as \begin{align} X_k&=\sum_{n=0}^{N-1}x_n\cdot \cos\left(\frac{\pi}{N}\left(n+\frac{1}{2}\right)\cdot k\right)&\text{where ...
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Where 2-D DFT is necessary in image processing applications instead of 2-D DCT?

As we know the 2-D DCT is a real-valued kernel and less computational complexity and it used in several image processing applications like image compression etc. 2-D DFT is a complex kernel and high ...
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Find the minimum number of arithmetic operations required for 2D Filters [closed]

Find the minimum number of arithmetic operations required for 2D Filters I could not understand the question 6 of Quiz-1. What is the number of operations (Multiplications and additions) per sample in ...
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Solve for minimum and maximum value of dct coefficient [closed]

Solve for minimum and maximum value of dct coefficient
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1 vote
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DCT with Matlab

I tried to create a Matlab/Octave code to implement this DCT formula. Is the code below correct? As a help I used the code from this site and modified it a bit ...
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Fast algorithm for n-dimensional DCT

I need to implement an encoder which compresses a 5-dimensional structure of 10 bits values. Each dimension has between 4 and 12 elements. If a dimension ever has more than 12 elements, it is ...
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Apply the Discrete Fourier Transform as a Matrix Multiplication in MATLAB

0 I have a vector x of length N x 1, I need to perform the iDCT operation for it using MATALB. I performed that using the below method: ...
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Is the DCT prone to spectral leakage like the DFT?

My understanding is that the DCT assumes the input to be an even periodic signal. This avoids the discontinuity that can occur in the periodic extension assumed by the DFT (see image). Does this lack ...
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DCT and Convolution, [1994, Martucci]

I am really trying to digest this paper, but the more I read it again, the more I realize that I never fully understood it. Basically, I am trying to get an example where I can check the similarities ...
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How does DCT decorrelate images?

I've read in multiple places that DCT decorrelates Toeplitz matrices and images usually have Toeplitz structure. Can you explain with an example how DCT decorrelates a Toeplitz matrix? Example for DFT:...
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1D DCT matlab code

I was writing MATLAB code to compute 1D DCT of sample y. On computing DCT for y=[0,1,2], code generates coefficient ...
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Inverse DCT via DFT formula deduction

Context I am reading this book Discrete Cosine Transform [...]. K.R. Rao and P.YIP. 1990. Given That From Equation (2.4.11.a)  X^{C(2)}(m) = \left ( \frac{2}{...
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Calculating DCT in reversed vector

I'm doing an exercise in which I need to show that the DCT of $\tilde{x} = (x_{N-1}, x_{N-2}, ..., x_1, x_0)$, with $\tilde x_m = x_{N-m-1}$, is equal to $\tilde{X}_k = (-1)^{k}X_{k}$, but I have ...
1 vote
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On the performance of DCT-based OFDM

I am trying to understand the OFDM based on DCT instead of DFT in order to compare between their performance. In case of AWGN, the performance is logic, but when I perform channel equalization in DCT-...
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KLT vs DCT basis restriction error

I want to implement 8x8 DCT and 8x8 KLT matrices to the 8-length vectors of 256x256 Lena image (e.g. each row of image there is 32 vectors 256/8 = 32 and for all rows 256x32 = 8192). I do the eigen ...
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Convolution Theorem using DCT

I am trying to digest this paper. [2002] Anna Usakova. Using Of Discrete Orthogonal Transforms For Convolution So far, I've been successful with DFT and DHT. Could someone give a hand with DCT? I am ...
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Can we use discrete cosine transform with imaginary part

I have been reading about the difference between the use of iFFT and iDCT with OFDM. What I understood that iDCT can only be used with one phase modulated symbol which is PAM/BPSK modulation. It ...
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Discrete Cosine Transform (DCT) Coefficient Distribution

I have two images : Original Image Binarize Image I have applied Discrete Cosine Transform to the two images by dividing the 256x256 image into 8x8 blocks. After, I want to compare their DCT ...
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