# 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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### 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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### 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 ...
212 views

### 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 ...
52 views

### 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 ...
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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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### 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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### 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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### 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 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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### 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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### How do you apply DCT steganography on an RGB image?

I am working on a DCT-based steganography program in Python and I found a working model in Github. The program, however, can only encode on one of the RGB channels. Resulting in a discolored image. ...
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### DFT vs DCT Discrete transform

The discrete Fourier transform transforms a sequence of $N$ complex numbers $x_n := x_0, x_1, . . . . x_{N-1}$ into another sequence of complex numbers $X_k := X_0, X_1, . . . . X_{N-1}$ , which is ...
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### Convolution Theorem using DCT

I am trying to digest this paper.  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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### Image Transformation Functions to Identify if the Text in the Document Originally There or Just Synthetically Overlaid

I have a copy of scanned ancient dirty document and synthetically generated ancient dirty documents. I want to use Discrete Cosine Transform to characterize noise types existing in the document and ...
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### Why do we use the term “cepstral” in MFCCs, and how does it related to the cepstral domain?

As I know, we can get the cepstrum by taking the Inverse Discrete Fourier Transform (IDFT) of the log of the power spectrum. And we can get the Mel-frequency cepstral coefficients (MFCCs) by taking ...
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### 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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### 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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### 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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### 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: ...