# Questions tagged [dft]

The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.

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### Is rotation of a Fourier transform the same thing as Fourier transform of a rotation?

I'm working on an image processing problem and wondering if DFT(rotation(image)) == rotation(DFT(image)) (1). My final goal is to apply rotations in the Fourier domain then do an inverse Fourier ...
100 views

### Anyone explain to me this video?

I was watching a video in time 24:48 I would like to know where you got the value .9 (1.14z + .941) and 1.0232 + .757 Does anyone explain how he got those numbers?
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### FFT algorithm for real-time analysis

In a project, I have real-time voice audio being delivered in buffers of around 128 samples at a time. I want to calculate the autocovariance of the signal and use it to control an AR filter. To do ...
211 views

### Prove that, in DFT, Upsampling in time domain is equal to replication in frequency domain

Given: $x[n]$ is an $N$-point sequence whose DFT is $X[k]$ $$x[n]\xrightarrow{\mathcal{DFT}} X[k]$$ then, Prove that: DFT of the same sequence after insertion of $(M-1)$ zeroes between successive ...
56 views

### DFT equivalent circular convolution weight matrix with a symmetric filter of length 2K+1

$\DeclareMathOperator{\diag}{diag}$In a research paper, I read that: For optimization, the $n\times n$ weight matrix of DFT can be equivalent to circular convolution with a symmetric filter of length ...
52 views

### How to select the sign of the square root of each element of a DFT in obtaining the square root of a polynomial?

I want to find the square root of a polynomial by the following process: Compute the N-element DFT of its coefficients, maybe padded with zeros. Compute the complex square root of each of the N ...
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### Variation in Signal Power in Mimo system

I am exploring methods for reducing computations required by MUSIC (Multiple Signal Classification) Algorithm. Most of the computational power is spent on calculating SVD. My approach is to take ...
951 views

### Instantaneous power estimation by discrete hilbert transform - how far does it smooth?

In my research area, instantaneous power in a specific frequency band is commonly estimated by the following procedure: Apply a bandpass filter on the raw signal (e.g. 80-90Hz bandpass). Estimate ...
157 views

### Multiply filter kernel by sine

1)Suppose that we have low-pass filter with cf equal to 0.1. How frequency response would look like if I multiply filter kernel by sine with frequency say 0.3? How this is related to converting low-...
519 views

### Using Fourier Transform on Gyroscope

The original idea is to calculate distance from accelerometer input. However, accelerometer reading also contains the gravitational values, thus to remove gravity, I tried using Gyroscope. The idea ...
719 views

### Extraction of fundamental signal information-Fourier full cycle algorithm

After filtering my noisy input signal using an anti-aliasing and FIR filter, I now wish to get the basic signal information (peak voltage and impedance; $R$ and $X$) from the pre-filtered as well as ...
1k views

### DFT, cepstrum, LPC for feature extraction

I am a newbie in speech processing and experimenting to get a feel. I have extracted some speech segments using a window function and I want to find distance between a pair of segments. First, I took ...
803 views

### FFT analysis of longer data sets

I have a problem with a FFT analysis in MATLAB, which is probably related to my limited understanding of the fundamentals of Fourier analysis. I use MATLAB’s built-in fft analysis function. The ...
24 views

### Distortion in phase difference measurement using FFT

I am doing distance measurements by transmitting a 100 kHz tone and receiving it and measuring the phase difference.The distance is simulated by a delay simulator which is very precise (around 10 psec)...
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### How do I calculate the correct amplitudes of a discrete Fourier transform (DFT)?

I have a set of samples values in time domain. I know they are uncorrelated and I have to extract the correct amplitudes. However, the values are only ~88% of what they should be. As a test see the ...