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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283 views

Analytical Expression for Convolution of Two 2D DFTs

I am trying to do an image analysis problem on some images, and I want to calculate some things in the frequency domain which are giving me problems. Say I have an (discrete) image $I(x,y)$ of size $...
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1answer
6k views

How to calculate the power of a discrete signal? / Clarification on PSD estimates

I want to calculate the channel power $ P_\mathrm{x}$ of a given discrete and complex signal $x[n]$ (with a length of N) in a given bandwidth $B$. I'm aware, that I could probably apply a sharp ...
3
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0answers
8k views

Horizontal banding (flickering) due to electronic rolling shutters

It is a well-known artifact that in CMOS cameras with electronic rolling shutter, horizontal banding (flickering), i.e. brightness intensity variations, are observed when the image is recorded under ...
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0answers
632 views

Incorrect Frequency results when using Multiple Signal Classification (MUSIC)

I am using MUSIC (Multiple Signal Classification) to determine Direction Of Arrival (DOA) and frequency of signals impinging on an Antenna Array. I am using a function ...
3
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0answers
5k views

1/3 octave spectra from fft

I have got a signal in frequency domain. This is a frequency response function from software, so I can do nothing about it and have to leave it in frequency domain. I want to transfer the data to 1/3 ...
2
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1answer
134 views

Flipping of x axis values when the Fourier Transform is compared to the FFT

EDITED 3-Jun-20 I have a lorentzian lineshape $$ f(z) = \frac{1+iz}{R(1+z^2)} \qquad (1)$$ where $$ z=\frac{-2\pi(f - F0)}{R} \qquad (2)$$ and $ R $ is the decay rate, $ f $ is the frequency, $ F0 $ ...
2
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0answers
49 views

Understanding convolution of Chirp z algorithm

I dont´t understand how works the convolution part of the Chirp z. I understand how the DFT is transformed \begin{align*} x(k) = \sum_{n=0}^{N-1} x(n) W_N^{kn} \end{align*} to this expresion: \...
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4answers
1k views

How do I calculate peak amplitude of the signal components after zero padding and FFT?

I am learning about DFT and trying to apply it to some audio processing. I am new to DSP but experienced in programming and have some background in math and physics. The FFT algorithm I use (lomontFFT)...
2
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0answers
679 views

discrete fourier transform circular symmetry

I was reading digital signal processing. In topic Discrete Fourier Transform, circular symmetry it is said that circular advance is obtained by shifting x(n) in clockwise direction. i.e. to obtain x(n+...
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0answers
61 views

DFT of signal with frequency-dependent time shift

I have a signal $s[n]$, and I want to compute the DFT of it with a frequency selective shift (computing all $k$ here but I really only care about $k > 0$) $$S[k] = \sum_{n=0}^{N-1} s[n-\dfrac{N}{...
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0answers
58 views

Separating out a sequence of DFTs with overlapping windows

Suppose I have a time series partitioned into $N$ equally-sized sections. Choosing some $k<N$, for each of the sections $i \in[0, N-k]$, I concatenate that section with the $k-1$ sections to the ...
2
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0answers
81 views

Why does filtering the same discrete dataset while choosing different sampling rates yield different results?

If I have a two-dimensional discrete dataset (one space, one time), and I create subsets of this dataset by "sampling" (although the original dataset isn't continuous) it at different rates, should I ...
2
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0answers
579 views

DFT sinusoid's fundamental frequency, intuitively

I am trying to understand, intuitively, the mapping of a sinusoidal signal's fundamental frequency from time domain to frequency domain using $\textrm{DFT}$ formula. Given the time domain samples $\{x[...
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0answers
258 views

Is there any problem with my FFT method?

I am trying to analysis a system by Fourier Transform. my system has 3 dominant modes. (1,0.05) (0.51,0.01),(0.46,0.01) the pairs are defined as (freq,damping_ratio) I've got those result with ...
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0answers
88 views

Alternative convolution theorem?

Instead of padding $x_1[n]$ and $x_2[n]$ then taking $$ \text{iDFT}(\text{DFT}(x_1[n])\cdot\text{DFT}(x_2[n])), \tag{1} $$ assuming we know $x_1(t)$ and $x_2(t)$, and their FT's, what if we do $$ \...
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1answer
34 views

What is the variance of DFT of Fourier coefficient of difference of a vector of white noise?

Consider, $\{x[0], x[1], \ldots, x[N-1]\}$. Suppose, $x[n] \sim N(0, \sigma^2)$, $\langle x[n], x[n-1]\rangle = \frac12 \quad \forall n$ and $\langle x[n_1],x[n_2]\rangle = 0$ whenever $|n_1-n_2| > ...
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0answers
88 views

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 ...
1
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1answer
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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0answers
132 views

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 ...
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2answers
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 ...
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0answers
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 ...
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0answers
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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0answers
77 views

Equivalence of the Power Spectral Density definitions

I am trying to show the equivalence of the following Power Spectral Density definitions in Matlab: Definition 1: $$ P(\omega) = \sum_{k=-\infty}^{\infty} r(k)e^{-j\omega k} $$ Definition 2: $$ P(\...
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0answers
83 views

Applying DFT to OFDM signals above Nyquist rate

Consider an OFDM signal which has $N=8$ subcarriers and is band-limited to $[-B/2,B/2]$, $\sum_k x_k e^{j2\pi kf_0t}$ where $f_0=\frac{B}{N}$. For this case the Nyquist rate is $2\times B/2=B$, i.e., ...
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0answers
166 views

How to sample a transfer function (angular spectrum) in the frequency domain?

I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given ...
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0answers
1k views

Acceleration time series to velocity conversion using DFTs

I have 1000 Hz time series data for acceleration (512 data points), which I want to convert to velocity. I am trying to use the omega arithmetic method to achieve this. Following are the steps I am ...
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1answer
167 views

Spatial spectrum of EEG data: non-uniform DFT?

I want to compute the spatial spectrum of EEG data collected using a non-uniformly sampled grid of sensors (as in the figure below). One way to do this would be to interpolate the data on a ...
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1answer
440 views

How to Combine 8 N/8 FFT's into one N FFT

I need to make in FPGA (using Verilog) an FFT. Input data is N=8192 points at 1 GSPS. However, the FPGA operates at 125 MHz, therefore the data is split into 8 channels (each one at 125 MHz). This ...
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0answers
75 views

Normalised magnitudes in sliding dft

I am new to signal processing. I am trying to use the output of a sliding DFT to analyse frequency peaks. Take for instance this implementation: https://github.com/bronsonp/SlidingDFT/blob/master/...
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0answers
760 views

Radix-8 butterfly with Winograd and Cooley-Tukey algorithm

I saw the Winograd radix-8 kernel algorithm below, shown in the image. Comparing to the mathematical formula of Cooley-Tukey, there is a multiplication by $\cos$ and $\sin(\pi/8)$, which can't be ...
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0answers
65 views

Determining periodic pattern when there is pattern which period is multiple of former

I have periodic signal, say, it has year period, yearly pattern. I want to check if also has quarterly pattern. Event if there is no visible quarterly pattern, Fourier Transform of this signal has ...
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0answers
847 views

How does the size of a spectrogram relate to window length and frame rate?

I'm trying to understand the methodology from section 4 in this report about audio classification but I have some trouble understanding how they pre-process the data (dsp is not my area). $30$ ...
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0answers
54 views

What is going wrong with my DFT program?

Please let me ask your help on my problem. My following DFT program outputs: [Testing frequency's amplitude: $56.9708$, and its phase: $1.32018 \pi \textrm{ rad}.$] Testing frequency's amplitude ...
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0answers
167 views

Zero padded-OFDM signal?

Why do we need 2N-FFT at the receiver when we want to demodulate ZP-OFDM signal ?
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0answers
100 views

Proving DFT equation

How can I prove the equation $(3)$? I can't understand why there is a $2/N$ in $(3)$. Why he just get the second term in DFT? Consider a sinusoidal input signal of frequency $\omega$ given by ...
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0answers
502 views

How to convert a spatial frequency in a 2D-DFT into the units radians per pixel?

Let's say I have a 2D image, and I take the discrete Fourier Transform (via FFT) of that image. In the frequency domain, I get the following image: In this image, let's just assume all the spatial ...
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0answers
448 views

Discrete Fourier Transform for text analysis?

I would like to determine the number of text-blocks verifying a roughly similar pattern. I have the intuition that I could do it using some Discrete Fourier Transform (DFT)-like methodology. Example: ...
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0answers
419 views

Short VHF pulse detection from SDR

I need to detect a short (10ms) VHF pulse that occurs every 1.5s at a specific frequency (e.g., 150.20 MHz). I have an SDR that support IQ sample rates up to 10MSPS but due to computing constraints 2....
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0answers
80 views

Is negative frequency important in calculating Spectral Moments

A follow on question form this one (What is meant by "spectral moment"?) In answers to the above referenced question spectral moment is defined as: $$ m_k=\int_{-\infty}^{\infty} f^k|X(f)|^...
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0answers
38 views

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 ...
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0answers
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 ...
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0answers
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-...
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0answers
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 ...
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0answers
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 ...
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0answers
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 ...
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1answer
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 ...
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1answer
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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0answers
23 views

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 ...
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0answers
32 views

DFT algorithm designed for a “sample-by-sample” senario

Suppose I have a system that wants to take an input signal (audio in this case) and wants to output a Discrete Fourier Transform of it in real time (ie every sample). My initial thought is that if you ...
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0answers
90 views

Why does time-domain convolution correspond to frequency-domain multiplication? (visual)

I seek a visual explanation of this. I've already seen the maths, and can derive the proofs - they amount to nill for an intuitive understanding. Any amount of math is welcome, as long as serving to ...