The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in the frequency and time domains. DFT requires an input function which is discrete and non-zero, such as a sampling from an analogue audio signal.

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Zero Padding of FFT

There are many question related to the zero padding a time domain signal to get more frequency bins after performing Fourier transform. As I understand this process is equivalent to trigonometric ...
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zero-phasing frequency components while keeping the same magnitude, in Matlab

How is it possible? I was thinking of taking just the real part of the DFT of my signal (isn't that zeroing out phases?) with real(fft(X)) but the magnitudes ...
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29 views

Frequency filtering with a DFT and meaning of removing complex conjugates

I've seen many implementations to filter out frequency components of some time domain signal by performing a DFT, zeroing the unwanted frequency bins, and performing the IDFT to get the filtered ...
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40 views

What is the statistics of the discrete Fourier transform of white Gaussian noise?

Consider a white Gaussian noise signal $x(t)$. If we sample this signal and compute the discrete Fourier transform, what are the statistics of the resulting Fourier amplitudes?
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38 views

Conditions on $v \in \mathbb{C}^{n}$ such that the complex to real DFT is sensible

I'm using FFTW to compute some DFTs, and as a memory space optimization, you can give it a $v \in \mathbb{R}^{n}$ and it will return a $\hat{v} \in \mathbb{C}^{\lfloor n/2 \rfloor + 1}$ via the call ...
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42 views

Computing cross-correlation of two images using OpenCV

I have a program that uses OpenCV to compute either the convolution or cross-correlation of an image with a specified kernel. I compute cross-correlation by setting the conjB flag to true when calling ...
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22 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} ...
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50 views

What is the reason for filtering out the negative frequencies of a signal?

I am reading this tutorial. Quoting the lines from the topic "Analytic signals and Hilbert transform filters": the corresponding analytic signal $ z(t)=x(t) + j {\cal H}_t\{x\}$ has the property ...
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1answer
44 views

What's the fastest way to get the phase angle and amplitude of a COSINUS 50hz signal?

I'm not a DSP specialist.I'm working in transmission and distribution. I need to retrieve the amplitude and phase angle of a discrete 50Hz COSINUS signal as fast as possible. Right now I'm using a ...
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108 views

Synchronizing data sent over sound beeps with Goertzel Detection, C#

I'm trying to send some text over sound. For example, I try to send the words "Hello John". I do it this way: Every char is converted into its binary ascii code. Then I construct a wav file with no ...
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31 views

How to show the time history of a signal down-sampled ? under the rate of 25Hz & 40Hz and find its DFT analysis?

How to show the time history of a signal down-sampled under the rates of 25Hz & 40Hz and find its DFT analysis using Matlab ? The sample signal is in a data file (sensor_data.mat) its sampling ...
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37 views

How to determine the filter type of a discrete frequency spectrum

I have the discrete impulse response of a filter and i want to determine which kind of filter it is by using the DFT. The impulse response is: h0 = [0,1,2,1,0] ...
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27 views

DFT dirac simplification

I found this equality in the middle of my DFT calculation. Can anyone help me to proof this. $ \frac{1}{N} \sum\limits_{k=0}^{N-1} \left(-W_N^n \right)^k \ = \ \delta[n-0.5 N] $ where $ W_N = e^{j ...
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75 views

FFT of signal with starting value zeros

I have a signal, ...
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1answer
44 views

How can I detect known frequencies using most efficient algorithm

I have a set of ultrasonic frequency that I am playing and I want to detect these particular set of known frequencies. I have already used fft but it is quite processing intensive and I am facing ...
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199 views

What is the most precise frequency analysis spectrography algorythm?

Everyone uses Fast Fourier Transform, which is fast at the detriment of precision. The input audio has sample accuracy and the FFT has 1/64 sample accuracy. What algorithms can output high resolution ...
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274 views

Fourier Decomposition

Hello everyone have a look at this video of Fourier Decomposition of an image(otherwise you can also refer the image which shows few plots of different extracted waves from an image) . We also know ...
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53 views

DTFT of beat signal with shift due to multiplication

I am simulating a FMCW radar (Ramp signal is used for transmission)and I have created the transmit signal from matlab FMCW model ...
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1answer
29 views

How does the OFDM system receiver decide the OFDM symbol length? [duplicate]

I am trying to understand how the receiver decides the length of OFDM symbol in time domain before it goes into DFT process at the receiver. The complete OFDM symbol (with Cyclic Prefix added) is ...
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68 views

recovering phase of sine signal from FFT

I have a simple sine function as $sin(2\pi ft + \phi)$. I want to obtain the phase signal $\phi$. I tried to use FFT to calculate $\phi$. In matlab I do the following ...
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3answers
72 views

Is there a method to compute an average amplitude for 2D sinusoids using the F.C.'s?

I am working on FFT analysis AFM like the one shown below. I am currently at a point where I understand fairly well what an FFT does, and how to think about the information it gives. I currently have ...
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4answers
557 views

What's the exponential term in Fourier Transform mean?

We know that Fourier Transform $F(\omega)$ of function $f(t)$ is summation from $-\infty$ to $+\infty$ product of $f(t)$ and $e^{-j \omega t}$: $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ ...
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60 views

How can I test an implementation of DFT for correctness?

A friend of mine implemented a DFT algorithm for a project we're working on, and we're not quite sure how to test whether or not its correct. We're only in the eleventh grade, so we have very little ...
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74 views

Sinogram Fourier Analysis Doesn't Show Clear Bow Tie Shape

I'm working on finding the center of rotation of a set of test tomographic projections in order to perform 2D reconstruction. I'm trying to implement the algorithm to find center of rotation as ...
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171 views

FFT on non-uniformally sampled signals

Most fft tutorials use sinusoidal signals for demonstration, which makes the user already know what the fft is supposed to give as an output, but what about real time signals where we don't have any ...
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How does we choose parameter in SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT,Fs)

I am facing problem in SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT,Fs) How would i choose Window, Noverlap,nfft parameter for spectrogram of children voices sampled at ...
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Decomposing a DFT into multiple FFT calls

I'm using a good fast FFT implementation (vDSP) that will only work on power of 2 blocks of audio data. Now I have a problem where I would like to be able to apply the calculations to non powers of 2 ...
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176 views

DFT vs FFT: does odd number works for DFT only?

I am always confused between FFT and DFT. In both algorithm, it has been assumed that the signal is periodic (so my understanding is that, if you have a 20 sample point signal, and you do DFT or FFT, ...
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52 views

I saw this question on one of the sites related to DFT

The analog signal x(t) is band-limited to 40 Hz. Suppose the signal is sampled at the rate of 100 samples per second and that at this rate 200 samples are collected. Then 200 zeros are appended to the ...
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38 views

Difficulties with derivative of convolutions in Fourier domain

I am trying to solve a minimization problem in the DFT domain. I have a formula where both dot products and convolutions are involved. Capital letters are the DFT of 2d images, the overline denotes ...
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46 views

Discrete Fourier Transform of PMF and PDF

I got this explenation: "It is well-known that an image’s histogram is essentially the probability mass function (pmf) of the image (only differing by a scalar). Multiplying each component of the pmf ...
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35 views

evaluating individual terms of 2D DFT (Goertzel?)

I'm looking for a fast way to do a 2D discrete Fourier transform of an image at many arbitrary frequencies. I know the Goertzel algorithm works for 1D, but is it possible to generalize it in 2D? Or ...
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How I can optimize the DFT become the FFT?

As title, I am trying to understand fast Fourier transform, but I have a little trouble, that is: The DFT said that we must multiply the matrix 2n x 2n with ...
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201 views

Deriviation of the “Twiddle Sum” property

I can't seem to understand how to derive the "twiddle sum" property: $$\sum_{n=0}^{N-1}W_{N}^{kn}=N \ \delta[k\bmod N] $$ where $$ W_{N} \triangleq e^{\frac{j 2 \pi }{N}} $$ and $$ \delta[n] ...
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The Phase Information of the DFT

As known, we can get a 'phase spectrum' from the DFT of a input signal. Assume, we do a DFT on a given equal interval sampled 50Hz AC signal, the signal is a complete whole cycle, but the start sample ...
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67 views

Discrete Fourier transform of even function

I have a cosine function - Hence it is even. Considering only the real parts of the DFT, on performing DFT, I am getting something like this. Could anybody tell me where I am going wrong: DFT: ...
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149 views

FFT: Removed padded zeroes?

I have an application where I do this: DFT->Filter->IDFT on a range For computational performance I'm zero-padding my FFT to a power of two, but when I ...
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244 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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1answer
63 views

Discrete Fourier Transform: Prove that only N distinct values of {X(k)} can be computed

Please can anyone answer this question: The Discrete Fourier Transform (DFT) is a sequence of $X(k)$ in frequency domain of the time sequence {$x(n)$} of $N$ terms. The periodic property of the DFT ...
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1answer
91 views

Conceptual question on FFT/IFFT (IFFT existence)

I was reading "Discrete and continuous Fourier transforms: analysis, applications and fast algorithms" written by E.Chu and, at some point, I found something that I could not completly understand. ...
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20 views

Are there condition numbers associated with the STFT, DWT?

Recently I learned that the DFT has good numerical stability since it can be represented as an orthogonal matrix, which has a condition number of 1. Is it possible to represent the STFT and DWT as ...
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applying convolution theorem swaps quadrants

For educational purposes I implemented the DFT and inverse DFT for images using OpenCV. Applying the DFT to an image and taking the inverse DFT of the spectrum yields the original image, so this ...
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29 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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81 views

non-equispaced DFT bandwidth

I need to construct Fourier transform of non-equispaced data. That is, I have signal $s(t)$, $t\in[0,T]$ sampled at non-equispaced points $t_k$, $k=0...N-1$ with sample values $s_k = s(t_k)$. For ...
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3answers
120 views

Why does an 8 point DFT behave differently from a 16 point?

I have a 50 Hz sine wave sampled at 1600 Samples/second.I'm computing the 16 point DFT.So my fundamental frequency is 100 Hz. I then decimated the 1600 samples to 400 samples.I then computed the 8 ...
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27 views

Limit of DFT from zero to N-1:

Why do we take the limit of DFT from 0 to N-1? If signal exists from let say -5 to 8. Then what will be the limit and how will we calculate DFT?
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DFT independent variable as fraction of sampling rate

When the frequency domain's independent variable is labeled as a fraction of the sampling rate, the values along the horizontal axis always run between $0$ and $0.5$, since discrete data can only ...
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When working with DFT of a real sinusoid why is the discrete time input taken over -N/2 to N/2, as opposed to 0 to N?

I know that when we take the input from 0 to N, the frequency component in the mth bin is the same as that in the N-mth bin, and when we take it from -N/2 to N/2 then the mth bin value is same as -mth ...
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2D FFT vs 2 Pass 1D FTT

We know that the 2D FFT can be performed by taking the FT along the rows and then taking the FT along the columns. I'm wondering how theoretical performance compares to the direct 2D FT case, which ...
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40 views

DFT of a pressure signal from space domain to wavenumber domain

When I do the DFT of the following signal: I get the following DFT which doesn't capture any peaks at all: Why is this? I'm not really able to identify what the error is?