Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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Estimate phase using STFT in Matlab?

My signal oscillates back and forth on the interval [-1, 1] at varying frequencies, with some added higher frequency noise components (example data shown below). I want to to estimate the phase of the ...
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1answer
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Is the discrete Gaussian kernel an eigenfunction of the DFT?

So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right? But this isn't true for the sampled Gaussian in the DFT because the tails of the ...
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1answer
206 views

What Are the Suggested Resources for Extensive Knowledge About the Fourier Transform (DFT, FFT, etc…)? [closed]

I would like to improve my knowledge about Fourier Transform related subjects. What are the recommended resources in order to self study about it?
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1answer
206 views

A kind of Phase Retrieval problem

I know there are lots of papers proposing algorithms for the problem of reconstructing a signal from modulus of its Fourier Transform (so-called Phase Retrieval Problem). Also, recently it is studied ...
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1answer
5k views

How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where ...
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201 views

Similarity in absolute value of nearby DFT coefficients

Is there any approximate relation in FFT coefficients? For example, consider time domain signal $x_n$. Its $N$ point (assume $N$ to be even) DFT is given as $X_0,X_1,...,X_{N-1}$ Can I say something ...
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1answer
128 views

Right algorithm for fourier transform on physical heights

I have data from a LIDAR unit that I would like to get the spectral density of. Unfortunately, the only thing I remember from my Fourier analysis class are the methods that I know will not work. The ...
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1answer
814 views

Units of FFT frequency

I'm having some trouble understanding FFT plots and measures. According to this, this will give me the magnitude plot of FFT, ...
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1answer
1k views

Example of Fourier Transform not existing for real-life signals?

I got curious based on this question here, but basically, is there ever a real-life signal that exists where its Fourier transform does not exist? If a signal is not finite energy, then its Fourier ...
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887 views

DFT and multiplication/convolution equivalence

Is there a simple or potentially intuitive explanation for, with the DFT, vector multiplication in one domain being equivalent to circular convolution of the transforms of the vectors in the other ...
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1answer
10k views

What exactly is a complex envelope?

I have seen this be mentioned a couple of times in some books I read, so I want to make sure. Is the complex envelope simply the summation of the real and quadrature components of a signal, whereby ...
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Spatial Aliasing - Wrap Around F-K Spectra

I've been using F-K Filter, for a while, but I guess I never had good basic understanding about it Math. Someone asked me what is the cause of frequency wrap around in F-K Spectra plot ? I know it's ...
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1answer
486 views

The Sinc Function and the Partition of Unity Property

For this question purposes a function, $ f \left( t \right) $ is said to hold the Partition of Unity if: $$ \forall t, \ \sum_{n \in \mathbb{Z}} f \left ( t - n \right ) = 1 $$ Using the Poisson ...
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Matching 2 audio files

I'm doing research on how we can do matching between 2 audio files using Android to see if they have the same content or not. After doing lots of research, I have concluded that I must do 2 main ...
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1answer
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how to compute a discrete fourier transform on fragmented data

I have a list of collected data points that I need to take a DFT of, however with the problem that about one quarter of the data points in the middle are missing, and so even though the existing data ...
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2answers
2k views

Getting the amplitude and phase of harmonics in C

I have a periodic series of 360 values. How can I use the fftw c libraries to get the amplitude and phase of the first, second, third and fourth harmonic? If I do this for N=360 ...
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1answer
161 views

What is the optimal adaptive grid for calculating a DFT using a fixed number of sampling points?

I'm currently facing the following problem: I want to approximate the Fourier transform $F(\omega)$ of a (let's say, $L^2(\mathbb R)$) function $f(x)$ by calculating the discrete Fourier transform, ...
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2answers
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How to Combine Low and High Frequencies of Two Images in MATLAB?

I would like to combine two images A and B in the following way: 1) I want to take a Fourier transform of both of them 2) For image A I want to apply a weighted filter, which gives more emphasis for ...
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1answer
2k views

Low pass signal filtering using FFT or simple infinite impulse response filter

I am currently in need for filtering accelerometer data for an Android application. First of all, I used a simple low-pass filter (simple infinite impulse response filter) as follows: ...
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3answers
184 views

Evaluating regular Fourier Transform from DFT

Suppose we know the DFT of a discrete limited sequence, some $X[k],\ k = 0, 1,\dots ,N-1$. How can we calculate the Fourier Transform of the same signal for a random frequency $\Omega$? EDIT: How ...
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1answer
120 views

Confusion related to DFT in a paper [closed]

I was reading a paper related to privacy where they perform fourier transformation of a time series data and retain few coefficients of the FFT. Then they apply some noise to these coefficients. These ...
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2answers
321 views

What does the uncertainty principle say about recursive filters?

The uncertainty principle is usually stated as a relationship between a continuous signal and that signal's Fourier transform, and says that $$ \int_{-\infty}^{\infty} \! x^2 f(x) \ \mathrm{dx} \int_{-...
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1answer
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How one apply correctly FFT in image denoising

I'm writing program (Qt widgets/c++) for removing noise from images. As denoising method, i selected non local means method. This method has incredible quality of restored images (that's why it's the ...
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1answer
561 views

Gain function calculation (frequency response)

Define moving average process $y_t := 0.5 x_t + 0.5 x_{t-1}$ where $x_t := e^{i2 \pi t}$. Its frequency response is then: $$H(f) = 0.5 + 0.5 e^{-i2\pi f}$$ Recall that the frequency response in ...
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2answers
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Artifacts in FFT

I recently realized that FFT's aren't perfect. Meaning if I take a signal and then take it's FFT, and then do an inverse FFT, the resulting output isn't exactly the same as the input. Here's an image ...
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847 views

Why integrate over $2\pi$ in inverse DTFT?

In DTFT of a signal, the spectrum of a sequence is periodic with period $2\pi$ and all the information needed for derivation of the original signal from its spectrum is contained in $\pi <\omega &...
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How were windows originally conceived?

I am aware of the common types of windows, (Hamming, Hanning, Kaiser, Tukey, etc etc). However while many books describe them - almost none tell me just how exactly they were derived. What is so ...
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1answer
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Plot the magnitude of coefficients against frequencies of DCT transform

When we perform DCT transform using matlab: ...
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1answer
55 views

Calculate maximum of filter kernel

I'm sure there must be an easy way to do this, but given the Fourier transform of an isotropic filter kernel, $\hat{f}(\mathbf{u}) = \mathcal{F}f(\mathbf{z})$, can one calculate the value of the ...
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3answers
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Mathematically inclined Signal and Systems/Signal Processing book?

I'm an electronics engineering student with high inclination to analysis and pure mathematics. I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal ...
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1answer
86 views

What is the meaning of $Ta_k$ of fourier series or transform?

What is the meaning of $Ta_k$ of fourier series or transform? I am taking a course on signal and systems. In 286 page of my textbook, it says that as T becomes arbitrarily large the original periodic ...
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3answers
2k views

Calculating an image's fourier spectrum by hand?

Suppose I have a $4x4$ image with the following values as its grey-level intensity for each pixel like this: I want to get its Fourier spectrum. Usually, I would just punch into Matlab and run a fft ...
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2answers
7k views

Centering zero frequency for Discrete Fourier Transform

I am working on a image processing application which uses a discrete fourier transform to implement blurring/sharpening. The application is more or less working, but something about the mechanics is ...
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1answer
318 views

Benefit to know Fourier series for image processing? [closed]

I know there's a benefit of knowing the Fourier Transform for image processing, but is there a benefit to know Fourier series, or could you just skip them? Would you recommend skipping Fourier series ...
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Phase Correlation - Poor Performance on Noisy/Blurred Images?

I have successfully tested 1D phase correlation algorithm to determine vertical shift between two synthetic images. When I moved to real images, however, it is not able to detect translation at all (...
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2answers
956 views

Phase Correlation and Negative Shifts

I am implementing phase correlation algorithm to determine shift between two images. It generally works, but I am not sure how to interpret the resulting shift. Pseudocode: ...
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1answer
138 views

Feature Selection by Filtering

so there is this paper I'm reading and trying to understand fully: Towards Practical Identification of HF RFID Devices http://dl.acm.org/citation.cfm?id=2240276.2240278 I don't want to link the PDF ...
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1answer
128 views

Fourier Transform Computer Vision Textbook

I am required extremely fast to fill the gap and learn Fourier Transform with application in Computer Vision. It was easy to find mathematical aspects of Fourier Transform, but I am more interested ...
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1answer
2k views

what is probability density function (PDF) of periodic signal

anybody knows what is the best pdf for periodic signal ? I have signal with 480 samples (16000*0.03=480) but I could not find the exact pdf for that. sometimes it appear like 2 mixed Gaussian.
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2answers
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Interpolation vs Interpolation Filter?

Hi guys, I've been reading some papers on - how to remove ghosting artefacts from the Fourier Slice theorem applied to a 3D discrete image volume. The papers mention that in order to remove ghosting ...
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3answers
653 views

FFT of input length 1536

Does anyone knows can i find a FFT of 1536 length input. Its a specification given in 3gpp Lte and we need a transform of 1536 input size which is neither a power of any number i would say. I just ...
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2answers
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FFT for a single frequency

I was looking for a more efficient way of finding the magnitude and phase of a signal at a certain frequency without performing an FFT because it produces more information than I need and I came ...
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0answers
111 views

A simpler method or more descriptive answer to the Fourier Transform

I'm trying to do a CT Fourier Transform of these two signals $$x_1(t)=e^{−a(t−1)} \cdot u(t−1)$$ and $$x_2(t)=e^{−a(t−1)} \cdot u(t)$$ Where $a$ is any real number, and $u(t)$ is the unit step ...
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3answers
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Image processing, recognizing a small feature in a larger image

I am trying to write an image processing program to recognize bubbles in oil. It has been suggested I try computing the convolution of the image and an image of a typical bubble. i.e. : ifft(fft(a)....
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1answer
874 views

How to calculate the energy levels of frequency intervals of an audio signal?

Using the Fourier transformation I can translate a signal from the time-domain to the frequency-domain. If I divide the frequency axis into intervals, how can I calculate the audios signals energy for ...
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1answer
455 views

What is the role of complex exponential?

What is the role of complex exponential $ e^{jθ} $ in Fourier Transform? Is it different in the continuous and in discrete time domain?
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1answer
324 views

Question about the Haar Wavelet transform

I'm trying to detect the presence of a sinusoid in 1/f noise conditions using the STFT and the DWT with Haar wavelets. I find this interesting phenomenon that I'm not able to explain (see plot at 1) ...
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4answers
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FFT of random binary data

I am trying to make sense of FFTs and binary data. Say I have a series of random binary data, which is measured with a repetition rate of 400Hz (interval time of 0.0025s). I have a total of 12489 ...
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0answers
583 views

How to convert a sound file to any other data format which can be manipulated

I know this is very basic question and i am new to this site. But can anybody help me with my question. How to convert a sound file to other data format say using some type of transform (FFT or DFT) ...
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1answer
179 views

Approximation using a Fourier transform with low pass filter

I need to approximate a function f, but I cannot do so with frequencies that exceed 1kHz What is the best approximation I can get? Is taking the Fourier transform then zeroing any term above 1kHz the ...