# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
967 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
### What is $F(0)$ is “dc” component in the context of image processing?
It has always been said that $F(0)$ is the "DC component" in fourier transform. However, I don't get what it means to say that $F(0)$ is "DC" in the context of image processing. The zero in this ...