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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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Finding n Amplitudes by DFT, what is correct normalization

Please forgive me if this has already been asked. Let us assume an example with $x(t) = \sum_{i=1}^N A_i \sin(2\pi f_i t) $ under a given sampling frequency $f_s$, frequencies $\omega_i$ and ...
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What is a correct way to find or “guess” a kernel which transforms an image into another image using Fourier Transformations?

Assuming I have two images, apple and orange; also assuming a filter kernel that transforms an apple image into an orange image possibly exists, how would some series of Fourier Transformations (and ...
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Is there a way to find a picture inside another picture, using only 2D Fourier Transforms of both images?

Can Fourier Transforms of both images tell anything about "likeliness" of two pictures? If yes, how precise? Can it still work if only several pixels are different or can it tell they are same if one ...
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Proving that the IDTFT is the inverse of the DTFT?

The DTFT is given by: $$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty}x[n]e^{-j\omega n}$$ The IDTFT is given by: $$x[n]=\frac{1}{2\pi}\int_{0}^{2\pi}X(e^{j\omega})e^{j\omega n}d\omega$$ I have been ...
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How to get a heartbeat signal from this data?

I am giving my first steps in data analysis, gathering/cleaning. To learn, I am trying to create a simple code that can detect heartbeats from color variations from the image coming from the camera ...
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Do I need equally paced values to do a Fourier Cosine Transform?

I am gathering data from a sensor, but the data gathering depends on a code running, so the timing is not precise to make it equally paced. What I mean is this, the time it takes to do measurement #1 ...
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What Is the Difference between Parseval's Theorem and Plancherel Theorem?

Wikipedia gives Parseval's theorem as follows. Parseval's Theorem , is the Fourier transform of x(t). And Plancheral's theorem is given as , where is the fourier analog. Plancheral ...
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Fourier transform of given signal

This is the signal whose FT i need to find, at first i thought that i could solve this as a convolution of two rectangular pulses, but i could not find pulses that fit into this (it turns out that ...
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FFT returns large low-frequency power - probably because signal is interpreted as containing cycles that do not fit. How is this called?

So I have a large number of signals like the one in the first picture below and I would like to extract and compare the frequencies within them. I applied a Fourier transform which resulted in ...
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Fourier Transform with both Time Delay and Frequency Shift

I know that the Fourier transform of a function with time delay can be written as: $$\mathscr{F}\big\{x(t-t_0)\big\}=X(f)e^{-j2\pi f t_0}$$ The Fourier transform of a function with frequency shift ...
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Sampling Frequency and Spectral Regrowth

Sampling a cosine wave of 10 Hz at Fs = 64 and number of samples Ns = 256 I setup my time vector for the cosine wave as n=(0:Ns-1)*(1/Fs) If I change the sampling frequency from 64 to 64.0005 I get ...
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Why are patterns repeated in the frequency-power graph of a periodic signal?

The original question was posted here. I have a signal, which I'd like to treat as a non-continuous function now, let it be $signal(t)$. It looks like this: Zoomed in a bit: I create a Lomb-Scargle ...
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DFT of a series of RC exponentials

Context: I'm trying use matlab to apply a single-pole filter to a time-domain ramp waveform that is generated by a sequence of time-shifted "RC steps" that are added together. The time domain voltage ...
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Why is the size of results from FFT half the size of the input, while that is not the case in image processing?

When dealing with real data, Fourier Transform produces symmetric results and FFT algorithms discards half of it. An input with 1024 points will yield only 513 points in the output. However, in image ...
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Artifacts observed in STFTs computed with C++ library FFTW3 or NE10

In one of my projects, I have to compute stfts with audio signals coming either from a microphone or a .wav file in a C++ based program. However, I am observing different artifacts due to my stft ...
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Wide-Band Lorentzian FDTD Algorithm

I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $g_i(f_i)$ ($f$ is for frequency) or $g_i(\lambda_i)$, into $\tilde g(t)$ for ...
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A question on Fourier Series and the frequency of the sinusoids

On studying about Fourier series, I encountered 2 doubts: How is it that a non-periodic function has a Fourier series? When expressing a periodic function as summation of sinusoids, why is the ...
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Reducing noise on several Transfer Function measurements

INTRODUCTION I want to obtain the transfer function of certain system (a ground "path", in this case) using an impact hammer for the excitation and one accelerometer (measuring vertical direction ...
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Scipy Welch's gives different first element

I've re-implemented Welch's method and want to compare it to scipy.signal.welch. However, the first two and last elements of the resulting array are different. My ...
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Why Coherence is not a valid metric when performing impact excitation?

INTRODUCTION I have understood that Coherence is a function that explains the linear relationship between an excitation signal and a response signal. I know how it is calculated and why it is bounded ...
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How do I find the transfer function in the frequency domain?

I was doing some exercises with transfer functions, they were always under the form of $H(z)$ and $H(e^{jw})$ for the frequency response. Today I have found one with $H(f)$. I would like to ask if my ...
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Generate time domain signal from frequency domain filter

I am familiar with using the Fourier transform to take a signal from the time domain to the frequency domain. What I would like to do is the reverse: describe a signal in the frequency domain and then ...
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Voice classification

I'm working to prepare research article for my project. While preparing for it, I've gone through the topics like Gaussian mixture model and Fourier transform for voice classification problems. I've ...
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What is the basic idea behind Fourier transform? [closed]

What is the basic idea behind (discrete and continuous) Fourier transform (FT)? In short, what is the difference between discrete and continuous FT? I have read multiple answers on the web related to ...
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How to custom optimize cuFFT for a mini batch of multi-channel images?

I am reading a paper, which has the following paragraph. Current GPU implementations of the FFT such as cuFFT are designed to parallelize over individual transforms. This can be useful for ...
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Performing inverse DFT after taking conjugate of the result of DFT

The following is a question I got in my school assignment. Pick an image and follow the operations Multiply image by (−1)x+y. Compute the DFT. Take the complex conjugate of the ...
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Performing DFT twice on an image. Why am I getting an inverted image? [duplicate]

I was asked to perform DFT on an image twice as a part of my school assignment. Why am I getting a blurry inverted image when I perform DFT on an image twice? Sorry, I'm new to image processing and ...
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Inverse Laplace transform of two-sided and one-sided Laplace transform

As I read in Wikipedia, there are two types of Laplace transforms One-sided Laplace transform: $F(s) = \int_{0}^\infty e^{-st} f(t) dt$ Two-sided Laplace transform: $F(s) = \int_{-\infty}^\infty e^{-...
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Frequency Domain - Meaning [duplicate]

I'm new in digital signal processing and having hard time understanding this. By Fourier Transform I mean Discrete Fourier Transform as it's the only one I'm learning. As far as I know Fourier ...
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Intuition behind FT of Dirac Comb [duplicate]

What is the intuitive explanation behind a dirac comb having a dirac comb as Fourier transform? How to calculate this is clear, but I cannot picture why this intuitively makes sense.
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Difference between the DTFT and DFT [duplicate]

I know this question has been asked before. It is, however, so confusing, that I'd like to give this another try: I have come across the following 2 definitions of the DTFT: So, the first line is the ...
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system function $H(\omega)$ relationship to odd and even components of h[n]

What qualities of $h[n]$ are necessary for: $$ H(e^{j\omega}) = DTFT\{h_{even}[n]\} + j\ DTFT\{h_{odd}[n]\} $$ Do all real / causal h[n] have the property that: $$ H(e^{j\omega}) = DTFT\{h_{even}[n]...
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Zero-padding, energy conservation

When calculating the FT of a signal, and the FT of that same signal but after having applied zero-padding to it, should't the amplitudes of the FT of the zero-padded signal decrease with respect to ...
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Use 2D FFT to replace 2D Discrete Fourier Transform (MATLAB)

I met a problem. I ran a code to implement the 2D discrete Fourier Transform, here is the code: ...
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Finding delay parameters for watermarked signal

I have a watermarked signal WATERMARKED SIGNAL And the actual watermark WATERMARK In Matlab, I need to find out the delay parameters $d_i$ which can be considered as the embedded information.such ...
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Audacity Spectogram view: how to see exact frequency and intensity under the cursor?

In the Spectogram view, simply clicking anywhere with the selection tool gives a vertical line to the top ruler, and shows at the bottom the exact sample, H:MM:SS, or other time coordinate you'd want. ...
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Sampling: How should I sketch a signal spectrum?

As revision, I am going through Signals and Systems, and in Section 7.1the authors are sketching representative spectra for x(t) and ...
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Convolution of signals sampled on a logarithmic grid

Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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Lowpass-filter necessary before DFT?

I'm trying to distinguish eletrical engines by the magnetic field they create. I have no idea whether this is a smart idea, it's possible at all, whatsoever. However it brought me to a basic question ...
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Correspondence between spatial frequency and pixel position

I have a very basic image processing question for which I have not been able to find an answer so far: On several occasions I have encountered descriptions of image filters given in the frequency ...
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Distortion in sound after multiplying frequency spectrum by constant

I make a simple sound equalizer that operates in frequency domain and lets user to adjust frequencies in sound by using 4 sliders. The first one responsible for 0 - 5kHz, the fourth one for 15-20kHz. ...
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Confused about Fourier transform output

I am new to signal processing, so I did a fourier transform on a frame of 200 samples with NFFT = 512 and then I took the absolute value : I am trying to understand these values on the output, are ...
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Burst Deblurring algorithm - Understanding the results

I've attempt to implement the algorithm from the paper "Burst Deblurring: Removing Camera Shake Through Fourier Burst Accumulation". The main idea is to take several frames of the same scene, each ...
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Mirrored Spectrogram Mp3

First of all sorry if this is a stupid question, but I am an absolute beginner in this field and have been trying for days now. I'm working on a java program that uses fft to analyze audio files. To ...
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What is exactly Power Spectrum Density? [closed]

In papers or textbooks, I have found several different definitions of PSD. I think I understand the meaning of PSD and all these papers or textbooks agrees that PSD and Fourier Series share a ...
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Correct form of discrete-time Fourier series representation

As I see in this slides, Fourier series representation for discrete-time signal $s[n]$ with period $N$ is $\sum_{k = 0}^{N-1} c_k e^{j2\pi k n / N}$ According to Wiki, Fourier series representation ...
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Relationship between Bandwidth and Bit Rate

In one of my classes I have learned that if we look at transmitting a binary signal with ASK, we can get the bandwidth (i.e. the width of the main lobe in the frequency domain) with BW = 2 * Fb, where ...
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Is it possible to recover the original signal from an LC circuit?

I'm using some photo detectors called Silicon Photo-multipliers (SIPMs) which produce a signal like the following: Now, I take this signal and pass it through an LC circuit to get the following ...
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Fourier Series Representation of Continuous-Time Periodic Signals [closed]

As a novice in signal processing, I have been going through Signals & Systems by Oppenheim to try and understand how continuous time periodic signals are represented by Fourier series coefficients....
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Deconvolve a FIR-filter using limits? Or: Are limits distributive with the inverse fourier transform?

Given $y[n] = f[n] * h[n]$ where $y[n]$ and $f[n]$ are two one-dimensional discrete signals that are given, find out: if $h[n]$ is a FIR-filter if it is a FIR-filter, what its kernel is. Obviously, ...