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

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Invariances in Neural Networks

I have a question about invariances in neural networks. In general, neural nets with enough layers can learn arbitrarily complicated nonlinear functions. Therefore, it's not hard to understand how ...
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62 views

Fourier transform 4 times = original function (from Bracewell book)

I was glancing through "The Fourier Transform & Its Applications" by Ronald Bracewell, which is a good intro book on Fourier Transforms. In it, he says that if you take the FT of a function 4 ...
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Evaluating the inverse Z transform on the unit circle

I am trying to understand the math. The inverse z-transform is given by: $x[n] = \displaystyle\frac{1}{j2\pi} \int_cX(z)z^{n-1}dz$ where $\int_c$ is a contour integral. The inverse Fourier ...
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32 views

How to find a certain frequency in a signal that varies in time?

I have an EEG signal. It is amplitude verses time. I want to find out how certain frequencies in that signal vary with time. One way I think I can do this is to do a short-time-Fourier-transform on ...
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35 views

Opposite of wavelet transform?

Wavelet transform gives good time resolution for high-frequency events and good frequency resolution for low-frequency events. => I want to have complete opposite of wavelet transform, where I get ...
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35 views

Filtering with filters without even or odd symmetry in the fourier domain

I am doing a project where I have to use the fourier domain for convolution. I have been reading Digital Image processing by Rafael Gonzalez but I unsure about one thing, and I could not find anything ...
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11 views

Where can I find images corrupted by periodic/coherent noise?

I found one here https://scipy-lectures.github.io/_images/moonlanding.png I would be more interested in photographs which are naturally corrupted by such noise. I am seeking them in order to use ...
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31 views

How to perform a time domain shift in the frequency domain without zero padding

Apologies in advance if my question doesn't make sense. I'm not the most fluent person in signal processing. I have an array of time domain values that I would like to apply a time delay to by ...
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41 views

Where is Fourier Transform useful in Image Processing?

I am aware of its use for correlation, and high/low pass filtering. Apart from these is there any case where modifying the image in the Frequency domain enhaces/restores the image ? Is there any kind ...
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70 views

How to interpret these different Fourier analysis of this audio signal?

This is my first dive in DSP. I would like to familiarize myself with frequency analysis. I have two audio tracks which should be digitized at 16bit-44.1kHz and 24bit-192kHz (music, presented as a ...
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46 views

What am I doing wrong?-Bode plots to get transfer function

I've noticed a couple of similar questions which haven't been answered such as: derivation of Transfer Function from bode plot Anyway, I thought I would ask since it hasn't been answered. So as I ...
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38 views

Why does the specgram of this simple sine wave look strange?

I'm trying to test some intuition using the matplotlib specgram routine. I first generate a simple sine wave ...
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50 views

Fourier transform of a sum

I have a function : \begin{equation} C(t)=\left(1.42*\exp^{-1.192t}- 12.44*\exp^{-1.192t} +11.02 \right) u(t) \end{equation} where u(t) is a unit-step function What is its fourier transform? a step by ...
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77 views

Uncorrelated but overlapping spectrum.

This answer may be straight forward but I cannot figure out. One can understand the difference between cross-correlation and convolution from the link below: What is the difference between ...
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44 views

Generate fourier transform signal

I'm newbie in DSP (maybe the question title is misleading for this reason, I apologize for this, please feel free to edit it) but not in programming. I want to experiment with Fourier (or FFT) ...
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113 views

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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105 views

Why do we discard imaginary part of the phase spectrum?

Suppose I compute phase spectrum from the fftn function in MATLAB as ...
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166 views

Fastest implementation of fft in C++?

I have a MATLAB program that uses fft and ifft a lot. Now I want to translate it to C++ for production. I used OpenCV but I ...
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79 views

How do u prove that a cosine signal with irrational period and another cosine signal with a rational period are orthogonal?

For example,cos(4t) and cos(4*pi*t) sum is aperiodic. Hence it is said that these two signals are orthogonal over infinite limits? But how to prove this? Normal integration of product of the two ...
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47 views

how to calculate the dc component of an energy signal?

Does the energy signal or finite energy signal have 0 dc component always?How to confirm this from the frequency spectrum?
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39 views

What is the effect of a sawtooth phase mask in the frequency domain?

We know that a linear phase ramp in the frequency domain corresponds to a time shift in the time domain. Qualititavely, it seems a sawtooth phase mask in the frequency domain could produce the same ...
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1D FFT on rotated image column by column

I am facing a problem: performing 1D FFT on a rotated column by column on a rotated image, described as following: Original Image: Rotated Image: What I have: original image convolution ...
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37 views

Doubt related to application of FFT

I found this formula in a paper : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=5655742 could someone explain the meaning of "j is frequency sample in the highlighted ...
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66 views

What is difference between outputs of Fourier transform and Fourier series of a periodic square waveform?

We can use Fourier transform of an aperiodic signal and Fourier series of periodic signal. But we can use Fourier transform formula for periodic function also. Now, let us consider a periodic square ...
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frequency spectrum of the conjugate of x(t)

Is the frequency spectrum of x*(t) the same as the one of x(t). I'm telling this because I found that X*(f) = (X(-f))* . So to find X*(f), intuitively i would just flip X(f) because of the minus sign ...
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144 views

How condition for existence of Fourier transform is valid?

The condition for Discrete time Fourier transform to exist for function $f(n)$ is given as $$\sum_{-\infty}^\infty |f(n)| < \infty.$$ In case of continuous Fourier transform the difference is ...
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113 views

Whether Fourier transform formula be considered as Convolution or Correlation?

The expression for Fourier transform is given as $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^{-j \omega t} \ dt \tag{1}$$ Now, let one function be $f(x)$ and other be $e^{j\omega t}$ ...
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47 views

Can realizations of a filtered Gaussian white noise process be represented as a Fourier transform?

Suppose we have a noise process $V(t)$ which is the result of passing Gaussian white noise through a filter with frequency response function $H(\omega)$. Can we represent realizations of this process ...
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Fourier Transform for speech signal [closed]

I need some clue on how to apply the Fourier transform to a wideband discrete signal like speech in Matlab. What I want to do is to apply the MUSIC algorithm to the speech recorded by a set of ...
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209 views

Meaning of Real and Imaginary part of Fourier Transform of a signal

Say $f$ is a signal of time $t$, $F$ its Fourier transform of the variable $v$. It is known that in polar coordinate, $|F(v)|$ tells us how much the frequency $v$ is present over the signal, and ...
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55 views

implementation of Fourier denoising with hard threshold

I just tried the Fourier denoising method with a hard threshold and my code is as follow: ...
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101 views

Recover signal from its spectral amplitude and envelope

I am given an amplitude spectrum (no phase) and the envelope of a signal. What I know about the original signal is, that it can be thought of as wavepacket like structure (sinusoids under a bell ...
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52 views

How do I perform Specral Analysis (FFT, Windowing, Detrending) on Sonic Anemometer Data?

I am having trouble with all of the forums that I have looked at thus far. I have one day's worth of Sonic Anemometer data. I want to see the specral analysis of this data. When the anemometer data ...
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75 views

Fourier transform of an image

I am doing a project where I need to take the FFT and IFFT of a photo in MATLAB. There is a principle in optics where the intensity distribution from a lens is equal to the Fourier transform of the ...
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275 views

Is it possible to do single vehicle tracking using Fourier transform?

I am working on a project in image processing which is based on importance of phase only reconstruction of a signal obtained using Fourier transform.For more information about phase only ...
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154 views

Conjugation in Fourier Transform

I have a very simple question. In Oppenheim book, it says that: If CT Fourier transform of $x(t)$ is $X(j\omega)$ then, CT Fourier transform of $x^*(t)$ is $X^*(-j\omega)$. What I can't ...
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80 views

Comparison between 2 images in Frequency domain

As you can see there are 2 images from the Tom and Jerry cartoon program. In the 1st image both Tom and Jerry are present. But in the 2nd one,only Tom is present.Now,we can clearly see this ...
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21 views

Inverse DTFT Problem

Having trouble finding the inverse DTFT of $\ X(\ e^{j \omega}) = \frac{3 - \frac{1}{4} e^{-j\omega}}{1 - \frac{1}{4} e^{-2j\omega}} $ Given the IDFT of $Xe^{j \omega}$ as : $x(n) = \frac{1}{2\pi} ...
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48 views

Sine wave phase shift from Fourier Transform

This is probably a really basic question but I'm a little stumped and would appreciate some practical input on how to go about doing this rather than reading dockets of equations semi-related to what ...
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50 views

How Fourier decomposition is performed?

The Fourier decomposition explains a time series entirely as a weighted sum of sinusoidal functions and with the Fourier series,it is possible to do it. But I have some doubts Suppose ,for any ...
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How modulation spectrum of zebra finch song is calculated

I read this advanced signal processing technique in Neuroscience Journel. Modulation spectrum is a spectral modulation vs temporal modulation plot. Please tell procedure of plotting it step by step. ...
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24 views

Classifying sleep stages from only EEG

I'm currently working on a project that requires me to classify sleep stages (Awake W, N1, N2, N3 and REM) based on only an EEG. Various algorithms and classifying standards (such as Rechtschaffen ...
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52 views

How to set sampling frequency of an acceleration data set

I have a set of accelerometer readings in $X, Y, Z$ axes obtained from an android based smart-phone. The data in $(X, Y, Z)$ was recorded at different time stamps and there is no uniform time period ...
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Energy-based speech recognition [duplicate]

I have a noisy recording with individual letters spoken. In a spectrogram view of the audio, the letters have higher energy. What can I use to isolate them? I'm fine with any tool.
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55 views

Fourier transform's sine and cosine count as N grows

I remember reading that in (discrete) Fourier transform for signals with even numbered N for length, the sine and cosine count is equal. Is this correct? A bit of analysis: N=1, there is only DC ...
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Can a infinite bandwidth signal Be a infinite Time SIgnal?

While Decomposing the impulse train using the Fourier series the no. of the samples are infinite hence representing a infinite length of train. But while studying the Nyquist Criteria in the ...
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67 views

LTI system, Fourier transform, unit step function, sine wave

I just finished learning about Fourier Transforms and don't understand this signal: $$x(t) = \cos(\omega t)u(t) $$ This is a cosine wave but only where $\omega$ is positive. My question is what can ...
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why do we use $X(e^{j\omega})$ instead of $X(j\omega) $ in Discrete Time FT

I am studying DT-FT. But I cannot figure out why we use $X(e^{j\omega})$ instead of $ X(j\omega) $ in DT FT Thanks in advance..
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what is the difference between $X(j\omega)$ and $X(\omega)$ notation

I am trying to understand Fourier Transform and Laplace Transform. What is the difference between $X(j\omega)$ and $X(\omega)$ notation? what is the meaning of $j\omega$ ? Is it represent frequency? ...
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What is Fourier transform in terms of area under the curve?

We know that integration gives area under the curve. And that FT is also an integration. How do we interpret FT in terms of the area under the curve especially because e^(jwt) is a complex term? In ...