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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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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43 views

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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257 views

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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56 views

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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27 views

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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206 views

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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33 views

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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132 views

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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112 views

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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28 views

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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103 views

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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146 views

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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50 views

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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35 views

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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34 views

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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62 views

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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36 views

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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117 views

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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36 views

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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24 views

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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177 views

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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115 views

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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49 views

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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25 views

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, ...
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121 views

Comparing FFT for increasing time intervals in a signal

Assume a dataset where the rows represent signals: each signal $s$ is sampled at a sampling rate $f_s$ and available as an array of common length $T$. For an increasing sequence of integer times $t_i &...
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301 views

What is the DFT of DFT of discrete signal [duplicate]

What is the discrete fourier transform of the discrete fourier transform of any discrete time signal. Is result same signal? How?
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137 views

Can a Fourier Transform exist even if the j$\omega$ axis is not in the Region of Convergence in it's Laplace Transform

A couple of confusions have been occurred. The Signal I'm considering is f(t) = sin(t)*u(t) Fourier Transform of it can be derived. $-i \pi (\delta (\omega -1)-\delta (\omega +1))$ According to my ...
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65 views

finding energy content of signal from “energy spectral density” function

from "Signals and Systems Demystified", 2006, page 142, Example 6-3: (http://www.gatestudymaterial.com/study-material/signals%20and%20systems/text%20books/SIGNALS%20AND%20SYSTEMS%20BY%20DAVID%...
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31 views

Determine 3 most dominant frequencies in a signal, PSD or just the absolute value of a Fourier transform?

I have a noisy ECG signal recorded for 5 minutes. My goal is to determine heart rate every 2 seconds. To find out 3 most dominant heart rates (Beats per minute) in a 2s-signal should I calculate its ...
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2answers
47 views

Fourier-Analysis of Stationary Random Signals

Let's say we have discrete-time stationary random signals with Gaussian PDF of mean value 0 and variance 1, whose individual signal values are uncorrelated. For such a signal, how can we determine ...
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42 views

DFT of Transient vs. Analytical Solution

I'm trying to compute the Fourier Transform of a lightning impulse waveform. The python code I'm using is below. The problem that I am running into is that the magnitude of the DFT and the magnitude ...
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121 views

Limitation on the shift theorem of DFT due to frequency resolution?

The shift theorem states that shifting a sine wave in time domain by t is equivalent to multiplying the corresponding DFT coefficient of the signal by a complex exponential e^(-jwt). Described by the ...
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47 views

IDFT of $Y[k]=2X[k]$ for even $k$

If the 16-point DFTs of $x[n]$ and $y[n]$ are given as $Y[k]=\begin{cases}2X[k], & k=0,2,4,...,14 \\ 0, & k=1,3,5,...,15\end{cases}$, where $x[n],y[n]=0, \forall n<0, n>15$, how can I ...
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45 views

Is the following property true?

I was looking at a solution of a Fourier Transform question and following property was used, if: $$ x(t)\rightarrow X(jw) $$ then: $$ e^{jw_ot}x(t)\rightarrow X(j(w-w_0)) ...
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23 views

Linearity with Difference Period in Fourier Transform

I know that a system is linear if it satisfies $$\mathscr{F}\{ a\,x(t)+b\,y(t) \} = a\,X(\omega)+b\,Y(\omega)$$ for Fourier transform, $X(\omega)\triangleq\mathscr{F}\{x(t)\}$ But what if $x(t)$ ...
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112 views

How to calculate the Fourier transform of a mean filter in Matlab?

In Matlab, how can I calculate the discrete-space Fourier transform of a mean which takes the average of 4 adjacent points, with this kernel $$\begin{pmatrix} 0 &1& 0\\ 1 &0&...
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52 views

Quite confused with Fourier Analysis results

So I'm meant to show how the DFT can find the frequencies, and respective amplitudes, associated to some data. And I have this data set from the curve $$ f(t) = 1 + 2\cos(2\pi t) + 4\cos(4\pi t) $$ ...
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107 views

How to calculate STFT of a function for a rectangular window

How to calculate the STFT (by hand) of $$u(n)\cos(0.2\pi n)$$ for a rectangular window of a length 20, positioned at $n = 5$. I know that to use STFT I need to divide longer signal to a shorter parts ...
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86 views

Is possible reach the DFT if I have the DTFT?

My teacher told me that DFT is DTFT sampled, i.e.: $$X[k] = X(e^{j \omega})\Bigg|_{\omega = \frac{2\pi k}{N}}$$ But, if I have the sine $$ x[n] = \sin(\omega_0 n) $$ the DTFT is: $$X(e^{j \...
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78 views

Figuring magnitude and phase response

I've got a linear time-invariant system $$y[n]=\frac{8}{9}y[n-1]+x[n]$$ which I transformed into a transfer function $$Y(z)=\frac{8}{9}Y(z)*z^{-1}+X(z) =>\frac{Y(z)}{X(z)}=\frac{1}{1-\frac{8}{9}*z^{...
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1answer
58 views

Given a plot of both the magnitude $|H(\omega)|$ and its angle, How can you find the $H(\omega)$?

I'm specifically trying to use an inverse Fourier Transform to find $h(t)$, but I'm finding it difficult to get $H(\omega)$ in the first place. I'm under the impression from my textbook that $H(\...
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1answer
1k views

Fourier Transform of ECG signal in Python

I have an ECG signal which I am analyzing using Python, as opposed to the mainstream MATLAB. So, I have digital form ECG in .dat file with .hea (header file). Below is the Fourier transform The ...
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92 views

Denoising a signal using eigendecomposition

I have a complex observable series $Y(t)$ which is the result of summing two complex r.v $X(t)$ (unobservable) and a $\epsilon(t)$ (unobservable). $$Y(t)=X(t)+\epsilon(t)$$ Assume that $X$ and $\...
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134 views

What Is the Point of Doing the Zero Padding? [duplicate]

What are the advantages and disadvantages of doing Zero-padding, in particular the case of speech signals?
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88 views

How do you apply a filter after DFT on an image?

Let's say size of the image is 100 x 100 and the kernel matrix is 5x5. I took the DFT of both the image and the kernel. But how do I multiple these two matrices? And which parts involve in these ...
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1answer
76 views

Fourier transformations of discrete time signals [closed]

How does one Fourier transform the following signals? $$x[n]=[0,9,0]$$ and $$y[n]=[9,0,19,0,9]$$ I've tried to get it along the way of $$X[\omega]=e^{-i\omega n}$$ but this seems incorrect. I'm not ...
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41 views

How to get general projection of rect function?

To be more clear I want to get a general expression for PƟ(t)= ∫∫rect(x)rect(y)δ(xcosƟ+ysinƟ-t)dxdy I also want to find particular projection for Ɵ=0 and Ɵ=45 and also Fourier Transform of the ...
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83 views

Discrete inverse Fourier transform

I have a question regarding discrete inverse Fourier transform, and no answer I found on the internet seem to be satisfying. This might be because I do not fully get some of them, so please excuse my ...