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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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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152 views

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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1answer
362 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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97 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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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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34 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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183 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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146 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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1answer
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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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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1answer
66 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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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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149 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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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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26 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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192 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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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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61 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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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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157 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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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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145 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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69 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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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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48 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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1answer
46 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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1answer
152 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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1answer
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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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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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131 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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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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129 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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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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81 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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60 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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1answer
105 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 $\...