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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Interpreting FFT Coefficients from System Matrix That Is Originally Toeplitz (Not Circulant)

If I have a measured signal $y$, true signal $x$, and a convolution matrix $A$ that is a Toeplitz but not circulant matrix, I can write the convolution as \begin{equation} y = A x \ . \end{equation} ...
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Fourier Transform and Delta Function

I am very new to Fourier analysis, but I understand that through the use of the Fourier transform a signal in the time domain is displayed in the frequency domain, where frequency values are normally ...
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255 views

What is the frequency of $\cos x -\sqrt 2\cos\sqrt 2 x$?

Question Considering that $1\over{2\pi}$ is the frequency of $\cos x$ and also of $\cos x - 2\cos 2x$, what is the frequency of $\cos x - \sqrt 2\cos\sqrt 2 x$? Thoughts Perhaps "frequency" isn't ...
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17k views

Energy Spectrum of a signal after FFT in Matlab

I have a vector of signal x(t) with its time vector. I want to obtain a frequency representation of the signal, in particular the energy spectrum of x(t). Can someone please show some light into ...
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202 views

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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298 views

Signal Processing using Fourier Transform

So I'm trying to understand how MRI machines work. I understand all the concepts of it, the parts, what they do, how the machine works, etc. The part I'm having trouble with is the fourier transform ...
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151 views

Techniques to deriving DTFTs

Are there general techniques to derive DTFTs? Given a bandlimited function $x(t)$, how do I find $$X(\omega)=\sum_{n=-\infty}^\infty x[n]e^{-i\omega n}$$ Generally, it is easier to derive the ...
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670 views

How to 'interpret' the Fourier Transform (specifically, of a convolution kernel)

As part of a homework assignment, I had to take the Fourier transform of the kernel I was using to convolve a signal. The kernel was a constant rectangular function, that was 1 within the square $(-1,...
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70 views

Difference between Fourier-Transform and FFT of rectangular pulse

I'm trying to find a link between the Fourier-Transformation of aperiodic Signals and the FFT of them. So to start with a basic example, let's take a rectangular pulse with width 0.1s and amplitude of ...
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How to get around the circular shift property of Discrete Fourier Transform?

I understand that when we introduce a linear time shift using DFT on a finite sequence, the algorithm assumes that the signal repeats itself outside of the given range. Here is an example explaining ...
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90 views

Maximum of cross-correlation not moving

I already asked this question here yesterday, but it was very poorly worded I think. I made a much more detailled post explaining my problem of stackoverflow, as it might also be a code problem. Here ...
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271 views

How does a Hermitian FFT work in Numpy?

Say, I create a Hermitian complex signal using, import numpy as np t = np.arange(-4, 4) z = np.exp(1j * t) Here z should be a ...
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318 views

Parseval's Theorem for discrete series

I need to use Parseval's Theorem to find \begin{equation} S\:=\:\sum _{n=-\infty }^{\infty }\:\left[\left(\frac{\sin\left(\frac{\pi }{4}n\right)}{2\pi n}\right)\left(\frac{\sin\left(\frac{\pi \:}{6}n\...
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Frequency response of $\mathrm{sinc}[n]$

In this image the frequency response of a discrete time filter given as $h[n]$. Can someone explain how the magnitude of the frequency response is found ?
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405 views

Determination of periodicity in data and finding mean

I have to find whether there is any pattern (I mean periodicity or close to periodicity) and if there is, for one cycle i have to perform numerical integration to determine mean. In the first picture ...
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577 views

Practical cross-spectrum estimation using Blackman-Tukey approach

I would like to estimate the cross-spectrum of two signals using the (lag-windowed) Blackman-Tukey approach but I'm having difficulties with proper practical implementation. As defined in equation 2.8....
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152 views

Faster way of getting 2D frequency amplitudes than DFT?

I'm making a small program which gets the DFT of an image to get a general idea of the image's overall orientation. It does this by rotating a line in a radar sweep type pattern, keeping track of ...
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Practical advices for applying phase correlation in image registration task

I'm using OpenCV to detect shift between 2 images, here is sample code (based on cv::phaseCorrelate function): ...
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194 views

Why is discrete cosine preferred to FFT in neuroimaging GLM

High-pass filtering is often used in neuroimaging data analysis. Commonly, whenever a general linear model is fitted to the data (as for instance in statistic parametric mapping) a number of columns ...
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Find time lag between two time series

I am trying to find the time lag between two time series over t = [0,1000] using MATLAB (not that it matters). The first time series is simply t^2. The second is (t-15)^2 which is, of course, shifted ...
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Fourier transform possible on non-rectangular part of an image

Dear Signal Processing readers, I want to introduce 'noise' into parts of images. Until now, I worked with rectangluar images for a similar purpose and did the following, using (inverse) Fourier ...
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492 views

Instantaneous frequency vs fourier frequency [closed]

Lets consider a pure sine signal at $\nu$ that is chopped using square pulses (like a burst mode on signal generators). My understanding is that instantaneous frequency is $\nu$ when oscillations are ...
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965 views

Working around FFT windowing?

I have the following problem, that I ran into recently, when calculating the spectra of data that I obtain from a measurement technique, we are using in our group. In short what we do in the ...
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167 views

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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429 views

Am I handling offline FFT correctly?

I need some help clarifying FFTs and what they represent. I have a buffer containing compressed audio. Due to limitations, I can't handle the full uncompressed audio but can decompress small segments ...
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Fourier transform and anti-trasform--identity missing

I have a very silly doubt: If we define the power spectral density: S(f)=$\frac{1}{2\pi}\int exp(-i\tau2\pi f)r(\tau)d\tau$ (1) where $r(\tau)$ is the correlation coefficient. If we do the Fourier ...
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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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343 views

Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
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653 views

Periodicity of the discrete-time Fourier Transform

The DTFT of a sequence $x[n]$ can be written as $$X(e^{j\omega}) = \sum_{n = -\infty}^{\infty} x[n] e^{-j\omega n}.$$ Is the smallest (fundamental) period in frequency of the DTFT always $2\pi$? Or ...
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FFT of resultant of signals

If one has two signals (say, two acceleromters mounted perpendicularly) and a piece-wise resultant acceleration signal is determined, it appears that frequency content information cannot be determined ...
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85 views

Spectrum analysis of a function

I asked this on Math SE but received no replies. I hope this is a relevant forum to ask in. I would like to analyze the spectrum of the following function: $$f(t)=\cos(t\cdot a(1+b\cos(ct)))$$ with $...
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230 views

Efficient FFT (or SFFT) for adjacent parts of signal with overlap?

Imaging we have a signal $x$, which is segmented to 50% overlapped vectors $x_1,x_2,..,x_m$ , and we intent to compute FFT of each segment. Is there anyway that we can reduce computation of FFT of ...
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102 views

Restriction of Fourier Transform

I am currently reading Candes et. al.'s 2006 paper[1] on recovery of sparse signals from incomplete frequency samples. I am having trouble figuring out what is the form of the Fourier transform ...
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Relationship Between Sampled Continuous and Discrete Time Signals

Consider the sketched system below. $x_c(t)$ is an arbitrary, continuous-time signal at the input and $s(t)$ is an impulse train, defined as $s(t)=\sum_{n=-\infty}^{\infty} \delta(t-nT)$, where T is ...
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390 views

Occupied Bandwidth

I am pretty new in the field of Signal Processing. I am a structural engineering graduate student at the UT at Austin. I am currently working on a project that regards acoustic emission monitoring of ...
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140 views

An effective algorithm for convolution of very many long signals

I need to calculate the following linear convolution $$ y[n] = h_1[n] \circledast h_2[n] \circledast h_3[n] \circledast \cdots \circledast h_{k-1}[n] \circledast h_k[n]$$ where $k$ exceeds $5000$ ...
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720 views

Fourier transform of Image to identify sinusoidal sources of interference

I'm a statistics grad student, and I just started getting into Digital-Image-Processing (an analogy for processing super-large contingency tables). In the book "Digital Image Processing" by Gonzalez ...
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Multiplication property DTFT

I was truing to solve an example of DTFT which is following multiplication property. The problem is $$ a^n \sin(\omega_0 n) u[n]$$ we know that the definition of DTFT is $$ X(j \omega) = \sum _ {n=-\...
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208 views

System Identification with periodic signal confusion

I want to find the ETFE (Empirical Transfer Function Estimate) of the system $G(e^{j\omega})$: Where $H(e^{j\omega})$ is some filter that zero-mean white Gaussian noise $e(k)$ passes through. Let's ...
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443 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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Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
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275 views

What is the general feature of a time domain signal that gives a step like spectrum?

I'm trying to study a nonlinear system by sending a pulsed signal into the system and look at the response spectrum. The signal I send to the system is something like and the response spectrum from I ...
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165 views

Underwater Acoustic Positioning

I have to develop an underwater positioning system which has to determine the position of a ROV. Four buoys will be placed on each corner of a swimming pool. Each one of these buoys will be equipped ...
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129 views

Correction of a signal through a transmitter

I am inquiring as to a practical way to solve a problem I have. Basically, I need to transmit a signal, $x[n]$, through a seismic transmitter. (It will go through a D/A, etc). The transmitter that ...
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362 views

General question about DFT

I am learning Fourier analysis and without any teacher, just trying to read books on my own. I think I have made some decent progress but they are a couple of points which are still very unclear to me ...
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847 views

What is the physics behind the width of a main lobe?

We know that the square window gives the lowest main lobe width possible, and that other windows after that trade main lobe width for side lobe height. I also understand that the main lobe width is ...
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234 views

Where does homomorphic filtering stand in regards to DSP applications?

I am studying my Oppenheim and Shaffer book, (New Edition), and the last chapter deals with something called homomorphic filtering. I have read the wiki and some other websites about it, but they do ...
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983 views

Phase Correlation and Negative Shifts

I am implementing phase correlation algorithm to determine shift between two images. It generally works, but I am not sure how to interpret the resulting shift. Pseudocode: ...
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140 views

Feature Selection by Filtering

so there is this paper I'm reading and trying to understand fully: Towards Practical Identification of HF RFID Devices http://dl.acm.org/citation.cfm?id=2240276.2240278 I don't want to link the PDF ...
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3k views

FFT spectre graph measurements y-axis

I am very new to this things. Sorry for probably stupid question. I don't understand what units and meaning have the values on Y-axis of Fourier Transform graph? On X-axis it is Frequency (Hz). Pretty ...