# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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 $... 1answer 230 views ### Efficient FFT (or SFFT) for adjacent parts of signal with overlap? Imaging we have a signal$x$, which is segmented to 50% overlapped vectors$x_1,x_2,..,x_m$, and we intent to compute FFT of each segment. Is there anyway that we can reduce computation of FFT of ... 1answer 102 views ### Restriction of Fourier Transform I am currently reading Candes et. al.'s 2006 paper on recovery of sparse signals from incomplete frequency samples. I am having trouble figuring out what is the form of the Fourier transform ... 1answer 2k views ### Relationship Between Sampled Continuous and Discrete Time Signals Consider the sketched system below.$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 ... 1answer 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 ... 1answer 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$5000$... 1answer 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 ... 2answers 2k views ### 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=-\... 1answer 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 ... 1answer 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 &... 2answers 1k views ### 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 ... 1answer 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 ... 1answer 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 ... 1answer 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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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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### 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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### 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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### 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: ...