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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225 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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2k views

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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568 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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1k 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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183 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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435 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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69 views

how to plot fft with imaginary and real part in 3d or calculate the degree of rotation

I would like to make a plot like 1 and see the real and imaginary part in a 3d space. I dont want to make exactly the same plot. for me it is okay if i see the peak for both signals shifted. it is ...
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88 views

Fourier coefficients of 1/(1+it)

I have to find the Fourier coefficients of $$ \frac{1}{1+ t^{2}} $$ I tried with $$ \frac{1}{T}\int_{0}^{T} \frac{1}{1+it}e^{-i 2 \pi f_0 T } $$ but I should do at least two integrals by parts , so I ...
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Why is a circular mask appropriate for Fourier filtering rectangular images?

Suppose I apply 2D DFT to an image with dimensions $H{\times}W$ where $H \neq W$, then shift the DC component to the center. Why does a circular mask capture the lowest frequency components, i.e. why ...
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42 views

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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262 views

Applying duality property to fourier transform of unit step function

For Continuous time aperiodic signals, the duality property of Continuous Time Fourier Transform (CTFT) is following $$\mathscr{F}\Big\{x(t)\Big\} = X(f), \qquad\text{then} \quad \mathscr{F}\Big\{X(t)...
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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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408 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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135 views

Use samples of Fourier transform as DFT?

Consider the LTI system given by: $H(z) = 1 - \frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$ Let $x[n] = (\frac{1}{2})^nu[n]$ be the input to the system. We want to find the output for $n = 0,1,...,N_a$, using ...
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181 views

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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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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258 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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104 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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428 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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146 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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840 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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246 views

System Identification with Periodic Signal Input

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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456 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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276 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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172 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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131 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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369 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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951 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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237 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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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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146 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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1answer
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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 ...
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312 views

Channel Vocoder producing output with “click” sounds

I'm trying to make a channel vocoder that takes two inputs, one a frequency rich carrier (a musical sound) and the other a modulator (vocals). Applying operations involved in the channel vocoder ...
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77 views

Impulse response of a time scaling system

Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system? \begin{array}{l} X( \omega ) \ =\ \int ^{\infty }_{-\...
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244 views

Fourier transform of a damped cosine wave with a linear frequency chirp

I want to take the Fourier transform of the following transient signal, $$f(t) = e^{-t/\tau} \cos((\omega_0 + m t)t)$$, where $m$ is some gradient parameter in units of $\rm{Hz}/s$. I thought this ...
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575 views

Evaluate Fourier coefficients at arbitrary point using Python

Lets say I have a sinusoidal function $s$ that looks like ...
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65 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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What's spectral “tilt”?

I am looking at article Speech-in-noise intelligibility improvement based on spectral shaping and dynamic range compression. In paragraph 2.2 the article mentions "tilt" of the spectral envelope. The ...
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Can you use Fourier transformations (or other) to read multiple superimposed barcodes?

If you printed bar codes on tracing paper/acetate etc. and then positioned several in front of one another, could you extract the individual codes from the aggregate overlaid image? I feel intuitively ...
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How to calculate the energy in the dirac delta function signal?

I'm having DSP for the first time, and after some classes I got confused about the following: Suppose I have a signal which its fourier transform in a frequency band $[ \omega_1,\omega_2] $ is just a ...
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282 views

Aliasing in the Short time Fourier Transform of a pulse

When attempting to take the Short Time Fourier Transform of a pulse, at the end of the pulse I'm running into problems. The signal looks like this at the end (it is a simple $sin^2$ pulse envelope, ...
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5k views

Discrete Fourier Transform by hand

I have an assignment where I'm given the DFT of a sequence $x[n]$ as $X[k]=\{4,3,2,1,0,1,2,3\}$ and also $$y[n] = \left\{ \begin{array}[cc] xx[n/2] & \text{if n is even} \\ 0 & \text{otherwise}...
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FIR filter design by the Fourier transform method

I am having some problems understanding how the Fourier transform method is used to determine the FIR filter. As far as i have understood, you start by using the ideal impulse reponse for the ...
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158 views

Understanding Walsh coefficients

I am working with Walsh coefficients. I know the intuitive understanding is almost that that they are the degree of connectivity, but it is there a better way of thinking about it? What is the ...
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406 views

Discrete Fourier transform in a multidimensional space

I want to measure the frequencies at which a point oscillates in a multidimensional space, let's take the example of a point on a 2d-surface. For now, I naïvely split the signal in two, along the ...
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110 views

Global Transforms besides the DFT?

This is a simple question. Fourier analysis gives us the DFT, which is known as a global transform of a signal. In contrast, the Discrete Wavelet Transform (DWT) has a plethora of wavelets, all of ...
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4k views

What does the exponential term in the Fourier transform mean?

We know that Fourier transform $F(\omega)$ of function $f(t)$ is summation from $-\infty$ to $+\infty$ product of $f(t)$ and $e^{-j \omega t}$: $$ F(\omega) = \int\limits_{-\infty}^{+\infty} f(t) \ e^...
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752 views

To what extent can we see signals that fall between frequency bins?

I have a simple problem I would like to figure out for fourier analysis of seismic data. Let us say that we have a signal $z[n]$, of length $N$. If I take its (same size) FFT, I will get $Z[k]$, ...

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