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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Phase spectrum: $\mathrm{arg}\mathcal{F}(\omega)$ or $\mathrm{-arg}\mathcal{F}(\omega)$?

Do we need minus or not? I need to extract phase spectrum from that thing $$f(x) = \frac{1}{2\pi}\int_{-\infty}^{\infty} e^{i\omega x}d\omega\int_{-\infty}^{\infty}f(t)e^{-i\omega t}dt$$ I can do it ...
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466 views

Relation between two k-spaces phase-frequency and spatial frequencies in

When I see MRI explained, two types of 2D k-space images seem to be described as if they were the same. Axes are the two spatial frequencies. This images is directly fourier-transformed into the ...
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53 views

Numerical Fourier transform for exact frequency

Mathematically, suppose I have a function $f(t)=\sum_k c_k e^{-i \omega_kt}$, where $\omega_k$ may not fall in $[0,2\pi]$. With an analytical Fourier transform, I can get a sum of delta functions ...
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410 views

How does both shifting and scaling a function affect the Fourier Transform?

I understand how shifting and scaling work separately, but I'm unsure how to put them together. That is to say, I understand if $x(t) = X(\omega)$, $x(at) = \frac{1}{|a|}X(\frac{\omega}{a})$ and $x(t-...
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Confusion in understanding the Proof of DTFT

While understanding the proof of DTFT from Signals and Systems by Oppenheim, I have confusion in understanding few steps. $$ x'[n]=\sum_ {k=<N>} a_ke^{jk(2\pi/N)n}$$ $$ a_k= \frac{1}{N} \sum_ {...
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228 views

Image processing: High pass filter to remove lowest 16 frequencies

How can I remove the lowest n frequencies of an image? Are the lower frequencies around the centre of the FFT result?
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142 views

What are the applications of Fourier Transform Power Spectrum?

What are the main applications of Fourier Transform Power Spectrum? Can somebody clarify with some examples. Also, what are the advantages of using Fourier Transform Power Spectrum over Fourier ...
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Is TOA is different for extended target?

The time of arrival (TOA) or time difference of arrival (TDOA) beteen two signals are seen extensively in literature. Are these algorithm applicable for point target as well as extended target? For ...
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How to take IFFT of Connes Window?

The Connes Window function is defined as : w(f)=$(1-(\frac{f}{ \Delta f})^2)^2$ for $f<|\Delta f| $ w(f)=0 otherwise The inverse fourier transform of this function can be ...
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208 views

How to find a certain frequency in a signal that varies in time?

I have an EEG signal. It is amplitude verses time. I want to find out how certain frequencies in that signal vary with time. One way I think I can do this is to do a short-time-Fourier-transform on ...
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Filtering with filters without even or odd symmetry in the fourier domain

I am doing a project where I have to use the fourier domain for convolution. I have been reading Digital Image processing by Rafael Gonzalez but I unsure about one thing, and I could not find anything ...
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237 views

What am I doing wrong?-Bode plots to get transfer function

I've noticed a couple of similar questions which haven't been answered such as: https://dsp.stackexchange.com/questions/24381/derivation-of-transfer-function-from-bode-plot Anyway, I thought I would ...
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490 views

Why does the specgram of this simple sine wave look strange?

I'm trying to test some intuition using the matplotlib specgram routine. I first generate a simple sine wave ...
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47 views

Doubt related to application of FFT

I found this formula in a paper : http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=5655742 could someone explain the meaning of "j is frequency sample in the highlighted ...
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569 views

Sine wave phase shift from Fourier Transform

This is probably a really basic question but I'm a little stumped and would appreciate some practical input on how to go about doing this rather than reading dockets of equations semi-related to what ...
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135 views

Fourier transform's sine and cosine count as N grows

I remember reading that in (discrete) Fourier transform for signals with even numbered N for length, the sine and cosine count is equal. Is this correct? A bit of analysis: N=1, there is only DC ...
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Can convolution of one signal with different signals give the same answer?

Let us consider $x_1(t)$, $x_2(t)$, $x_3(t)$, all the same within some some duration 0 to $T$ but all different outside this interval. Now let us multiply each of these signals with $w(t)$, a window ...
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Length and spacing autocorrelation with FFT

I have calculated, with FFT and A-FFT, the autocorrelation of a discrete signal (coming from an integration) with spacing $\Delta T$ composed by $N$ samples padded to $2N$ with zeroes. What is the ...
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170 views

How does the OFDM system receiver decide the OFDM symbol length? [duplicate]

I am trying to understand how the receiver decides the length of OFDM symbol in time domain before it goes into DFT process at the receiver. The complete OFDM symbol (with Cyclic Prefix added) is ...
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Inferring space domain signal from 2D DFT

By just looking at the 2D Fourier Transform of a signal, can it every be known precisely which values in the space domain are zero?
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62 views

What is the 2D Fourier Transform of this function?

$ f(x, y) = \begin{cases} 1,\hspace{30px} x > 0 \\ 0,\hspace{30px} else\\ \end{cases} $ i.e. $f(x,y)$ is a bi-variate function which is zero everywhere to the left of the y-axis and one ...
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115 views

Correction of signal after High-pass RC-filter

I have one question about digital correction of signal after RC filter which is high-pass. Let me explain detail. I have one simple signal conditioner. It has RC filter on the signal input with cut-...
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How to implement Fourier Descriptor of an image?

I want to implement Fourier Descriptor of an object. I have read link. However, I have some questions about normalizing Fourier Descriptor. First, if I want to normalize the position of the starting ...
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133 views

“Normalizing” PSD of unequal window lengths

I am acquiring time-varying data with unequal sampling (nature of the source). When building a spectrogram, I have the algorithm choose sample blocks that are are -nearly- the same length -but, they ...
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424 views

How to narrow the frequency band of a wavelet

I have a ricker wavelet with a dominant frequency of 15 Hz. The fourier transform shows its frequency band is almost to 50 Hz. How can I narrow the frequency band of this 15 Hz ricker wavelet? I have ...
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281 views

Psudocode implementation of true envelope

I am trying to implement the algorithm described in this paper, I'll quote the relevant portion: http://recherche.ircam.fr/equipes/analyse-synthese/roebel/paper/trueenv_dafx2005.pdf Let $V_i(k)$ be ...
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57 views

why is the DFS of a delta function equal to 1

I have a x[n] = $\delta$[n]. By formula is should be $$ X[k]= \sum_{n=0}^{N-1} \delta[n]W_N^{kn} X[k]= \sum_{n=0}^{N-1} e^{-j2*pi*kn/N} $$ The formulae isn't showing for some reason. I took a ...
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260 views

How do I take the real part of this bandpass filter system's output?

I'm stuck on a final step in this problem. Essentially, there are the two systems above, which we'll call System 1 (Fig. 4.26, with ideal lowpass $H(jw)$) and System 2 (with $H_1(jw)$). The question ...
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400 views

Fourier Transform Problem - absolute value, time-saving tricks, etc

I am given the following signal: $$[e^{-at}cos(w_{o}t)]u(t),\ a>0$$ Then I am told to find the Fourier Transform, which tells me I need an answer of the form: $$X(jw)=\int_{-\infty}^\infty \! x(...
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60 views

Frequency of the wave in frequency domain

If we have a 1-dimensional wave in time domain, it can be represented in frequency domain with x axis indicating the frequency of the wave and y axis indicating amplitude/magnitude of the wave. But ...
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1answer
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Signal Plus Weakly Stationary Noise

I was reading the book "Spectral Analysis of Time Series" By Herman Koopmans. On Page 55, he explains that a specific type of non-stationary signal which is the result of adding weakly stationary ...
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57 views

Filtered backprojection implementatoin

I am wondering the detail of the filtered backprojection. Suppose I have a projection file: $p(s,\theta)$=[1 2 3 1 2] Then to get its filtered backprojection ...
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935 views

Inverse Chirp Z Transform

I am working to understand and use the Chirp Z-Transform. I want to use the algorithm for simple signal processing on data sets that are not a power of two. I need to be able to inverse transform as ...
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1answer
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How to perform a Stockwell Transform on a 2D matrix

I was looking at performing a Stockwell transform on a matrix (or an image as it has two directions - the matrix I am interested in has a spatial dimension and a time dimension, but this should make ...
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931 views

Fast Fourier Transform and Clustering of Time Series

I'm making a project connected with identifying dynamic of sales. That's how the piece of my database looks like: There are free columns: Product - present the group of product Week - time since ...
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Why does the inverse fourier transform of a lowpass filter have complex components in matlab?

I am quite confused whether the following numerical differences i find are just severe round off errors made by matlab, or something i am doing wrong. The following happened when trying to see what a ...
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218 views

Determining Valid DTFT's

Are the following frequency domain signals valid DTFT's (Discrete Time Fourier Transforms)? Answer yes or no, and justify your answer. a) $X(\omega) = \omega + \pi$ b) $X(\omega) = i + \pi$ c) $X(\...
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discrete fourier transform in Matlab - theoretical confusion

I have a periodic term $V(x) = \sum_K \exp(iKx) V_K$ where $K =2\pi n/a$ where $a$ is the periodicity of the term and $n =0,1,2,3....$ Now I want to find the Fourier coefficient $V_K$ corresponding ...
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148 views

Suggestions for FFT based tools to analyze music - Preferably MATLAB/free software packages [closed]

I am interested in analyzing full length songs for general features of the track which are not otherwise apparent. For e.g., I want to look at various parts of the song with time-frequency plots/...
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130 views

Estimating and Improving the accuracy of fourier transform in the low frequency sector

I have a time series file which starts with 1 and then quickly tends to oscillating about 0.001. The time series has a resolution of 0.01s and has 10^6 sequential points starting from t=0. The goal is ...
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133 views

Fourier Transform & Convolution to get response - confused

in the past couple of years I've always been using Laplace transform for system responses, but today tried to do it with Fourier transform and failed. What am I doing wrong? If we have a signal $x(t) ...
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283 views

How is it possible to find the Fourier transform of unit impulse function?

Since Fourier transforms are applicable to only periodic functions, and unit impulse function{..0,0,1,0,0..} doesn't seem periodic, is this possible? Is it like we are considering unit impulse ...
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Covolution of DTFT [duplicate]

Possible Duplicate: Convolution and DTFT $x_1(n)=x_2(n)=1$ where $0 ≤ n ≤ N-1$ 1)The linear convolution of the signal gives a triangle how you write it in mathematical form? The DTFT of the ...
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618 views

How to understand FFT results of scipy.fftpack?

I calculated FFT for a speech wav-file using scipy.fftpack. How do I read (understand) the return of FFT? I have read that it supposed to be like so: y[0] is 0Hz loudness, y[1] is 1Hz loundess, ... y[...
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Problem designing a specific filter

I have the next problem. $H_{c1}(j\omega )$ is the ideal antialising filter and $H_{c2}(j\omega )$ is a real one. I'm asked to design $H(e^{j\Omega })$ so that $y[n]$ in the second diagram (the one ...
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Simulation of a pressure field developed by a song

Greetings! What I am doing: In short, I want to write a program that is fed a song as a wav file, and spits out an animated contour plot indicating the relative pressure/loudness/quantity indicating ...
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1answer
227 views

UWB radar to find heartbeat

I have a UWB radar that Im playing with. The problem is that my algorithms at the moment can clearly, reliably and validly pick up 1-2mm movements of a pendulum i've set up. However, when I use it on ...
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1answer
113 views

Basic Confusion About the DFT and Convolution

I am learning DSP (with Digital Images) and I have some elementary confusion about the convolution between two discrete periodic signals. Specifically, I have learnt that when filtering an image, we ...
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1answer
158 views

why $-$ sign in DTFT pair for constant

In discrete time Fourier transform, The DTFT of constant 1 is $$\sum_{l=-\infty}^{+\infty} \delta(\omega-2\pi l) $$. I have confusion that why there is $-$ sign, why it can't be $$\sum_{l=-\infty}^{+\...
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How to compute the Fourier Transform of this ramp-like signal?

I have the following signal: and this as the solution to the problem: $$\begin{align} X(j\omega) &= \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \\ &= \int_0^\tau \frac{E}{\tau}t\; e^{-j\...