The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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Comparison between 2 images in Frequency domain

As you can see there are 2 images from the Tom and Jerry cartoon program. In the 1st image both Tom and Jerry are present. But in the 2nd one,only Tom is present.Now,we can clearly see this ...
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16 views

Inverse DTFT Problem

Having trouble finding the inverse DTFT of $\ X(\ e^{j \omega}) = \frac{3 - \frac{1}{4} e^{-j\omega}}{1 - \frac{1}{4} e^{-2j\omega}} $ Given the IDFT of $Xe^{j \omega}$ as : $x(n) = \frac{1}{2\pi} ...
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36 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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1answer
37 views

How Fourier decomposition is performed?

The Fourier decomposition explains a time series entirely as a weighted sum of sinusoidal functions and with the Fourier series,it is possible to do it. But I have some doubts Suppose ,for any ...
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9 views

How modulation spectrum of zebra finch song is calculated

I read this advanced signal processing technique in Neuroscience Journel. Modulation spectrum is a spectral modulation vs temporal modulation plot. Please tell procedure of plotting it step by step. ...
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18 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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1answer
21 views

How to set sampling frequency of an acceleration data set

I have a set of accelerometer readings in X, Y, Z axes obtained from an android based smart-phone. The data (in X, Y, Z) was recorded at different time stamps and there is no uniform time period for ...
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9 views

Energy-based speech recognition [duplicate]

I have a noisy recording with individual letters spoken. In a spectrogram view of the audio, the letters have higher energy. What can I use to isolate them? I'm fine with any tool.
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23 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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38 views

Can a infinite bandwidth signal Be a infinite Time SIgnal?

While Decomposing the impulse train using the Fourier series the no. of the samples are infinite hence representing a infinite length of train. But while studying the Nyquist Criteria in the ...
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49 views

LTI system, Fourier transform, unit step function, sine wave

I just finished learning about Fourier Transforms and don't understand this signal: $$x(t) = \cos(\omega t)u(t) $$ This is a cosine wave but only where $\omega$ is positive. My question is what can ...
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30 views

why do we use $X(e^{j\omega})$ instead of $X(j\omega) $ in Discrete Time FT

I am studying DT-FT. But I cannot figure out why we use $X(e^{j\omega})$ instead of $ X(j\omega) $ in DT FT Thanks in advance..
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what is the difference between $X(j\omega)$ and $X(\omega)$ notation

I am trying to understand Fourier Transform and Laplace Transform. What is the difference between $X(j\omega)$ and $X(\omega)$ notation? what is the meaning of $j\omega$ ? Is it represent frequency? ...
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2answers
63 views

What is Fourier transform in terms of area under the curve?

We know that integration gives area under the curve. And that FT is also an integration. How do we interpret FT in terms of the area under the curve especially because e^(jwt) is a complex term? In ...
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38 views

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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22 views

Changepoint Detection of a 2D signal

Consider the 2D signal below I would like to find the changepoints in the signal (using a hierarchical approach). Based on our visual observation, we can see there are 2 main changepoints where the ...
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1answer
103 views

How to find phase values on precise pixel locations of a given Image? [closed]

I have computed magnitude and phase spectrum of cameraman Gray scale image using fft function. Here, we get magnitude and phase spectrum of the whole image. .Please see the reconstruction of image ...
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27 views

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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1answer
31 views

Testing discrete data for periodicity

I have some data which looks roughly periodic - is there a nice way to measure this? This is an example I'm working on and I'd like a metric that I will be able to just threshold to give a decision ...
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19 views

frequency domain image analysis for recognition purposes

There are many areas like, gait analysis, where we recognize persons by analyzing their silhouettes taken while they are at different stages of their walking where analysis also carried on in ...
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259 views

Fourier Decomposition

Hello everyone have a look at this video of Fourier Decomposition of an image(otherwise you can also refer the image which shows few plots of different extracted waves from an image) . We also know ...
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2answers
127 views

Finding the Harmonics contained in an Image?

I am beginer in image processing. Any signal whether it is 1D,2D or any multidimensional signal can be represented using combination of number of sine and cosine wavesforms (harmonics). Similerly any ...
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71 views

Dominating frequency in a “clear” 50 Hz signal

I am trying to find out the dominating frequency of a signal with a frequency of 50 Hz (sampled at 200 Hz - every 5 milliseconds). The python code I am using to do this is the following (based on ...
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1answer
37 views

How to choose between taking the real part or the absolute value of an inverse discrete Fourier transform?

I kind of expected this to of been asked before, so if this is duplicate please point me in the right direction, however I couldn't find anything. I am currently experimenting with low pass ...
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1answer
83 views

Intuitive explanation of cross-correlation in frequency domain

According to the cross-correlation theorem : the cross-correlation between two signals is equal to the product of fourier transform of one signal multiplied by complex conjugate of fourier transform ...
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1answer
103 views

Shift in Time-Domain after FFT-Convolution

To my understanding, multiplying a signal in the frequency-domain is equal to a convolution in the time-domain. I wrote a small python program, but i always end up with a shift in the time domain. ...
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41 views

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
26 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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2answers
178 views

Can anybody explain about phase shift and phase spectrum terms in case of multidimensional signal?

I know about phase of a 1D signal. But when I go into higher dimensions like 2D,3D etc, it becomes headache to grasp the concept. What are the terms phase shift and phase spectrum mean in case of ...
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182 views

Whether phase congruency and phase coherence terms are same or different?

I am beginner in Image processing.I am studying the importance of phase in signal.Can anybody explain what is phase congruency ? Also,I am confused between terms i.e. phase congruency and phase ...
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63 views

Normalize Fourier Transform For Video Game

I am in the process of developing a video game where I would like to sync a character's mouth with an audio clip of their speech that is playing. I found this great website that shows the profiles of ...
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4answers
476 views

What's the exponential term in 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) \ ...
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45 views

Exact formula for alias of Discrete Fourier transform for periodic sigals

Suppose that $f(t): \mathbb{R} \to \mathbb{C}$ is a $T$-periodic signal, with highest frequency $f_h$. Now suppose that our sampling rate frequency is lower than $f_h$, and is not any multiples of ...
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implementing bandwidth filter in R

I am reading this "how to" in R: http://www.inside-r.org/howto/time-series-analysis-and-order-prediction-r I am confused about the tutorial's implemented band pass filter. In particular, here's the ...
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40 views

MFCC from DFT (FFT)

I want to write an speaker recognition application (based on some password recorded few times for the authorized person). I've decided to do it with C++ and BASS library (http://www.un4seen.com/). I ...
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33 views

Help with Fourier transform [duplicate]

Firstly I must say that I'm beginner in field signal processing. I'm familiar with Fourier series but I have some hard times in learning Fourier transform. Why we use it? What's purpose of Fourier ...
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25 views

How can I make the mean of samples be approximately equal to the mean of actual continuous signal?

Suppose there is signal $f(t)$ that is continuous and periodic. It is known that this $f$ is $T$-periodic. (but it's not necessarily a single cosine $f(t)$.( I'd like to make the mean of samples be ...
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69 views

Can I study continuous time Fourier Transform and treat the rest as special cases

Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to Lapace transform, Z transform, DTFT, DFT, Fourier sequence ...
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11 views

Transposing pitch profile of one audio on another

I have one audio file with rap music and one audio with sound record of my friend's reading some text. I want to transpose pitch profile of rap music on sound recording, is that possible? I can ...
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133 views

Skew detection and correction using Fourier transform

I was trying to implement skew correction method for scanned documents using the method described in this paper. The algorithm steps: 1- Threshold the image . 2- Find the fourier transform. 3- ...
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1answer
32 views

Filtering and Fourier Transforming, does the order matter?

I have a signal $x(t)$. I want to find the Fourier Transform of it, $X(f)$, and then extract a narrow frequency range from $X(f)$ by use of a Band Pass Filter (BPF) in frequency domain. Can I instead ...
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1answer
18 views

How to equalize frequency contents using filter?

Suppose there is a bounded continuous signal $f(t)$ that can be fourier-transformed into $F(\omega)$ of frequency contents. $|F(\omega)|$ is non-zero for only finite number of frequencies: ...
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1answer
37 views

Compute Similarity between Fourier Transforms

I'm looking to compare the Fourier Transforms generated by accelerators and gyroscopes that collected data of people walking. I've looked to see if there is a standard form of comparison, but I have ...
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26 views

Does the enlarged photo benefit from shrinking it?

Take a look at the following diagrams: The original picture: The upscaled (2x, bilinear) picture: In both cases the first item in first row is the input image. There is it's 2d fft next to it. ...
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13 views

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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48 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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23 views

energy and power type signals [duplicate]

How can I determine if the signal $$\begin{array} \\g_1(t)=A\cos (2\pi f_c t), & \frac{-T}{2}<t<\frac{T}{2} \\ 0, &\text{otherwise} \end{array}$$ and: $$g_2(t)=\cos(t), -\infty < ...
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86 views

Signal Processing using Fourier Transform

How can I derive the fourier transform of ...
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21 views

How to determine stopband of discrete Gaussian, stdev sigma, support N

I would like to analyse a gaussian smoothing kernel with a set standard deviation and support (let's say, in MATLAB, fspecial('gaussian', [5 1], 1.3) so sigma is 1.3 and support is 5) in the DTFT ...
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1answer
23 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 ...