The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
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Artifacts in FFT
I recently realized that FFT's aren't perfect. Meaning if I take a signal and then take it's FFT, and then do an inverse FFT, the resulting output isn't exactly the same as the input. Here's an image ...
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2answers
63 views
Why integrate over $2\pi$ in inverse DTFT?
In DTFT of a signal, the spectrum of a sequence is periodic with period $2\pi$ and all the information needed for derivation of the original signal from its spectrum is contained in $\pi <\omega ...
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2answers
130 views
How were windows originally conceived?
I am aware of the common types of windows, (Hamming, Hanning, Kaiser, Tukey, etc etc). However while many books describe them - almost none tell me just how exactly they were derived.
What is so ...
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1answer
29 views
Plot the magnitude of coefficients against frequencies of DCT transform
When we perform DCT transform using matlab:
...
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1answer
34 views
Calculate maximum of filter kernel
I'm sure there must be an easy way to do this, but given the Fourier transform of an isotropic filter kernel, $\hat{f}(\mathbf{u}) = \mathcal{F}f(\mathbf{z})$, can one calculate the value of the ...
4
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3answers
168 views
Mathematically inclined Signal and Systems/Signal Processing book?
I'm an electronics engineering student with high inclination to analysis and pure mathematics. I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal ...
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1answer
38 views
What is the meaning of $Ta_k$ of fourier series or transform?
What is the meaning of $Ta_k$ of fourier series or transform?
I am taking a course on signal and systems.
In 286 page of my textbook, it says that as T becomes arbitrarily large the original periodic ...
2
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3answers
113 views
Calculating an image's fourier spectrum by hand?
Suppose I have a $4x4$ image with the following values as its grey-level intensity for each pixel like this:
I want to get its Fourier spectrum. Usually, I would just punch into Matlab and run a ...
3
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2answers
69 views
Centering zero frequency for Discrete Fourier Transform
I am working on a image processing application which uses a discrete fourier transform to implement blurring/sharpening. The application is more or less working, but something about the mechanics is ...
2
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1answer
112 views
Benefit to know Fourier series for image processing? [closed]
I know there's a benefit of knowing the Fourier Transform for image processing, but is there a benefit to know Fourier series, or could you just skip them? Would you recommend skipping Fourier series ...
5
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1answer
81 views
Phase Correlation - Poor Performance on Noisy/Blurred Images?
I have successfully tested 1D phase correlation algorithm to determine vertical shift between two synthetic images.
When I moved to real images, however, it is not able to detect translation at all ...
2
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0answers
55 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:
...
3
votes
1answer
65 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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0answers
31 views
Fourier Transform Computer Vision Textbook
I am required extremely fast to fill the gap and learn Fourier Transform with application in Computer Vision.
It was easy to find mathematical aspects of Fourier Transform, but I am more interested ...
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1answer
53 views
what is probability density function (PDF) of periodic signal
anybody knows what is the best pdf for periodic signal ?
I have signal with 480 samples (16000*0.03=480) but I could not find the exact pdf for that. sometimes it appear like 2 mixed Gaussian.
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2answers
69 views
Interpolation vs Interpolation Filter?
Hi guys, I've been reading some papers on - how to remove ghosting artefacts from the Fourier Slice theorem applied to a 3D discrete image volume. The papers mention that in order to remove ghosting ...
4
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2answers
186 views
FFT of input length 1536
Does anyone knows can i find a FFT of 1536 length input. Its a specification given in 3gpp Lte and we need a transform of 1536 input size which is neither a power of any number i would say. I just ...
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2answers
125 views
FFT for a single frequency
I was looking for a more efficient way of finding the magnitude and phase of a signal at a certain frequency without performing an FFT because it produces more information than I need and I came ...
2
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0answers
82 views
A simpler method or more descriptive answer to the Fourier Transform
I'm trying to do a CT Fourier Transform of these two signals
$$x_1(t)=e^{−a(t−1)} \cdot u(t−1)$$
and
$$x_2(t)=e^{−a(t−1)} \cdot u(t)$$
Where $a$ is any real number, and $u(t)$ is the unit step ...
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3answers
75 views
Image processing, recognizing a small feature in a larger image
I am trying to write an image processing program to recognize bubbles in oil.
It has been suggested I try computing the convolution of the image and an image of a typical bubble.
i.e. : ...
0
votes
1answer
72 views
How to calculate the energy levels of frequency intervals of an audio signal?
Using the Fourier transformation I can translate a signal from the time-domain to the frequency-domain. If I divide the frequency axis into intervals, how can I calculate the audios signals energy for ...
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1answer
51 views
What is the role of complex exponential?
What is the role of complex exponential $ e^{jθ} $ in Fourier Transform? Is it different in the continuous and in discrete time domain?
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1answer
42 views
Question about the Haar Wavelet transform
I'm trying to detect the presence of a sinusoid in 1/f noise conditions using the STFT and the DWT with Haar wavelets. I find this interesting phenomenon that I'm not able to explain (see plot at 1)
...
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2answers
93 views
FFT of random binary data
I am trying to make sense of FFTs and binary data.
Say I have a series of random binary data, which is measured with a repetition rate of 400Hz (interval time of 0.0025s). I have a total of 12489 ...
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0answers
29 views
Differentiate between two sounds made by same person
I want to know if i pronounce alphabet "A" then i pronounce alphabet "B" how can i detect the difference between these two sounds. I know a sound is characterized by its frequency and amplitude but ...
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0answers
26 views
How to convert a sound file to any other data format which can be manipulated
I know this is very basic question and i am new to this site. But can anybody help me with my question. How to convert a sound file to other data format say using some type of transform (FFT or DFT) ...
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1answer
73 views
Approximation using a Fourier transform with low pass filter
I need to approximate a function f, but I cannot do so with frequencies that exceed 1kHz
What is the best approximation I can get? Is taking the Fourier transform then zeroing any term above 1kHz the ...
2
votes
1answer
50 views
How can I find the amplitude of the 20 Hz frequency component of a signal faster?
I have a time varying discrete signal x(t) sampled at 5ms rate.
I need to find the amplitude of the 20 Hz frequency component for each sample.
What I do today is that for each sample I do a Short-time ...
2
votes
2answers
106 views
What is $F(0)$ is “dc” component in the context of image processing?
It has always been said that $F(0)$ is the "DC component" in fourier transform. However, I don't get what it means to say that $F(0)$ is "DC" in the context of image processing.
The zero in this ...
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1answer
47 views
Which approach is better for decomposing a image into high frequency and low frequency component?
Which approach is better or there is mathematical justification for using Bilater filter and Fourier Transform to decompose a image into High Frequency and Low Frequency Component.
Both Bilateral ...
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1answer
58 views
How can I detect clicks/ticks in a wav file?
I have a long recording of a train (here is a small sample) there are a number of clicks as the wheels go over joins in the tracks. I would like to detect the location of these.
Looking at the ...
3
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0answers
31 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 ...
3
votes
0answers
77 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 ...
2
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1answer
193 views
About the fourier transform of Periodic Signal
I cannot understand some part of the period signal's Fourier transform.
Here this my note's methods,
For periodic signal with period $T_0$, define as $s_{T_0}(t)$ as
$$
s_{T_0} (t) =
...
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1answer
161 views
DFT as convolution question
I have tried to make this question as readable and consistent as possible. The short of it, is that I am trying to ascertain how one gets from the math equation shown, (which I understand), to the ...
3
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0answers
78 views
Global Transforms besides the DFT?
This is a simple question. Fourier analysis gives us the DFT, which is known as a global transform of a signal. In contrast, the Discrete Wavelet Transform (DWT) has a plethora of wavelets, all of ...
3
votes
1answer
86 views
Finding out modulation index and dc offset
I have a question form my teachers, and I cannot understand why I can find out the modulation index form the figure.
The question provide a Figure like this.
And the information signal is a ...
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votes
1answer
88 views
How do I find the power of a specific frequency at a specific sample of a discrete time varying signal?
EDIT:
First off let me explain that I understand that frequency makes no sense for a single sample. What I am actually talking about is the power spectrum within a short time window around a specific ...
3
votes
0answers
49 views
What are the uses of those three types of wavelet transformations?
In my studies of wavelets, there appear to be 3 different families of them:
The Continuous wavelet transform
The Discrete wavelet transform
The Redundant wavelet transform
They are all based on ...
2
votes
1answer
116 views
How to find the envelope of a wide-band signal?
I would like some feedback on possible techniques that one may use to determine the envelope of a broad-band time domain signal. I have heard anecdotally, that it is not as straight-forward as it ...
4
votes
1answer
113 views
What happens if we change the limits of integral in Fourier transform?
By definition of fourier transform
$$X(w)=\int_{-\infty}^\infty x(t) e^{-jwt} dt $$
Now what will happen to the answer of transform for example in case of $x(t)= cos(w_ot)$ if limit is 0 to A ...
4
votes
3answers
197 views
What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?
At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
2
votes
2answers
84 views
Determining the period of a discontinuous function
I'm new to the field of DSP.
I'm trying to determine the period and shift of the function. I've tried using FFT, but haven't had much luck. Seems like it should be simple.
Signal (pastebin of ...
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0answers
24 views
Covolution of DTFT [duplicate]
Possible Duplicate:
Convolution and DTFT
$x_1(n)=x_2(n)=1$
where $0 ≤ n ≤ N-1$
1)The linear convolution of the signal gives a triangle how you write it in mathematical form?
The DTFT of ...
1
vote
3answers
132 views
Chop out frequencies outside human hearing range
I have a bunch of audio files all sampled at 44100 Hz sample frequency. I am trying to remove all the frequencies which are outside the human hearing range (I use the following as reference: Frequency ...
0
votes
1answer
187 views
FFT of color images incorporated into an Object Recognition method?
Is there any instance where Fourier transforms of color images have been used in conjunction with other object recognition method?
Any instance of usage of Fourier transforms in color images? I ...
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2answers
69 views
Obtaining the Impulse response from the frequency of a discrete system
I have the following discrete system's transfer function (Z domain):
$$h[z] = {z \over z - \frac{1}{2} }$$
I need to obtain the following:
The frequency response.
The impulse response.
The fourier ...
1
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1answer
49 views
Vestigial Filter problem?
I have been stuck on this question for a while now. It has to do with vestigial sideband.
I wasn't sure if I should be dividing $H(\omega)$ graph values by 2 because only the positive side of the ...
3
votes
1answer
140 views
Signal Processing using Fourier Transform
So I'm trying to understand how MRI machines work. I understand all the concepts of it, the parts, what they do, how the machine works, etc. The part I'm having trouble with is the fourier transform ...
5
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2answers
200 views
Fourier Transform of cosine to the power of 3
How can I find the Fourier transform of
$$ f(x) = ( \cos(x) )^3$$
I know that for $ g(x) = \cos(x) $
$$ F \Big\{ g(x) \Big\} = F \Big\{ \cos(x) \Big\} = \pi \Big [ \delta(w-\pi / 2) + \delta(w+\pi ...
