Questions tagged [fourier]

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1 vote
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41 views

A different FFT algorithm that achieves the result of zero-padding?

I have been figuring out how the Cooley-Tukey FFT algorithm works out of curiosity. After succesfully (re)creating the algorithm in python I started wondering if I could add another 'stage' to the ...
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1 answer
43 views

Trying to find the Fourier Series Representation of a sum of Sinusoids

Given a signal: $$x(t) = -5\cos{(93.6\sqrt{2}\pi t - 2\pi/3)} + 3 \cos{(135.2\sqrt{2}\pi t + \pi/13)}$$ I am confused about the right process to take or if there is an easier way than following all ...
0 votes
2 answers
35 views

Problem with transforming a tophat to obtain a sinc?

I have observed that the Fourier transform of a tophat function is a Sinc-like function with higher peak sidelobes than an actual Sinc. However, the Fourier transform of a Sinc is a tophat-like ...
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1 vote
3 answers
152 views

Sample Frequency does not matter if it is sufficiently large

I'm not able to convince a colleague on the following topic. Statement: If, and only if, the sample frequency is sufficiently large and above the Nyquist frequency it does not matter what fs is as ...
0 votes
1 answer
27 views

perform fourier-type integration using DFT misunderstanding

I need to perform the following integral ($i^2 = -1$) (with a fixed value of $m$): $ \int_{\phi=0}^{\phi=2\pi} \psi(\phi) e^{-im \phi} \hspace{0.7mm} d\phi $ for all values of $m$ in $\{-N_{\theta}, -...
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1 answer
110 views

sampled FT of Continuous time LTI output

I am trying to compute the sampled Fourier Transform of a Continuous Time LTI system output. $x(t)$ is the input of LTI and $h(t)$ is the impulse res. $y(t)$ is the output. we know that $$ y(t) = \...
1 vote
0 answers
58 views

Fourier transform of a top-hat function in the Faraday Measurement synthesis context

I'm currently trying to calculate the Fourier transform of a top-hat function in the context of Faraday Measurement Synthesis. This is pretty straightforward, however, I cannot understand why I cannot ...
0 votes
0 answers
23 views

Fractional Fourier Transform of a Scaled and Shifted Function

I am trying to figure out what the Fractional Fourier Transform of the signal $\sqrt{c} x(c(t-\tau))$ would be with respect to that of $x(t)$. According to the paper "The Fractional Fourier ...
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33 views

How to calculate DFT of signal which occurs from 3 to 8?

How can I calculate discrete fourier transform of this signal? I'm confused as in the normal cases signal always start from 0 to N-1 but in this case it starts from 3 to 8 instead. So what would be ...
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0 votes
1 answer
74 views

Given the Fourier Transform of a continuous signal how can I sketch the sampled signals discrete time fourier transform

I am given the frequency response for a continuous time signal $X(j\omega)$ = 2 at $\omega=0$ and 0 at $\omega = -10000\pi$ and $10000 \pi$. Looks like a triangle. I am told to sketch $X(e^{jw})$ ...
0 votes
0 answers
25 views

What can I do to improve the sound of a signal?

I want to improve the sound of my signal, I know I can do it by increasing or decreasing the amplitude of the signal itself. Are there any other ways to do this? How can I apply the Fourier transform ...
0 votes
1 answer
52 views

What's the difference between male and female voice? [duplicate]

If I record the voice of a man and a woman, what are the main differences I get in the various spectra and harmonics in Fourier analysis?
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0 answers
42 views

What happens if I register my entry?

Taking as an example that I want to record my voice. How does it appear in the frequency spectrum? Can I also view it on other spectra?
1 vote
1 answer
45 views

Computing the frequency response using fourier transform of an unstable LCCDE system

Given LCCDE system. Is it possible to calculate the frequency response using Fourier transform?
0 votes
1 answer
42 views

Continuous Inverse Fourier Transform [closed]

How to find inverse Fourier transform of: $ X(j\omega) = \frac{cos(3\omega) \cdot cos(\omega)}{\omega^2} $ The answer to this question is: $ x(t) = \frac{1}{2} y(t + 1) + \frac{1}{2} y(t - 1) $ where $...
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0 votes
0 answers
60 views

Fourier Transform: $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$

I'm currently studying Fourier Transforms and do not understand the Fourier Transform of $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$ My solution states that it is $X(\omega)=\frac{2}{2\pi}(-j\pi[\delta_0(...
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0 votes
2 answers
143 views

What is the reason of existence of Fourier transform? (Why we use Fourier transform?)

I'm currently trying to understand Fourier transform and I've got curious about why Fourier transform exists. Let's suppose that we have a 10 seconds of non-periodic wave. For example: As far as I ...
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0 answers
46 views

What is the trigonometric form of the discrete-time Fourier series or inverse discrete Fourier transform?

As we know, the continuous-time Fourier series (CTFS or just FS) has three forms: the trigonometric, the amplitude-phase or compact trigonometric, and the complex exponential. I've found formulas for ...
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0 answers
62 views

Transform fourier a cos wave [duplicate]

I have this $\cos(100\pi t)$ or $\cos(100\pi t)$ wave. How can I Fourier-transform this function? One of my thoughts is that $π[ δ(f-100)+δ(f+100)]$. So the transfer is good or wrong?
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0 votes
1 answer
83 views

What is the transform of δ(5t)?

So my question is here: How to transform the function $\delta(5t)$? I know that this function when is transformed on Fourier it will be $1$, but the $\delta(5t)$ is going to be and this $1$ or ...
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0 votes
1 answer
327 views

What is The Fourier Transform Formula for 1/(j*pi*t) Types?

I have old homework and solution of that but i didn't understand actually solution. Because i didn't see continous-time fourier transform formula for that. $g(t)$=$\frac{1}{j\pi*t}$ and it asks ...
1 vote
1 answer
112 views

2D Fourier transform over mask of an image

I have an image, which has an inherent mask built into it. The exact shape isn't super important, but it looks something like a circ multiplied by a rect. I would like to calculate the 2D Fourier ...
1 vote
0 answers
85 views

Confusion regarding STFT phase vocoder-based pitch shifting

I'm currently working on a phase vocoder implementation based on the Short-Time Fourier Transform; it's heavily based on the models described here and here. I have successfully completed the analysis ...
0 votes
1 answer
64 views

Fourier Series of a piecewise function

I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
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-2 votes
1 answer
66 views

Why don't we use partial Hz? [closed]

Hertz seems to be considered a fundamental and atomic unit that we modulate or analyze. 112Hz, 113Hz, etc. Wouldn't we have more to work with if we considered sub-Hertz granularity, e.g. 112.5Hz, ...
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1 vote
0 answers
57 views

How to find sharpness of an image?

I have a rather difficult image processing image. I would like to rank order a set of images I have by their sharpness. The issue is the images themselves are not of the exact same thing. Usual ...
0 votes
0 answers
98 views

Approximation of Periodic Parabolic Function by Fourier Series!

I've just tried to approximate the periodic-parabolic signal by Fourier Series. I know, this sounds a bit strange. I am just trying to figure out relationship between Fourier Series and Taylor ...
0 votes
1 answer
222 views

Prove Discrete Time Fourier Series Multiplication property

Note: This is not a homework problem. I'm just stalled at a point because I think I might be interpreting the duality property incorrectly. If $x_1[n]$ and $x_2[n]$ are periodic with period N, then if ...
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0 answers
85 views

Gabor uncertainty and time-frequency resolution

I have a question about Gabor's uncertainty theorem, and how it relates to time and frequency resolutions. As I understand it, Gabor's uncertainty theorem states that the standard deviations of a ...
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0 votes
1 answer
74 views

How is this given impulse response of infinite duration? Isn't it just from -π to +π?

How is hd(n) infinite duration when it is from -π to +π. Book says as it is infinite duration, we in the next step take-: h[n]=hd[n] from n=-(N-1)/2 to (N-1)/2 and 0 otherwise. I can't see how this ...
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-2 votes
3 answers
321 views

Convolve with a box filter in time domain

To low pass filter a signal, we have to convolve it with a sinc function because it's the same as multiplying the Fourier transform of the signal with a rect function, resulting in the high frequency ...
0 votes
1 answer
74 views

Can FFT tells us existance of same frequencies with different phases?

So I know that applying FFT on a time-domain signal, shows which frequency components exists and what amplitudes each frequency signal has. My question is, suppose the signal contains same frequency ...
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-1 votes
1 answer
106 views

Inverse discrete Fourier transform or inverse Fourier transform of composite function?

I collected spectrometric data which produced a graph with the intensity of each frequency of light. What more do I need to perform an inverse fourier transform of this data? Should I attempt an ...
0 votes
1 answer
150 views

Why do we use the DFT instead of the DTFS? Or, why was the FFT algorithm built for the DFT instead of the DTFS?

As we know, both the DTFS (discrete-time Fourier series) and the DFT (discrete Fourier transform) are used to represent discrete-time periodic signals for all time (or the periodic extension of ...
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2 votes
3 answers
144 views

Some signals whose Fourier transform are a particular rotation of its self

Let $N\in \mathbb{N}$. I am looking for a non-zero scalar $\lambda$ and a nonzero vector $$f=(f(0),f(1),\cdots,f(N-1)) \in \mathbb{C}^N$$ satisfying the following equations for $l=0,\cdots,N-1$: $$\...
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3 votes
1 answer
660 views

Fourier Transform: $\omega$ vs $f$ as frequency variable

I try to understand how the Fourier transform changes when I try to compute $X(\omega)$ or $X(f)$. Can someone work me through the maths please for two examples, $x(t) = \exp(j\omega_0 t)$ and $x(t) = ...
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1 vote
2 answers
220 views

Where to start with DSP?

I have a DSP exam coming up this summer and I got an abysmal mark on an assignment earlier this year. Obviously, the lecture slides are not enough for me to understand DSP, so I am wondering where can ...
1 vote
1 answer
261 views

How to compute correct phase in FFT even after applying phase unwrap and zeroing round off error?

I am converting a time-domain synthetic 1D signal to frequency domain using MATLAB fft. In the frequency domain, the amplitude vs frequency plot is coming reasonable which means it is showing the ...
-1 votes
2 answers
232 views

Calculating cross-correlation using Walsh-Hadamard transform

I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
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0 votes
1 answer
30 views

DTFT Pairs confusion

When I am in the DT Fourier Domain, and I want to come back to the time domain, which pair do I use? Asking because both pairs have the exact same "form" in the Fourier domain, and that is ...
1 vote
2 answers
222 views

Difficulty with a Fourier Transform

What would be the best way to take the Fourier transform of $$ f(t)\cdot \cos\big(\pi(t-1)\big) $$ I'm aware that when you take the Fourier Transform of $\cos(kt)$ you get two impulse at the location ...
9 votes
2 answers
677 views

Fourier series of cycloid

What is the Fourier series representation of a cycloid? The parametric representation of the curve is as follows. $$ t=\dfrac{\theta-\sin\theta}{\pi}\\ x=\dfrac{1-\cos\theta}{\pi} $$ The period is $2$...
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1 vote
1 answer
77 views

MIT 6.003 HW#8 Problem 4 - Fourier Coefficients of Triangle Wave

In the mentioned homework, part of the solution involves finding the Fourier coefficients of the triangle wave. The solution mentions that we can express this function as follows: What does that ...
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0 votes
1 answer
53 views

multiplication of a function with a Fourier-transformed equals to Fourier-transformed with a function

I already showed b item using the fact that it is $h\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$ I struggle a lot of hours trying to find the trick in item C. Can anyone help please ?
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0 votes
1 answer
39 views

Is it common to impose the sparsity on the Fourier coefficient itself?

In compressive sensing, I see many works to impose the sparsity on the wavelet coefficients (e.g., by minimizing the L1 norm of such coefficients.) Another example in MRI is to impose sparsity on the ...
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0 votes
2 answers
572 views

Normalization factor in the convolution theorem

Maybe it's a trivial question, but I couldn't find any explanation for this. According to the convolution theorem, in the continues case we add normalization factor, i.e. $$ \mathcal F\left\{h\star g\...
1 vote
1 answer
126 views

what does frequencies in non periodic signals mean?

What do the frequencies in the a Fourier transform of a non-periodic signal mean physically? Are there another definition of frequency that doesn't include the FT?
-1 votes
1 answer
201 views

DFT Signal DFT Length N , FFT

If we sample a signal let say sine(2 * pi * f) with f=1Hz and a sampling Frequency of Fs = 8Hz, is it right that the length of the data should be N = Fs/f or multiple of Fs/f like N= d*(Fs/f) with d=...
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0 votes
1 answer
254 views

If a time-series has odd number of samples does it have no energy at Nyquist frequency?

Suppose I have real time series A with n samples and time-spacing dt and I want to analyze ...
  • 103
0 votes
0 answers
38 views

Something like Hilbert Transform to obtain arbitrary Phase Shift? [duplicate]

I was wondering if there is something like a Hilbert Transform but that can implement an arbitrary phase shift to every frequency component. I mean, I know that the magnitude response of a "...

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