Questions tagged [fourier]

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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(jw) = 2 at w=0 and 0 at w = -10000pi and 10000pi. Looks like a triangle. I am told to sketch X(e^jw) the frequency response of a ...
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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 ...
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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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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?
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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?
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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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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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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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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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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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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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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 ...
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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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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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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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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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 ...
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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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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 ...
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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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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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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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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 ...
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1 answer
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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 ...
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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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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 ...
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2 answers
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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 ...
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9 votes
2 answers
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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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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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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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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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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\...
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1 vote
1 answer
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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?
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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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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 ...
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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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1 vote
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even symmetry of magnitude and odd symmetry of phase [closed]

I'll appreciate it if any of you guys could help me with this question: Suppose that x(t) is a real signal, prove that the magnitude of its Fourier transform has even symmetry and its phase has odd ...
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Are there standards/references for determining spatial scale in photographic images?

EDIT, 12/12/20: Images below are of the radial sinusoid pattern. Left side is the "unrotated" version. Right side is what the a photograph of the pattern would look like if the disc was ...
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2 votes
2 answers
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IDTFT of convolution in the frequency domain

I have tried everything. If you actually know how to solve this could you provide a hint? $$ e^{-2j\Omega}\frac{ \sin\left( \frac{7\Omega}{2}\right)}{ \sin\left( \frac{\Omega}{2} \right)}\star \frac{\...
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Fourier transform and energy of a convolution

Hi guys i have to find the fourier transform of the convolution: $$ sinc(t/2T)*\sum\limits_{n-\infty}^{+\infty} (-1)^{n}\delta(t - nT) $$ i was thinking of express the summatory as : $$\sum\limits_{n-\...
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Why do we scale bins in FFT in this code?

Hi I am learning FFT I am confused about this bit of code: what is the reason for scaling the sampling frequency and what is bin scale and why and when do we use it? thank you ...
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Find CT Fourier transform of $ \left[ \frac{ \sin(\pi ~ t) }{\pi ~t} \right] \left[ \frac{ \sin(2\pi ~ (t-1)) }{\pi ~(t-1)} \right] $using properties

Use properties of Fourier Transform to solve the question. The question is in the imgur link below. I got $f_t$ of $\frac {sin(pi \cdot t)} {pi \cdot t}$ as rectangular pulse with value $1$ from -pi ...
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Can different Discrete-Time-Fourier-Series(DTFS) coefficients have the same discrete sequence in the time domain?

Please, check the following discrete periodic sequence when the period $N=2$. $x[k]=\exp(j\frac{2\pi}{N}k), N=\text{period}$ $..., x[0]= 1, x[1]= -1, x[2]= 1, x[3]= -1, ... , N=2$ According to my ...
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2 votes
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What is the variance of DFT of Fourier coefficient of difference of a vector of white noise?

Consider $\big\{x[0], x[1], \ldots, x[N-1]\big\}$. Suppose, \begin{cases} x[n] \sim \mathcal N\left(0, \sigma^2\right)\\ \big\langle x[n], x[n-1]\big\rangle = \frac12 & \forall \ n\\ \big\langle x[...
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Why is the continuous time Fourier series of DC signal an impulse?

In case of continuous time Fourier transform(CTFT), I can easily calculate the Fourier transform of DC signal by using Fourier duality or inverse CTFT. But I don't know how to calculate the continuous ...
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