Questions tagged [fourier]
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262
questions
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0answers
13 views
inverse fourier transform of multi pole zero model [closed]
I need to find the inverse fourier transform of the function given below
$$ S(f) = \prod_{n=1}^{3}\frac{1+{\frac{f}{a_n}}^2}{1+{\frac{f}{b_n}}^2} $$
For the denominator, the fourier transform pair ...
1
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1answer
38 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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1answer
19 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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0answers
35 views
How to compose a Discrete Prolate Spheroid (DPSS) dictionary?
I have a model of signal as
$$
Y=AX + N
$$
where $Y$ is received data in a linear array, $A$ is steering matrix, $X$ is data of sources and $N$ is noise. If $A$ has the form of $A=\exp(\alpha \sin(\...
0
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1answer
34 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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2answers
48 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\...
2
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1answer
39 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?
0
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1answer
39 views
DFT Signal DFT Length N , FFT
If We sample an Signal let say sine(2 * pi * f) with f=1Hz and a sampling Frequecy of Fs = 8Hz, is it right that the length of the data schoul be N = Fs/f or multiple of Fs/f like N= d*(Fs/f) with d=...
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1answer
55 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 ...
0
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0answers
36 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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0answers
27 views
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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2answers
42 views
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 ...
2
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2answers
79 views
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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0answers
34 views
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-\...
-1
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1answer
30 views
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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0answers
38 views
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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0answers
80 views
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 ...
2
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1answer
49 views
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[...
1
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1answer
49 views
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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0answers
14 views
Amplitude Matching for Exponential Swept Sine
I am working in the area of aerospace vibration testing and we use swept sine tests on structures and measure the response using the accelerometers. I tried implementing the technique "...
4
votes
3answers
167 views
Why does DFT have only $N$ components?
Why does the DFT have only $N$ components in it? I can see that after N components the frequency component is periodic and repeats with the same values but that does not seem to explain why we can ...
0
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1answer
78 views
frequency domain to time domain with magnitude and phase
I have a signal magnitude and phase in frequency domain. I need to have it in time domain but I really have no idea how to do it. I heard something about mirroring the signal but I'm kinda new at this....
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2answers
106 views
How to plot thermal noise in the “time domain”?
$P = 4kT$ (where $k$ = Boltzmann’s constant, and $T$ = temperature of the instrument ($K$))
And the mean voltage is thus, of course, $V^2/R = 4kT$
And the voltage is distributed as a Gaussian around ...
0
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1answer
38 views
2D Fourier Transform [closed]
Is it possible to get a 2D Fourier Transform by first taking 1D Fourier transform in first dimension and then performing another 1D Fourier Transform in the other dimension? If yes, can you explain
1
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1answer
81 views
Prove a property using shift theorem and duality
I'm reading Lectures on the Fourier Transform and Its Applications and I'm going to prove shift theorem for the inverse Fourier transform using duality. According to the mentioned source, the duality ...
0
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0answers
20 views
Fundamental frequency in DFT [duplicate]
I was looking into the fundamental frequency in DFT and I noticed many sources mention that the fundamental frequency is $1/N$, where $N$ is the number of samples. (When doing the DFT, we have $k/N$, ...
5
votes
2answers
195 views
Amplitude after Fourier transform
How to obtain the correct amplitude after the numerical Fourier transform of a signal?
Example: consider an exponential decaying wave $y(x)=e^{-x}\sin(100\pi x)$ with Fourier transform $y_f(x_f)$ ...
0
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0answers
36 views
I need help in understanding “Nyquist Criterion” definition
I am researching the split-step parabolic equation and its split step solution as in:
Ozgun, Ozlem & Apaydin, Gokhan & Kuzuoglu, Mustafa & Sevgi, Levent. (2011). PETOOL: MATLAB-based one-...
1
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1answer
55 views
Time scale and Fourier transform
Consider the Fourier transform $F(\omega)$ of the function $f(t)$. The magnitude of $F(\omega)$ depends on $\omega$ and thus also depends on the scale of the $t$-axis. For example, when $f_1(t)$ is a ...
1
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1answer
52 views
What's the relation between frequency band of $X(j\omega)$ and $\Phi_{xx}(j\omega)$?
in which:
$x_{c}(t)$ is a continuous-time signal
$X(j\Omega)$ is the Fourier Transform of $x_{c}(t)$
$\Phi_{xx}(j\Omega)$ is the Power Spectrum Density of $x_{c}(t)$ which defined as Fourier ...
1
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1answer
59 views
Frequency response and sampling theorem for triangular function
The triangular function is defined as follows:
$h_l(x) = \begin{cases}1-|x|,&|x|<1;\\0&\text{otherwise}.\end{cases}$
According to ccrma.stanford.edu:
"If the output of the interpolator ...
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0answers
36 views
How to downsample a fourier transformed signal?
I have a signal of length 100000 timestamps sampled at a frequency of 25kHz. First I apply a high pass filtering at (300Hz) and then do the Fast Fourier Transformation. Then the absolute values are ...
0
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2answers
81 views
Why the Nyquist frequency is 0.5 of Fs, why not 0.55 or 0.65?, brief explanation [duplicate]
This my elaboration of the aliasing issue:
a continuous signal can be represented by factors of :
$e^{(i2{\pi}ft)}$ if we sample this signal then I will get:
$e^{(i2{\pi}fk/N)}$ where $k=0,1,2.., N-1$
...
0
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1answer
51 views
Receiver function, frecuency domain deconvolution not giving logic results
I'm working on some code for receiver function method in seismology. For anyone one not into the topic, it's just a deconvolution of two time series (seismograms). This can be done in the time domain ...
1
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2answers
77 views
Question on N point DTFT - Fourier transform
I have been trying to use the logic that both X and Y should have same Z transform, but according to the definition, Y is not anti causal.
0
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1answer
177 views
Conjugate symmetry of the DFT of real-valued sequences
I have read about Fourier transformation that real signals are "mirrored" in the real and negative halves of the Fourier transform because of the nature of the Fourier transform. For ...
0
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1answer
32 views
Understanding index transformation in derivation of Fourier transform for sampling rate reduction
Was going over some notes regarding deriving fourier transform equation for Sampling Rate Reduction. Reference to Notes from below link https://ocw.mit.edu/courses/electrical-engineering-and-computer-...
0
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1answer
48 views
Fourier transform of an integrator filter
I have to find the Fourier transform , and $y(t)$ of an $ x(t) = e^{- \frac {t}{T} } u(t) $ that passes into a integrator filter. I know that $ Y(f) = X(f) H(f) $ so I first calculate the Fourier ...
3
votes
2answers
531 views
Duality Property for DFT
I was watching a youtube video for the duality property for continuous time Fourier transforms, which shows that if
Fourier transform of $x(t)$ is $X(\omega)$
then Fourier transform of $X(t)$ is $2\pi ...
0
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0answers
10 views
What is the Effect of Multiplying a Function by the Unit Impulse Function in the Frequency Domain? [duplicate]
I know about the the shifting property of the impulse function in the time domain as can be seen in the picture.
But what is the effect of multiplication of a function by the impulse function in the ...
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0answers
31 views
$2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal
please help me find the error in the following counter example.
Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
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2answers
44 views
Where did the length of time’s period disappear in Periodic Fourier Series Discrete Time
In continuous time Periodic Fourier Series has smallest n as possible, since it is an integral and a length of the repeating time (period time) which is T0. In discrete time however we don’t have ...
5
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3answers
525 views
Why do we get different imaginary parts of a zero centered Gaussian for the the same number of data points N?
Suppose we have a total number N= 2048 points in a data and we wish to have zero centered Gaussian. There are two possibilities that we use the x-axis as
...
0
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2answers
29 views
How can it be that there is a series of integrals in Fourier Series if it’s a projection on a continuous basis?
If the process of finding Fourier coefficient is finding the projection of a signal on a member from an orthonormal basis, basis which is continuous in frequency. How can it be that Fourier ...
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0answers
34 views
frequencies in frequency spectrum with no correlation together
I have a lack of understanding of the following questions:
If I have a signal from a motor that is recorded with an accelerometer. And the rotating speed of the motor is 150Hz(rpm 9000 ), I can see in ...
0
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1answer
80 views
Fourier transform of t*rect(t)
In my previous post I asked for help for a Fourier transform of $$ t \text{rect} ( t- \frac{1}{2} ) $$ and I think I’ve understand the process. Now I’ve 2 another similar Fourier transform to do , I ...
0
votes
2answers
41 views
difference in spectrum
First I defined 5 signals with same length (40 samples) with different frequency and sampling frequencies, then I've put them together like [X1 X2...] and took it's fourier transform and the result is ...
0
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3answers
120 views
Fourier transform of a rect*half triangle
I have to calculate the analytic expression of Fourier transform $$ x(t) = t{\rm rect} ( t- \frac{1}{2} ).$$ First I made the graph of these two signals and I obtained the graph I posted.
Now I ...
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1answer
269 views
Characteristic function of a random Gaussian variable
I have to find the characteristic function of a random Gaussian variable of $$ \sigma_z (w) = E e^{i w z } $$. This is the variable and I know , from the theory that the characteristic function of ...
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1answer
36 views
Confusing regarding triangular wave vs square wave?
I am reading signal processing first by Mcclellan. In chapter 3, I came across the term "discontinous" as shown underlined in attached photo.
Apparently "discontinuous" means having a gap/break but ...
