Questions tagged [fourier]
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268
questions
0
votes
1answer
62 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 ...
0
votes
3answers
104 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 $l=0,\cdots,N-1$:
$$\...
0
votes
1answer
54 views
Fourier Transform: $\omega$ vs $f$ as frequency variable
I try to understand how the Fourier transform changes when I try to compute $X(\omega)$ or $X(f)$. Can someone work me through the maths please for two examples, $x(t) = \exp(j\omega_0 t)$ and $x(t) = ...
1
vote
2answers
183 views
Where to start with DSP?
I have a DSP exam coming up this summer and I got an abysmal mark on an assignment earlier this year. Obviously, the lecture slides are not enough for me to understand DSP, so I am wondering where can ...
1
vote
1answer
36 views
How to compute correct phase in FFT even after applying phase unwrap and zeroing round off error?
I am converting a time-domain synthetic 1D signal to frequency domain using MATLAB fft. In the frequency domain, the amplitude vs frequency plot is coming reasonable which means it is showing the ...
0
votes
1answer
47 views
Calculating cross-correlation using Walsh-Hadamard transform
I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse ...
0
votes
1answer
22 views
DTFT Pairs confusion
When I am in the DT Fourier Domain, and I want to come back to the time domain, which pair do I use? Asking because both pairs have the exact same "form" in the Fourier domain, and that is ...
1
vote
2answers
209 views
Difficulty with a Fourier Transform
What would be the best way to take the Fourier transform of
$$
f(t)\cdot \cos\big(\pi(t-1)\big)
$$
I'm aware that when you take the Fourier Transform of $\cos(kt)$ you get two impulse at the location ...
0
votes
0answers
18 views
What is the requirement to reconstruct a spatial domain signal if we sample in the frequency domain?
I've come across an interesting question with regarding to signal reconstruction.
The sampling theorem states that a signal in the time or spatial domain must be sampled at twice a rate twice the ...
9
votes
2answers
539 views
Fourier series of cycloid
What is the Fourier series representation of a cycloid?
The parametric representation of the curve is as follows.
$$
t=\dfrac{\theta-\sin\theta}{\pi}\\
x=\dfrac{1-\cos\theta}{\pi}
$$
The period is $2$...
1
vote
1answer
50 views
MIT 6.003 HW#8 Problem 4 - Fourier Coefficients of Triangle Wave
In the mentioned homework, part of the solution involves finding the Fourier coefficients of the triangle wave.
The solution mentions that we can express this function as follows:
What does that ...
0
votes
1answer
41 views
multiplication of a function with a Fourier-transformed equals to Fourier-transformed with a function
I already showed b item using the fact that it is $h\left(0\right)=\int \:f\left(t\right)g\left(0-t\right)dt$
I struggle a lot of hours trying to find the trick in item C.
Can anyone help please ?
0
votes
0answers
37 views
How to compose a Discrete Prolate Spheroid (DPSS) dictionary?
I have a model of signal as
$$
Y=AX + N
$$
where $Y$ is received data in a linear array, $A$ is steering matrix, $X$ is data of sources and $N$ is noise. If $A$ has the form of $A=\exp(\alpha \sin(\...
0
votes
1answer
37 views
Is it common to impose the sparsity on the Fourier coefficient itself?
In compressive sensing, I see many works to impose the sparsity on the wavelet coefficients (e.g., by minimizing the L1 norm of such coefficients.) Another example in MRI is to impose sparsity on the ...
0
votes
2answers
156 views
Normalization factor in the convolution theorem
Maybe it's a trivial question, but I couldn't find any explanation for this.
According to the convolution theorem, in the continues case we add normalization factor, i.e.
$$
\mathcal F\left\{h\star g\...
1
vote
1answer
59 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
votes
1answer
79 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=...
0
votes
1answer
67 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
votes
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 "...
1
vote
0answers
33 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 ...
0
votes
2answers
47 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
votes
2answers
84 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?
$$ e^{-2j\Omega}\frac{ \sin\left( \frac{7\Omega}{2}\right)}{ \sin\left( \frac{\Omega}{2} \right)}\star \frac{\...
0
votes
0answers
54 views
Fourier transform and energy of a convolution
Hi guys i have to find the fourier transform of the convolution:
$$ 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
votes
1answer
33 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
...
0
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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 ...
0
votes
0answers
110 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
votes
1answer
72 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
vote
1answer
70 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 ...
0
votes
0answers
15 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
187 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
votes
1answer
200 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....
-1
votes
2answers
133 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
votes
1answer
41 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
vote
1answer
97 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
votes
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
322 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
votes
0answers
43 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
vote
1answer
106 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
vote
1answer
65 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
vote
1answer
118 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 ...
1
vote
0answers
37 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
votes
2answers
100 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
votes
1answer
66 views
Receiver function, frequency 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
vote
2answers
95 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
votes
1answer
355 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
votes
1answer
34 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
votes
1answer
61 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
998 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
votes
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 ...
0
votes
0answers
34 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 ...
