Questions tagged [fourier]
The fourier tag has no usage guidance.
187
questions
0
votes
1answer
33 views
What determines peaks in FFT?
I ran FFT on three audio files and found that the results for some have more peaks than the other. Could anyone give me any conceptual explanation as to what determines these peaks? Below are plots of ...
0
votes
1answer
39 views
What is Imaginary in Fourier transform?
How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
1
vote
1answer
23 views
Impulse response of a 3x3 PSF - how to find analytical expression for fourier transform of a 3x3 matrix?
I have a filter $\mu[n_1, n_2]$ with taps:
$$ (1/8) (1/4) (1/8)$$
$$ (1/4) (1/2) (1/4)$$
$$ (1/8) (1/4) (1/8)$$
How do I find an analytical expression for $\hat\mu(w_1, w_2) $?
Since it looks so ...
15
votes
4answers
4k views
“The Fourier transform cannot measure two phases at the same frequency.” Why not?
I have read that the Fourier transform cannot distinguish components with the same frequency but different phase. For example, in Mathoverflow, or xrayphysics, where I got the title of my question ...
0
votes
0answers
56 views
Range Doppler Maps
I would like to understand from a high point of view how these maps are computed.
On the y-axis we have m/s and in the x-axis the range.
I read something about the Fourier transform etc, but I don'...
0
votes
1answer
44 views
Is it correct to assume that $(-1)^n = \cos(\pi n)$ while computing the DTFT of $(-1)^n$?
$\cos(\pi n)$ fluctuates between $-1$ and $1$ depending on the values of $n$, and it would be the same as computing it with an exponential but the problem is that I just get part of the right answer......
1
vote
1answer
28 views
Is fft2 in MATLAB unitary? Some differences happen
I meet a problem when implementing fft2 in MATLAB.
The question is I try to simulate the realistic measurements $Y = |FCXF^H|^2$ - the intensity of Fourier domain of object $X$, where $F$ denotes ...
1
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0answers
33 views
When plotting the cosines of the phases of some sensors, I got an interesting plot
I have a laser that I modulate at some frequency, typically 1250 Hz. I have a sensor that tracks what happens inside a reactor when it's illuminated. I am doing Fourier analysis on both the laser ...
0
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0answers
49 views
DFT truncation of signals
How can I calculate 8 point DFT of signals whose length is less then 8 ( say 2,4) then what will I assume other members in formulae "0" or rotation or keep repeating the same two numbers
Consider I ...
-1
votes
1answer
36 views
How do I obtain the fourier series coefficients for a signal obtained by multiplication of two signals of different frequency?
What i assume here is that LCM of time periods of the two taken signals exist that is signals periods are not like pi/2 and 1 but are rather like 1 and 2 (just an example)
I am given fourier series ...
0
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0answers
25 views
urgent: MRI calculations question
I have a biomedical imaging exam tomorrow and I'm struggling quite a bit with this question below (from b-d). I was hoping someone could help answer these questions or at. I'll describe my approach to ...
0
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1answer
39 views
What happens if I zero out the initial terms of the fft output and take inverse fft? [duplicate]
I am new to signal processing domain. When I run fft on data of length 1000, I get 1000 complex numbers. Now, if I want to extract the low frequency information or signal approximation, I take the ...
2
votes
2answers
68 views
DFT: a function of $n$?
I‘m a high school student and I haven’t studied physics or anything.
Why does the DFT depend on an integer, say $k$ or $n$ (it’s usually expressed like $F(n)=...$ or $F(k)$ or $F_k$, etc.) if it is ...
0
votes
1answer
40 views
Hilbert transform of symbolic function in Matlab
I have a signal of the form $f(\omega,x) = g(\omega) e^{i \omega (x +c)},$ for $g: [\omega_1 , \omega_2] \rightarrow C, \, x\in R$ and some constant $c.$ I want to get the function
$$
F (\omega,x) = \...
0
votes
2answers
85 views
My impulse response does not tend to zero
I am doing an IFFT of frequency response data achieved with Simulation tools.
When I plot my impulse response it looks wrong as the response does not tend to zero as it should. Instead there seems ...
0
votes
3answers
48 views
How transmission speed and bandwidth are linked?
I don't understand why if I have a larger bandwidth I can transmit data faster.
Is this linked with this property of fourier transform?
thanks.
0
votes
1answer
64 views
Fourier transform of dirac comb with function: The scaling factor
Multiplication in the time domain corresponds to convolution in the frequency domain:
$$
f(t) \cdot x(t) \iff F(j \omega) * X( j \omega) \tag*{No scaling factor}
$$
I know the fourier transform of ...
0
votes
2answers
76 views
What is the interpretation of Fourier Transform containing only imaginary part?
The FT of a unit step function is taken as:
$$
X(\omega) = \int_0^\infty e^{-j\omega t}dt = \frac{-1}{jw}e^{-j\omega t} \Biggr |_{0}^{\infty} = \frac{j}{\omega}
$$
The transform only has the ...
2
votes
2answers
220 views
Do Fourier frequencies actually exist in real life in form of “fundamental frequency”?
For me, this is a very awkward question to be asked, as at this point in my studies I'm supposed to be quite expert with elementary mathematical tools like Fourier transforms, but this has always ...
0
votes
0answers
25 views
how to calculate a SNR?
i had some question.i have do some some filtering FFT using a matlab program.but,i need to compared the original signal,noise signal,and filtering signal based on SNR.but i dont understand how to ...
1
vote
1answer
353 views
Autocorrelation of sinc function
I'm having trouble on computing the autocorrelation of the sinc function
I want to compute
$$R_{hh}(\tau)=\int_{-\infty}^{\infty}\operatorname{sinc}(t) \ \operatorname{sinc}(t-\tau) \ \mathrm{d}t$$
...
-1
votes
1answer
30 views
How to get descrete fourier tarnsfom [closed]
Could anyone explain me please how to produce descrete fourier transform of such signal? There are no anymore information besides the picture in this task.
3
votes
2answers
155 views
Fourier Transform of Alternating Periodic Rectangular Pulse
I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem.
Given the signal is periodic I could use formula for Fourier transform of periodic signals:
$$...
1
vote
1answer
36 views
How would I find the function given the magnitude plot and the phase response?
I'm wondering how I'd find the Fourier Transform X(jw) given the following information:
My understanding is that the expression for the continuous time fourier transform (CTFT) is magnitude(CTFT)exp(...
0
votes
0answers
75 views
Filtering out different narrow-band frequencies at once
I have asked a closely related question on SO at https://stackoverflow.com/questions/55168460/python-implementation-for-filtering-out-multiple-distinct-narrow-band-frequencie
but I am still unclear ...
0
votes
1answer
46 views
Help me understand the stages involved in filtering a signal using Discrete Fourier Transform
I have a series of discrete values measured from a sensor. I want to filter the frequencies coming from this sequence of values. Then, if I understood the process correctly this is what I do:
I ...
0
votes
1answer
66 views
How to detect the maximum resolvable spatial frequency of camera?
I am trying to calculate the minimum line pixel width that can be distinguished from noise as shown in the camera test chart in Figure 1 where the thinner lines on the left are getting more and more ...
0
votes
0answers
44 views
Fourier decomposition in Matlab
I am doing a Fourier decomposition of sea level series ( to find out one particular contribution within the sea level height). it should be applied subsequently on shifted (by one hour) windows of 96 ...
0
votes
1answer
218 views
Detrend data with no clear secular trend prior to Fourier analysis?
I am completing Fourier analysis on many different time series of sediment particle flux exiting an experimental flume. Data is collected at a resolution of 1 Hz for durations ranging from ~5,000 to ...
0
votes
2answers
99 views
What is the basic idea behind Fourier transform? [closed]
What is the basic idea behind (discrete and continuous) Fourier transform (FT)? In short, what is the difference between discrete and continuous FT?
I have read multiple answers on the web related to ...
0
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0answers
16 views
Extracting straight line and curves from an edge image using fourier coefficients
I came across Fourier coefficients and my understanding is that it is very efficient in analysing image properties such as shape etc.. I know we can use Fourier descriptors to describe shape... But in ...
1
vote
1answer
24 views
Linearity with Difference Period in Fourier Transform
I know that a system is linear if it satisfies
$$\mathscr{F}\{ a\,x(t)+b\,y(t) \} = a\,X(\omega)+b\,Y(\omega)$$
for Fourier transform, $X(\omega)\triangleq\mathscr{F}\{x(t)\}$
But what if $x(t)$ ...
0
votes
1answer
74 views
Calculating fourier transform
I have just recently started doing fourier transforms and I'm a little confused.
Can someone walk me through in detail how to calculate the Fourier transform of
I'm not looking for answer, just an ...
0
votes
1answer
145 views
Ambiguity in the IFFT process in OFDM
I am still trying to iron out some ambiguities in my understanding of the IFFT component of OFDM modulation schemes.
So here we have a QAM symbol $s_0$ being multiplied with the subcarrier for that ...
3
votes
1answer
220 views
Discrete Harmonics - Why multiplying digital frequency by k does not get next harmonic
For continuous time $ e^{jk\Omega_0t} $ gives a complete set of orthogonal harmonics for fourier decomposition but for discrete $ e^{jk\omega_0n} $ does not form a complete set orthogonal basis set ...
2
votes
1answer
105 views
Does the Fourier series coefficient of AC components remains same if DC component is subtracted form the given signal?
Suppose a signal is defined by
$
x(t)= \begin{cases}
t & 0\leq t \leq 1 \\
2-t & 1\leq t\leq 2 \\
\end{cases}
$
Since $x(t)$ has even symmetry, I can calculate fourier coefficient as
$$
a_n = ...
1
vote
3answers
117 views
How the FFT takes a cosine or sine and outputs the frequencies of the complex form?
If i take the Fast Fourier Transform (FFT) of a cosine function, what has turned this cosine function into its complex exponential form which consists of $e^{i \omega t} + e^{-i \omega t}$ ?
Because ...
1
vote
3answers
239 views
Intuitively, what is fourier series representation of a signal? Also intuitively what is frequency response? [duplicate]
I know these formulae and can solve problems mechanically but i never got the core concept. Please help me out with this.
0
votes
1answer
75 views
help in understanding cosine filter
I was referring to this link https://cdn.selinc.com/assets/Literature/Publications/Technical%20Papers/6059_HowMicroprocessor_Web.pdf?v=20180606-230156 . I am not very clear about the derivation of the ...
0
votes
1answer
92 views
Using the given identities, find the inverse DTFT
Using the given identities,
$ a^nu[n]$ <===> $\frac{1}{(1-ae^{-jw})}$
$\delta[n-k]$ <===> $e^{-jwk}$
Find the inverse DTFT of,
$ H(e^{jw}) = B \frac{e^{-jw}}{(1-ae^{-jw})}$
my attempt:
$ ...
0
votes
0answers
43 views
From Fourier (k space) to wavelet domain in MRI sensing
In compressed sensing MRI (cSENSE MRI) technology the idea seems to entail sampling from the Fourier domain (k space) in a way that, when transformed to the wavelet domain ("sparsification"), the ...
1
vote
3answers
437 views
Deconvolution Using Complex Division in The Frequency Domain
Consider these two signals:
a = [1 1 0 0 0 0 0 0]
b = [1 0 1 0 0 0 0 0]
their convolution is
c = a * b = [1 1 1 1 0 0 0 0]
...
1
vote
2answers
801 views
Hilbert transform of unit step function
How to calculate Hilbert transform, if it exists, of the signals like $u(t)$, $sgn(t)$.
What properties should a function satisfy for existence of Hilbert transform.
Absolute integrability of a ...
1
vote
1answer
176 views
Averaging magnitude squared coherence across multiple time series
In a previous post, A. Donda had suggested that, in order to calculate the average magnitude squared coherence of more than one pair of time series (e.g. y1 and x1, and y2 and x2), one ought to follow ...
1
vote
2answers
167 views
Resampling with and without replacement for estimating significance of spectral components
In order to test the significance of spectral components, it seems reasonable to randomly sort the data in order to destroy all the serial correlations / spectral order e.g. 100,000 times, and then ...
0
votes
3answers
753 views
Correct magnitude spectra of a cosine DFT?
I've just started my course on DSP and haven't laid my hands on MATLAB yet. I was wondering if the plot of the magnitude spectra was correct for the below shown $x(n)$:
1
vote
1answer
3k views
Impulse response of ideal filters
I am aware that an ideal low-pass filter in both continuous time and discrete time has a $\mathrm{sinc}$ impulse response. What would the impulse response of an ideal high-pass or band-pass filter ...
1
vote
2answers
477 views
BIBO Stability and the convergence of the frequency response of a system
It is my understanding that an LTI system is BIBO stable if and only if its impulse response $h(t)$ is absolutely integrable. This also happens to be one of the Dirichlet conditions for the ...
1
vote
1answer
432 views
Time scaling of discrete-time sequences and the DTFT
In the second edition of Signals and Systems by Alan Oppenheim, he discusses the DTFT of a "time-expanded" sequence that is effectively a slowed down version of the original sequence and can be ...
1
vote
2answers
518 views
Fourier transform of even/odd parts of a complex signal
Why does Oppenheim state the following properties:
\begin{align}
\mathcal F\big\{x_e (t) \big\} &= \Re\big\{ X(j\omega) \big\}\\
\mathcal F\big\{x_o (t) \big\} &= j \Im\big\{ X(j\omega) \big\...
