Questions tagged [fourier]
The fourier tag has no usage guidance.
239
questions
0
votes
1answer
29 views
2D Fourier Transform
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
54 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
113 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
33 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
44 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
33 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
36 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
33 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
70 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
37 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
vote
2answers
61 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
34 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
30 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
44 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 ...
0
votes
0answers
9 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
27 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 ...
0
votes
2answers
35 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
votes
3answers
513 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
votes
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 ...
0
votes
0answers
33 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
votes
1answer
66 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
40 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
votes
3answers
97 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 ...
1
vote
1answer
67 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 ...
-1
votes
1answer
33 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 ...
1
vote
1answer
73 views
What is issue in square wave reconstruction?
As shown in attached photo:
What is the reason that the approximate square wave $$x_N (t)$$ at right side is not like the original $$x(t)$$ at left side .?
Is the only reason is that number of ...
1
vote
2answers
50 views
Confusion regarding sinusoidal synthesis formula,
I am reading signal processing first by McClellan
As shown in attached snapshot, we have formula of sinusoidal synthesis
I am confused ,why in expression of x(t), there is a '2' in first line ...
1
vote
3answers
92 views
Complex exp. Fourier series, finding $x(t)$ when $X(j\omega)$ is given as magnitude and phase plot
I'm watching Neso Academy series on Signals and Systems, and in one of the videos the problem is to find $x(t)$ when magnitude and phase plot are given. The plot looks like this:
When he finishes ...
0
votes
0answers
30 views
Short Time Discrete Fourier Transform to detect time dependent changes in a frequency of interest & Filter
I am working in matlab to compute the fourier relative phase of two signals as per https://sci-hub.tw/10.1123/jab.2017-0250
I have identified the fundamental frequency ($f_1$) for the signals (1.7 Hz)...
2
votes
0answers
67 views
Solving nonlinear Fourier relation
I'm trying to solve the following nonlinear cross-correlation problem for the time-domain signal $f(t)$:
$S(\omega) = \overline{\mathcal{F}\left[f(t)\right]} \mathcal{F}\left[f^n(t)\right]$
with $n&...
0
votes
1answer
66 views
How to understand the sum of all “fourier frequencies”?
I got the data of an acceleration sensor to analyze. It consists of special terms of 30 Hz, 60 Hz and 120 Hz. In the following you can see in the first plot the 60 Hz data and in the second one the ...
0
votes
1answer
46 views
How do I deconstruct a signal with fast fourier transformation in Python?
I want to use the fast Fourier transformation in python to deconstruct a periodic signal into its harmonic periodicities.
Since the FFT of the original signal is the same as adding the FFT of the ...
0
votes
1answer
59 views
What kind of periodic signals cannot be represented with the Fourier Series?
Oppenheim et al. state in Signals and Systems that there exist periodic signals which cannot be represented with Fourier series. What signals are these?
Although Euler and Lagrange would have been ...
0
votes
0answers
12 views
USRP N210 and FFT
I am getting IQ data from my usrp N210. It has been written in a file as a complex number and I can analyze it with matlab. The IQ data actually resembles the power of my processor. The sampling ...
0
votes
1answer
127 views
How to do the Fourier Transform of bounded function?
I was trying to solve a Fourier transform of a function using the properties of Fourier transforms. The function is given as:
$\frac{At}{2}$ for $-2<t<2$ and $0$ for all other $t$. Doing the ...
0
votes
1answer
49 views
Math.Net and alglib returning different FFT outputs by default
I am developing an application in C# with spectrogram drawing functionality.
For my fist try, I used MathNet.Numerics, and now I am continuing to develop with alglib. When I changed from one to the ...
1
vote
1answer
81 views
y(t) a of an integrator circuit
I have a signal $$ x(t)= \frac{1}{T} e^{-\frac{t}{T}} u(t) - \frac{1}{T} e^{\frac{t}{T}} u(-t) $$
and I know that it transits in a integrator circuit and I have to find y(t) in time and frequency ...
0
votes
0answers
13 views
average value of modulated signal with Fourier Analysis
I am using an instrument that uses a modulated heating program. The instrument returns an average heat flow signal calculated from the modulated heat flow. I would like to understand how this average ...
2
votes
2answers
88 views
Inverse Fourier transform Of a triangular impulse
I have to find the expression of this graphic and after find the inverse Fourier transform of it. First of all I found that the expression of the graphic is $$ X(f) = \frac{1}{2} tri (\frac{f+f_0}{B}) ...
1
vote
1answer
27 views
Discrete Fourier transform - Norms of complex input signals and their transformation
Given a signal $\mathbf{z} \in \mathbb{C}^n$ and its Discrete Fourier transform $\hat{\mathbf{z} }$, does $||\mathbf{z}|| = ||\hat{\mathbf{z} }||$ hold?
The question is given to me like this with ...
0
votes
1answer
58 views
Discrete Fourier Transform in Signal Processing - Interpreting graphs of transformed signals
Given above are the real parts of the signals I to IV. Which of the following statements are correct?
(i): Signal III is the result of the discrete Fourier transform of signal I. The associated ...
0
votes
0answers
17 views
I Q Frequency spectrum
While calculating the I Q spectrum of a complex signal m(t)
M_q(f) = 1/2j( M(f) -M*(-f))
If M(f) is a square pulse symmetric around origin. And phase is 0.
How should I represent the M_q. I am ...
0
votes
0answers
48 views
express pass band filter as sum of low pass filter
I have to find impulsive response of an ideal pass band filter, but I have a problem to express $$ H_{BP} (f) $$ as a sum of $$ H_{LP} (f) $$. I mean that $$ H_{BP} (f) = rect ( \frac{f-f_0}{B} ) + ...
0
votes
0answers
68 views
Energy of a sinc signal
My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me
$$ x(t)=\operatorname{sinc}(t) $$
and
$$ s(t)=x(t-T)$$
and I found that ...
0
votes
2answers
69 views
Fourier transform properties
I have to find the Fourier transform of $$ x(t)= \frac{1}{T}e^{-\frac{t-T}{T}}u(t-T) $$
First I applied traslation property , so $$ F[x(t-T)] = X(f) e^{-i 2 \pi f T} $$
after I applied time scaling ...
0
votes
1answer
93 views
Finite sequence input to DTFT
i'm studying the practical utility of Fourier transforms and i have some questions. I hope to receive answers in layman terms.
1) Does the DTFT take only infinite input sequences?
2) If i apply the ...
1
vote
1answer
80 views
Fourier coefficients of odd and even part of a signal
I have this signal and I have to find the Fourier coefficients of the odd and even part. First I found that $$ x_p(t) = \frac{1}{2} ( x(t) + x(-t) ) $$ and I made the graphic of this part and I ...
3
votes
1answer
88 views
Fourier coefficients of 1/(1+it)
I have to find the Fourier coefficients of $$ \frac{1}{1+ t^{2}} $$ I tried with $$ \frac{1}{T}\int_{0}^{T} \frac{1}{1+it}e^{-i 2 \pi f_0 T } $$ but I should do at least two integrals by parts , so I ...
0
votes
1answer
23 views
E of a signal using Rayleigh
I have to find The energy of a signal using Rayleigh th. the signal is $$ x(t) = A e^{-At } u(t) $$ assuming A>0
Using the classic definition of E , I found that it should be $$ \frac{A}{2} $$
Using ...
