Questions tagged [fourier]

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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 ...
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9 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 ...
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1answer
51 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 ...
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1answer
22 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 ...
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1answer
65 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 ...
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11 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 ...
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2answers
65 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}) ...
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1answer
25 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 ...
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1answer
40 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 ...
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14 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 ...
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44 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} ) + ...
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49 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 ...
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2answers
66 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 ...
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1answer
56 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 ...
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1answer
65 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 ...
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1answer
76 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 ...
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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 ...
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3answers
231 views

Sawtooth wave Fourier coefficients

I have to calculate the Fourier coefficients of this signal. I found that signal equation is $$ y = \frac {A(2t-T)}{T} $$ To find Fourier coefficients I wrote $$ x_k = \frac{2A}{T} \int_{0}^{T/2} \...
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1answer
24 views

Why does DTFT start and end at the same magnitude?

I would like to know why the spectrum of FIR filters (and maybe all DTFT spectra) start and end at the same magnitude. I guess there is something related to $H(e^{j\omega})$. Thanks
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2answers
119 views

Fourier coefficients of |A cos (x)|

I have to find Fourier coefficients of $x(t) = |A \cos (2 \pi f t )|$. The problem also give me $y(t) = |x(t)|$. To find Fourier coefficients I wrote $$ \frac{1}{T_0} \int_{0}^{T_0} |A \cos (2 \pi f ...
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0answers
26 views

I want to invert my fourier transform components to waves again

Hi I am using R to analyze some data I basically did fft(data) and got a vector of complex numbers but from that now I want to remove certain harmonics from my actual wave but how do I convert one of ...
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1answer
28 views

Bin sizes for non-uniform discrete Fourier transforms

For a non-uniform discrete Fourier transforms, do the specified frequencies – i.e., $f_k$ in – refer to the midpoint of the bin or the lower bound? I read the answer here, but that stated that ...
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1answer
104 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 ...
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1answer
44 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 ...
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1answer
30 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 ...
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4answers
5k 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 ...
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0answers
109 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'...
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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......
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1answer
48 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 ...
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0answers
36 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 ...
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72 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 ...
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1answer
40 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 ...
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0answers
30 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 ...
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1answer
48 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 ...
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2answers
71 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 ...
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1answer
51 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) = \...
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2answers
99 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 ...
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3answers
51 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.
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1answer
121 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 ...
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2answers
98 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 ...
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2answers
238 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 ...
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0answers
33 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 ...
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1answer
627 views

Autocorrelation of sinc function

I'm having trouble on computing the autocorrelation of the sinc function I want to compute $$R_{hh}(\tau)=\int_{-\infty}^{\infty}\operatorname{sinc}(t) \ \operatorname{sinc}(t-\tau) \ \mathrm{d}t$$ ...
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1answer
32 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.
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2answers
417 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: $$...
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1answer
48 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(...
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0answers
136 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 ...
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1answer
54 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 ...
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1answer
125 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 ...
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0answers
51 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 ...

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