Questions tagged [fourier]

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3
votes
1answer
94 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 ...
1
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1answer
159 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 ...
0
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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 ...
1
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3answers
867 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} \...
0
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2answers
176 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 ...
1
vote
1answer
29 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
3
votes
1answer
663 views

Amplitude of an Image

If I take a two dimensional image and conduct a fourier transform on it, I would get a two dimensional matrix of complex values. If I want to find the amplitude of each value, is that the same as ...
1
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1answer
245 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
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1answer
91 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
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1answer
64 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 ...
0
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0answers
150 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't ...
0
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1answer
57 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
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0answers
37 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
147 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
148 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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1answer
83 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
81 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
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1answer
58 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
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2answers
235 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
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1answer
274 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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0answers
76 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 ...
3
votes
2answers
287 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
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2answers
238 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
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3answers
242 views

Real world application of signal sparsity?

There are theories based on signal sparsity in frequency domain like Compressive Sensing, Sparse FFT, etc. Throughout searching and studying papers I found out Cognitive Radio is a good example of ...
0
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2answers
147 views

Explanation of fundamental filtering's consequences on signal

Can anyone explain why exactly an "Overshooting" phenomena is observed when the fundamental harmonic is removed as seen on the figures? Is it technically right to call this "overshooting" at all ? If ...
1
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1answer
2k views

Autocorrelation of sinc function

I'm having trouble on computing the autocorrelation of the sinc function I want to compute $$R_{hh}(\tau)=\int_{-\infty}^{\infty}\operatorname{sinc}(t) \ \operatorname{sinc}(t-\tau) \ \mathrm{d}t$$ ...
5
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2answers
2k 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
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1answer
33 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.
1
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1answer
70 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
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0answers
300 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
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1answer
60 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
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0answers
70 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
539 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
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2answers
212 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 ...
3
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5answers
12k views

Fourier Transform minimum sample requirement

Assuming a signal is sampled adequately, what is the minimum size of an FFT window that would allow detecting a specific frequency? Is it necessary to have samples for at least one complete period at ...
3
votes
1answer
534 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 ...
1
vote
1answer
46 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 $x(t)$ ...
2
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1answer
293 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 = ...
3
votes
3answers
1k 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 ...
9
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2answers
2k views

Fourier transform artifacts

My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in ...
1
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3answers
1k 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
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1answer
2k views

How to get the data (pointwise frequency, amplitude and phase) in a FFT performed on ImageJ?

How to find pointwise readouts of the amplitude, frequency and phase of the DFT underpinning the FFT image? Once an image is FFT-ed in ImageJ, placing the cursor over any points on the FFT plot ...
0
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2answers
653 views

Non Periodic, Deterministic Power Signals

Any one know of work on non-periodic but deterministic power signals? Now one member in this class would be the quasi periodic signals. I wonder if there is a generalized Fourier analysis of non-...
0
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0answers
59 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 ...
2
votes
3answers
1k 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] ...
4
votes
1answer
206 views

Time domain basis

I have some troubles with understanding time domain, not on the intuitive level, but in math terms. For example I have a vector signal $$ x = [x_0,x_1,x_2,...,x_{N-1}]$$ I understand that generally ...
1
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2answers
1k 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 ...
2
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3answers
2k views

“Fourier Transform can localize signals in frequency domain, but not in time domain.” — What does it mean in layman's terms?

I was studying the introduction to wavelets and its benefit over the frequency domain. I said that: Fourier analysis can't localize signals both in time and frequency domain. Fourier analysis can ...
1
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1answer
280 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 ...
3
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1answer
6k 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 ...