Questions tagged [fourier]
The fourier tag has no usage guidance.
317
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Does upsampling require a low-pass filter?
I am currently wondering about the frequency spectrum when performing upsampling using linear interpolation. As far as I know, linear interpolation corresponds to a $\text{sinc}^2$ function. If I ...
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Why is the time domain low-pass filter the "sinc" shape?
Consider:
I'm looking at low-pass filters, and I see that the time domain representation of an "ideal" filter resembles the shape above whereas the frequency domain is a box. I also get the ...
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CFO Estimation in LoRa Chirp Signal (Preamble part)
I am trying to estimate CFO in LoRa chirp signal (preamble part). I have seen the discussion about CFO on this forum but it is mainly related to CFO estimation in OFDM.
I want to estimate the CFO in a ...
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What's the meaning of the amount of frequency 0 in the Fourier Transform?
In the Fourier series, I knew that the coefficient $a_0$ represents the DC value, shifting the signal up and down by the amount.
Then, what's the actual meaning of the amount of frequency $0$ in the ...
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How can I plot a sinc function correctly?
I am generating a rectangular pulse using a piecewise function on Matlab. I have listened to some advice to use a normalization coefficient and the amplitude appears correct now. However, my issue is ...
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How to adjust the length of the window of the Fourier transform with respect to the length of the signal in Python
I ran the following code in Python, setting the window length to 5s, but he reports an error as the window length does not match the signal length. How should I adjust it please?
code:
...
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90
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Having problems with convolution in Fourier space
First attempt:
I tried convolution in Fourier space.
step: transform grayscale image ==> (real1,imag1)
step: transform kernel (a simple box filter) ==> (real2, imag2)
step: multiply (complex) ==...
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400
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Integer multiples of fundamental period in sine wave
I have a simple question.
Suppose I have a signal : $f(t)=\sin(2\pi \, 25t)$
We know that it's CTFT(continuous time fourier transform) will result in 2 delta's at +- $2\pi\,25$ [rad/sec].
Or ...
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1
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Finding a discrete signal using some information about its Fourier coefficients
I'm struggling to solve the following question. I've solved it partially, but I can't get complete it.
We have the given information about a signal of the form ...
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What is the symbol for angular frequency?
I am reading the book
Signals and Systems Laboratory with Matlab Book by Alex Palamides and Anastasia Veloni
I was going through chapter 6 (Fourier transform) and I came across a confusing thing ...
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346
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Removing zero frequency peak in fourier spectrum
I have been looking at the FFT (in python) of various simple functions. Everything was working as expected, except when I take the Fourier transform of the function:
$$ f(t) = e^{-\gamma t}\cos^2\...
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Real and imaginary parts of the Fourier transform of a pure cosine wave
My understanding of the Fourier transform is that the FT of a cosine wave should be non-zero in the real part and all zero in the imaginary part. This follows from the orthogonality of sine and cosine:...
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Representation of Sampling Frequency in the Fast Fourier transform
I have 21600 data in the time domain. What Sampling frequency should I use? can someone explain the effect of showing the result by selecting different sapling frequencies?
Cheers
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129
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How to get DFT spectral leakage from convolution theorem?
I have an issue, where my numerically calculated leakage from a DFT of a simple cosine does not match the theoretical prediction from the convolution theorem. I will try to present the example using ...
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pulsating current in the PWM amplifier vs. the RMS current of the fundamental sine wave after the filter
I want to know how calculate pulsating current on FET switches in a PWM class D amplifier versus RMS current of the fundamental sine wave after the filter.
It depends on the positive and negative ...
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Can a large drop in the PSD indicate the presence of a periodic noise?
I was wondering if a large drop in the plot of the PSD of a sensor measurement could indicate the presence of a periodic noise.
Here is my PSD:
Thank you.
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Discrete Fourier transform of a 2D exponential decay
The Discrete Fourier transform of a 1D discrete decay function $d[n]=e^{-a n}$ is simply computed as the sum of a geometric series: $$\tilde{d}[k] = \sum_{n=0}^{N-1}e^{-a n}e^{2 j \pi n k/N} = \frac{1-...
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Finding $A_k$ coefficients
I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as:
$x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the ...
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For a real-world system of oscillating mechanical components, what kinds of frequencies should I seek in DFT?
I have a real world system I am analyzing consisting of actual mechanical components that oscillate by rotating back and forth in a fixed axle (kind of like those finger fidget spinners but my system ...
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Combining audio and image filters in matlab
I am trying to write audio and image filtering together code in my project.
Purpose: The main aim of this project is to combine audio with image filters; like for example passing low frequencies of an ...
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What happens if you use the Fourier transform of the autocorrelation of a non-WSS process to compute power spectral density?
The Wiener–Khinchin theorem states that the power spectral density of a wide-sense stationary stochastic process can be obtained through the Fourier transform of the autocorrelation of the signal i.e.
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How can I use the FFT in MATLAB to get the time domain equation representation of an image? [duplicate]
My goal is to take any image and break it down to obtain its time-varying equations so it can be redrawn and store the picture as two equations. One for $x$ and one for $y$.
As I understand, MATLAB's ...
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Proof that DFT is symmetric
I am working through the proof that the DFT is symmetric from Lyons - Understanding Digital Signal Processing
I don't quite understand the use of the $N$ variable. My understanding is that in $X(N-m)$,...
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How to generate a sound closer to a saxophone using sinusoids after Fourier Transform?
Generate a sound wave of saxophone frequency and compare it to the original sound clip and play both to listen to if there is a good match.
I am trying to generate a sound closer to a saxophone using ...
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131
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Trying to find the Fourier Series Representation of a sum of Sinusoids
Given a signal:
$$x(t) = -5\cos{(93.6\sqrt{2}\pi t - 2\pi/3)} + 3 \cos{(135.2\sqrt{2}\pi t + \pi/13)}$$
I am confused about the right process to take or if there is an easier way than following all ...
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2
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100
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Problem with transforming a tophat to obtain a sinc?
I have observed that the Fourier transform of a tophat function is a Sinc-like function with higher peak sidelobes than an actual Sinc.
However, the Fourier transform of a Sinc is a tophat-like ...
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3
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208
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Sample Frequency does not matter if it is sufficiently large
I'm not able to convince a colleague on the following topic.
Statement: If, and only if, the sample frequency is sufficiently large and above the Nyquist frequency it does not matter what fs is as ...
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perform fourier-type integration using DFT misunderstanding
I need to perform the following integral ($i^2 = -1$) (with a fixed value of $m$):
$
\int_{\phi=0}^{\phi=2\pi} \psi(\phi) e^{-im \phi} \hspace{0.7mm} d\phi
$
for all values of $m$ in $\{-N_{\theta}, -...
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sampled FT of Continuous time LTI output
I am trying to compute the sampled Fourier Transform of a Continuous Time LTI system output. $x(t)$ is the input of LTI and $h(t)$ is the impulse res. $y(t)$ is the output. we know that
$$ y(t) = \...
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Fourier transform of a top-hat function in the Faraday Measurement synthesis context
I'm currently trying to calculate the Fourier transform of a top-hat function in the context of Faraday Measurement Synthesis. This is pretty straightforward, however, I cannot understand why I cannot ...
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How to calculate DFT of signal which occurs from 3 to 8?
How can I calculate discrete fourier transform of this signal?
I'm confused as in the normal cases signal always start from 0 to N-1 but in this case it starts from 3 to 8 instead.
So what would be ...
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Given the Fourier Transform of a continuous signal how can I sketch the sampled signals discrete time fourier transform
I am given the frequency response for a continuous time signal $X(j\omega)$ = 2 at $\omega=0$ and 0 at $\omega = -10000\pi$ and $10000 \pi$. Looks like a triangle. I am told to sketch $X(e^{jw})$ ...
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What can I do to improve the sound of a signal?
I want to improve the sound of my signal, I know I can do it by increasing or decreasing the amplitude of the signal itself. Are there any other ways to do this? How can I apply the Fourier transform ...
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What's the difference between male and female voice? [duplicate]
If I record the voice of a man and a woman, what are the main differences I get in the various spectra and harmonics in Fourier analysis?
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What happens if I register my entry?
Taking as an example that I want to record my voice. How does it appear in the frequency spectrum? Can I also view it on other spectra?
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Computing the frequency response using fourier transform of an unstable LCCDE system
Given LCCDE system. Is it possible to calculate the frequency response using Fourier transform?
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Continuous Inverse Fourier Transform [closed]
How to find inverse Fourier transform of:
$ X(j\omega) = \frac{cos(3\omega) \cdot cos(\omega)}{\omega^2} $
The answer to this question is:
$ x(t) = \frac{1}{2} y(t + 1) + \frac{1}{2} y(t - 1) $
where
$...
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Fourier Transform: $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$
I'm currently studying Fourier Transforms and do not understand the Fourier Transform of $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$
My solution states that it is
$X(\omega)=\frac{2}{2\pi}(-j\pi[\delta_0(...
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315
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What is the reason of existence of Fourier transform? (Why we use Fourier transform?)
I'm currently trying to understand Fourier transform and I've got curious about why Fourier transform exists.
Let's suppose that we have a 10 seconds of non-periodic wave. For example:
As far as I ...
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What is the transform of δ(5t)?
So my question is here: How to transform the function $\delta(5t)$?
I know that this function when is transformed on Fourier it will be $1$, but the $\delta(5t)$ is going to be and this $1$ or ...
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What is The Fourier Transform Formula for 1/(j*pi*t) Types?
I have old homework and solution of that but i didn't understand actually solution. Because i didn't see continous-time fourier transform formula for that.
$g(t)$=$\frac{1}{j\pi*t}$ and it asks ...
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2D Fourier transform over mask of an image
I have an image, which has an inherent mask built into it. The exact shape isn't super important, but it looks something like a circ multiplied by a rect. I would like to calculate the 2D Fourier ...
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286
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Confusion regarding STFT phase vocoder-based pitch shifting
I'm currently working on a phase vocoder implementation based on the Short-Time Fourier Transform; it's heavily based on the models described here and here. I have successfully completed the analysis ...
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112
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Fourier Series of a piecewise function
I've been given the task to find the Fourier Series Representation. All I'm given is this $$x(t)= \begin{cases}-t & \text { for } 0 \leq t<1 \\ 1 & \text { for } 1 \leq t<2 \\ 0 & \...
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Why don't we use partial Hz? [closed]
Hertz seems to be considered a fundamental and atomic unit that we modulate or analyze. 112Hz, 113Hz, etc. Wouldn't we have more to work with if we considered sub-Hertz granularity, e.g. 112.5Hz, ...
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How to find sharpness of an image?
I have a rather difficult image processing image. I would like to rank order a set of images I have by their sharpness. The issue is the images themselves are not of the exact same thing. Usual ...
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Approximation of Periodic Parabolic Function by Fourier Series!
I've just tried to approximate the periodic-parabolic signal by Fourier Series. I know, this sounds a bit strange. I am just trying to figure out relationship between Fourier Series and Taylor ...
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Prove Discrete Time Fourier Series Multiplication property
Note: This is not a homework problem. I'm just stalled at a point because I think I might be interpreting the duality property incorrectly.
If $x_1[n]$ and $x_2[n]$ are periodic with period N, then if ...
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Gabor uncertainty and time-frequency resolution
I have a question about Gabor's uncertainty theorem, and how it relates to time and frequency resolutions.
As I understand it, Gabor's uncertainty theorem states that the standard deviations of a ...
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How is this given impulse response of infinite duration? Isn't it just from -π to +π?
How is hd(n) infinite duration when it is from -π to +π. Book says as it is infinite duration, we in the next step take-:
h[n]=hd[n] from n=-(N-1)/2 to (N-1)/2 and 0 otherwise.
I can't see how this ...
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