# Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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### How to calculate RMS of a sampled analog signal

Consider the below given discrete signal which has been gathered via sampling of an analog current waveform with sampling period $T_s=100\,\mu s$. I would like to evaluate the RMS value of its first ...
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### How to reconstruct original signal using IFFT after cutting past Nyquist limit

I'm working on a pitch shifting program. Everything works up to the point where I try to do the IDFT. Because I cut the DFT array past the Nyquist limit, when I run the IDFT, I don't get the same ...
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### Is the negative spectrum (by DFT) of a real signal "needed" to reconstruct it?

I'm trying to grasp the "ah-ha!" moment for the DFT/FFT. One of the points I struggle with is: if the original time signal $x[n]$ is real, then the values of the DFT $X[k]$ are (correct me ...
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### How is pitched changed using phase vocoder?

I've been attempting to create a phase vocoder program. However, I have found that sources explaining how the actual pitch shift is calculated, are limited. On Wikipedia I found these instructions ...
1 vote
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### How do I estimate possible aliased frequencies in sampling limited measurements?

Say I've got some data made from measurements with a too infrequent sampling rate; I know for certain there is aliasing. What I'm interested in is figuring out what frequencies are likely present ...
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### Frequency probabilities from Fourier transform

Fourier transform is an estimator of frequency. Because its an estimator, there is always some uncertainty associated with my coefficients as described by the Fourier/Gabor limit. I'm wondering how to ...
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### Other end of Nyquist limit

Say I perform FFT on some data. If the underlying (measurement) sampling rate is not twice the highest frequency, I will almost assuredly get aliasing. This limit on sampling we call the Nyquist limit....
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### How to remove a known smooth signal with known location and unknown amplitude from an unknown signal?

I have a known smooth complex signal $f(x)$: It's added to an unknown complex signal $g(x)$ after being multiplied to an unknown complex amplitude $A = u+iv$ (this image is just for illustration, in ...
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### How to change fundamental frequency with DFT?

I'm working on a voice changer. My plan is to make it so that it can change your voice in various different ways, but right now I'm just trying to make it change your voice to "chipmunk voice&...
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### How to Find "pitch" from Fourier Series

The end goal of my project is to create an autotune program, But the problem I'm trying to solve right now concerns finding the pitch of someone singing a note. I have written some code that performs ...
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### Need help with DTFT problem

Prepping for exam and this is one of the practice problems: I just want some clarification on some of the steps my professor took. This is the answer in the answer sheet Only thing I dont understand ...
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### What are some approaches / algorithms for reducing size of numerical data of large size with redundancies?

I'm dealing with bunch of .asc(ascii) files that are the output of continous monitoring of various electronic equipments for certification purposes. We monitor various parameters of the equipments ...
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### Removing once per revolution variation from data

I’m looking for help to find a robust technique to remove a once per revolution variation in some vehicle test data. The data is collected by driving a vehicle around a circular path at increasing ...
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### Fourier transform why can I convert one of the axes into an imaginary number?

Contextualizing This question is inspired by the following video: https://www.youtube.com/watch?v=-qgreAUpPwM&t=60s&ab_channel=3Blue1Brown I own a sign, a drawing of a square with 200 points ...
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### Fourier transform of periodic functions

The Fourier transform is derived from the Fourier series by considering a non-periodic signal, thinking of it as a infinitely long periodic signal, putting it into the Fourier series and making this ...
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### Rayleigh Bandwidth Calculation-Radar

I am trying to generate a simple Gaussian pulse that has a 1 ns pulse width. However, when I generate the pulse, I realized that I did not meet the condition that calculates Rayleigh Bandwidth (1/...
1 vote
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### Convolution of squares / boxcars

$$\Pi(t/A) \star \Pi(t/B)$$ where $$\Pi(t) = \begin{cases} 1,\ -1/2 \leq t \leq 1/2 \\ 0,\ \text{otherwise} \end{cases}$$ How to compute? Derivation/steps optional but welcome. Note: I'm aware of ...
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### creating a power vs frequency graph on for different harmonics Matlab

I am trying to create a Power vs Frequency graph for different harmonics(x_5(t), x_20(t), and x_100(t)) of the half triangular wave. I want to see how the difference in power between the original and ...
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### Convolve sinc trains

\begin{align} & \mathrm{sinc}(As + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/A)\ \star \\ & \mathrm{sinc}(Bs + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/B) \end{align} How to compute? ...
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$$x(t) = |\cos(\omega_0 t) + \cos(\omega_1 t)|$$ with $\omega_0, \omega_1 > 0$. Is there a known result for $\mathcal{F}\{x(t)\}$? Derivation not needed but is welcome. Of main interest is the ...