# 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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### Why is the DC component of discrete fourier transform not the same as the signal's arithmetic mean?

In this question we have a mathematical proof that the DC component of normalized discrete Fourier transform should be the same as the signal's arithmetic mean. However, in the following example I ...
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### 3D convolution product with Fourier transforms, FFTW and MPI in C

My question is not really from the field of signal processing but I think you are the most suited for answering my question. I am willing to compute the gravitational potential which can be written as ...
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### What is the sparse Fourier transform?

MIT has been making a bit of noise lately about a new algorithm that is touted as a faster Fourier transform that works on particular kinds of signals, for instance: "Faster Fourier transform ...
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### Calculating k-space coverage from antenna positions

I work with radar and I want to understand which spatial frequencies I can measure, i.e. the k-space coverage, given a set of coordinates of transmitter-receiver combinations. The ideal coverage for a ...
1 vote
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### Is fft` always the best choice?

I hope this is the right place to ask this question since it is partially a note which might help others. Until recently, I always used the fft-algorithm ...
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### How to Use Convolution Theorem to Apply a 2D Convolution on an Image

How do I actually apply the convolution theorem? I have my fourier transformed image matrix, and a Fourier transformed kernel, but how do I actually multiply these together to achieve the intended ...
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### How to identify square wave in audio signal

I'm interested in identifying a square wave signal from recorded audio. This subject may be a complex problem so I would like to present the problem where I'm currently stuck at. I recorded the audio ...
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### Steering Vectors and Bluetooth Low Energy for computing Angle of Arrival

I am new to signal processing, but I have background in mathematics. I am trying to use Bluetooth Low Energy (BLE) on three mobile devices, where one device is being tracked and the other two act as ...
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### Amplitude and Phase spectrum from fourier transform of sawtooth [duplicate]

Let the following $T$-periodic signal : then \begin{align}F(x(t))(\omega) =& \int_{-\infty}^\infty x(t) \exp(-i\omega t) \mathrm{d}t = \sum_{k=-\infty}^\infty \int_{kT}^{(k+1)T} x(t) \exp(-i \...
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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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### “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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### Determine reflections from received signal

I have a reference signal $r(t)$ and the correlation between that reference signal and the received signal : $C_{XR}(\tau)$. The signal I receive contains reflections on walls. I have to build a ...
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### Fourier Transform and Music Analysis

I am a senior in high-school and am currently trying to conduct an exploration on Fourier Analysis, specifically using the Discrete Fourier Transform to analyze a chord played on my piano. Basically, ...
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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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### Frequency response of $\mathrm{sinc}[n]$

In this image the frequency response of a discrete time filter given as $h[n]$. Can someone explain how the magnitude of the frequency response is found ?
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### Why does applying Fourier Transform on point Spread Function yield h(t) which is complex-valued

I wanted to understand why this text talks about applying the Fourier transform on H(f) to obtain h(t). I view Fourier transform as moving from the time or spatial domain to the frequency / spatial ...
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### How to get the scale bar of an FFT for a 2d image

I've been analyzing some images from a transmission electron microscope, including their FFTs, and I'm not sure how to apply a scale bar to the FFT images. I have calibrations for the real space image,...
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### How to determine the nature (real or complex valued) of a signal?

A signal X(t) is a real valued time domain signal and Y(t) is a signal that only contains the non-negative spectral components of X(t). How do I determine whether Y(t) is real-valued or complex? I ...
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### FMCW radar: understanding of doppler fft

I am using fmcw radar to find out distance and speed of moving objects using stm32l476 microcontroller. I transmit the modulation signal as sawtooth waveform and I read the recieved signal 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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### PSD of the sum of two zero-mean white noise signals

I am trying to solve the following exercise, where $y(t)$ is the sum of two signals $x_1(t)$ and $x_2(t)$ with each of them being the product of the convolution of $e_i(t)$ with $h_i(t)$. So far I ...
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### What is the phase of $Y(\omega)$ in relation to the phase of $X(\omega)$ where $x(t)$ modulated with an exponential carrier that has no phase shift?

A homework problem of a free online course I am taking, asked to draw the magnitude and phase of $Y(\omega)$ where $y(t) = x(t) c(t)$ where $c(t)$ is $e^{j 3 \omega_{c} t}$ and where $X(\omega)$ is: ...
I took the one-sided FFT of a signal and plotted up until the Nyquist frequency. Then, I took the real part of this FFT multiplied by $i\omega$ following a calculation that I'm trying to do of a ...