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# 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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### Discrete Time Fourier Transform (DTFT) for an unstable system (Ideal Low Pass Filter)

The Dirchlet conditions state that if the signal is absolutely summable then it the DTFT of the signal definitely exists. This is a sufficient condition but not necessary condition. There are ...
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### Window functions with rippleless spectra

On Wikipedia I found the Hann-Poisson window, and the article claims the spectrum is smooth, but it isn't theoretically smooth, as it turns out. In practice you achieve partial smoothness by jacking ...
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### What are the uses of those three types of wavelet transformations?

In my studies of wavelets, there appear to be 3 different families of them: The Continuous wavelet transform The Discrete wavelet transform The Redundant wavelet transform They are all based on the ...
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### Variance of periodogram estimate of the power spectrum

I have been reading chapter 13.4. ("Power Spectrum Estimation Using the FFT") of the Numerical Recipies Book. Some things related to the expectation value of the "periodogram estimate of the power ...
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### How to combine bins of my DFT

I have a time series and apply the FFT to get a spectrum. Let's assume that my sampling frequency and the length of the time sample are chosen such that I end up with a $\Delta f = 0.1$ Hz. As this ...
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### Why do we discard imaginary part of the phase spectrum?

Suppose I compute phase spectrum from the fftn function in MATLAB as ...
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### Correlation filter output range normalization

I'm developing correlation filters based image recognition. I implemented MACE correlation filter in matlab: training code: ...
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### Fourier domain: temporal versus spatial

I am little bit confused over these two. As per my understanding, spatial domain is the usual method we did in matlab by using the function fft2, which will return ...
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### Is Gabor uncertainty a feature of the Fourier transform, or of nature?

By Gabor uncertainty, I mean the principle of uncertainty as applied to signals — with the result that you can't have arbitrary time and frequency localization. By way of background to my question, ...
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### Impulse Response / Frequency response Question [closed]

I have a major question. Please take a look. I have this differential equation (DE): $$\frac{d^2y(t)}{dt} +\frac{dy(t)}{dt} +4y(t)= \frac{dx(t)}{dt} +2x(t)$$ And I have to find impulse response (...
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### Removing values from FFT result same as filtering?

I don't quite understand why the textbooks say it is impossible to implement an ideal low pass filter. If I was to take the FFT of a discrete signal x[n], with Matlab's fft function I'd be returned ...
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### Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
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### FFT of input length 1536

Does anyone knows can i find a FFT of 1536 length input. Its a specification given in 3gpp Lte and we need a transform of 1536 input size which is neither a power of any number i would say. I just ...
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### About Discrete Fourier Transform vs. Discrete Fourier Series

I am new to the field of signal processing. I am wondering what is the difference between DFS(Fourier Series) vs. DFT(Fourier Transform). For common applications, usually we get a segment(length <...
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### Analysing 2500 frequencies using FFT with an input vector of 2048 samples?

I am currently reading the paper A Highly Robust Audio Fingerprinting System and on page 4 one can read about the technical parameters they use: Sampling rate of 5000 Hz, frames of 2048 samples as ...
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### Scaling property of Fourier Transform

Problem 4.6(b) from Oppenheim, Wilsky & Nawab (2nd ed) reads: Given that $x(t)$ has the Fourier transform $X(j\omega)$, express the Fourier transform of $x(3t - 6)$ in terms of $X(j\omega)$. The ...
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### What is the Fourier Transform of a constant signal?

I am trying to figure out what the fourier transform of a constant signal is and for some reason i am coming to the conclusion that the answer is 1. Or better yet a step function.
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### What's the impact of aliasing in the time domain?

I've been studying digital audio and come across something I can't understand. There appears to be something like a consensus (among those capable of understanding such things) that the impact of ...
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There are many question related to the zero padding a time domain signal to get more frequency bins after performing Fourier transform. As I understand this process is equivalent to trigonometric ...
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### Why can't DFT be used when samples are not equally spaced in time?

I found the following comment here The DTFT can be used when the samples are not equally spaced in time, the DFT cannot My initial thought was that this had to do with periodicity of the basis ...
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### Fourier transform of given signal

This is the signal whose FT i need to find, at first i thought that i could solve this as a convolution of two rectangular pulses, but i could not find pulses that fit into this (it turns out that ...
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### What will be the filtered output?

I tried to solve this question from basic Here is my work Image 1 Image 2 But the correct answer is Option $(B)$.What is the mistake i am doing?
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### Which information do we get from magnitude and phase spectrum?

I am learning image processing. I want to ask very basic question related to FFT topic Which information do we actually get from "phase spectrum" and "magnitude spectrum" about an image?
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### Difference between Convolution and multiplication [duplicate]

I read that multiplication is convolution in frequency domain. I also understand that convolution is just polynomial multiplication. Can somebody explain what are the advantages of doing convolution ...
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### Finding out modulation index and DC offset

I have a question form my teachers, and I cannot understand why I can find out the modulation index form the figure. The question provide a Figure like this: And the information signal is a ...
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### Count Matches to a Kernel

So, I have this problem where I want to apply a kernel to an image and count the number of matches that happened. So for example, if I have the kernel: \begin{bmatrix} 1 & 2 & 1\\ 1 & ...
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### Can I assume system is LTI when given by DTFT of impulse response

I'm having hard time to grasp it probably because i don't fully understand it. I understand that when a system is given by $h(t)$ (in general $h(t-\tau)$) i can assume that it is a LTI system. So i ...
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### Is sampling a Fourier transformed signal and fourier transforming a sampled signal the same?

I'm having a hard time understanding an assignment that states: Draw the complex spectrum of the sampled signal $f(t)$ (periodic and continuous). Do this, by first calculating the Fourier ...
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### Image Processing and applicability of 2D Fourier Transform

As a newbie in the world of signal processing, I am having a hard time in appreciating image 2-D fourier transforms. I am fully able to appreciate the concept of 1-D Fourier transform. Essentially, ...
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### Does “keying on” a sine wave at a zero-crossing reduce its bandwidth?

I understand that a pure sine wave of infinite duration occupies no bandwidth, i.e. it is only the modulation of a carrier that gives it sidebands. Does the exact timing of a sudden modulation make ...
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### DFT of discrete signals, why do we only analyze frequency bins equal to number of input samples?

If we have a signal $x[n]$ such that we have $N$ samples i.e. $n=0, \ldots, N-1$, then when we analyze the DFT $X[k]$ we only analyze for $k=0,\dots,N-1$ as well. Why is the range of $k$ tied to the ...
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### Implementation of wideband beamformer for planar array

I would like to obtain a good reference (or references) on the implementation of a wideband beamformer for a small planar (rectangular) array comprised of 4 rows by 6 columns, for 24 elements in total....
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### Whats the optimal window function to use for analyzing real-time data samples?

Say you wanted to run a X point FFT on the last X audio samples that were played. The problem being, using a normal hann window function would place emphasis on the "middle" of the audio sample. ...
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### Why edge sharpening produces high frequency?

I have a low-resolution image in which the high frequencies are missing. When I apply an edge sharpening filter some of the missed high frequency is recovered. I am wondering why this edge sharpening ...
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### What is difference between terms $X(j \omega) ,X(\ e^{j \omega })$ and $X(\omega)$?

While studying frequency transforms ,I get confused with the terms like $X(j \omega) ,X(\ e^{j \omega })$ and $X(\omega)$ ,where $\omega = 2 \pi f$. So what is the difference between them ?
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### Implementing Convolution in Frequency Domain?

Suppose, we have a bitmap image represented as a 2D integer array, int [,] image2D; whose FFT is Complex[,] fftImage2D; ...
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### A kind of Phase Retrieval problem

I know there are lots of papers proposing algorithms for the problem of reconstructing a signal from modulus of its Fourier Transform (so-called Phase Retrieval Problem). Also, recently it is studied ...
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### FFT, How to decide if there is a signal among noise?

I have sets of data of different deep sky objects. My job is to check for any periodicity. I use IDL to run an FFT and wavelet methods to check for a signal. To test my code I ran the IDL built in ...
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### How can understand periodicity of a Signal from frequency domain representation?

Is it possible to say a signal is periodic from its frequency domain representation? A periodic signal is sum of its sinus and cosinus. Frequency translation of sinus and cosinus functions are ...
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### How does Adobe After Effects generate its “audio spectrum” effect?

I'm trying to replicate the "audio spectrum" effect from Adobe After Effects. An example can be seen in this video: Obviously, it has to be some variant of a fourier transform, but I've tried taking ...
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### Is it possible to do single vehicle tracking using Fourier transform?

I am working on a project in image processing which is based on importance of phase only reconstruction of a signal obtained using Fourier transform.For more information about phase only ...
### Is $O (N \log N)$ FFT speed the fastest we can ever attain?
I am wondering about whether or not there is a theoretical limit as to the speed at which we can compute a DFT. We all know that the FFT executes in $O (N \log N)$ time. However, is this a lower bound ...