Questions tagged [fourier-transform]
The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
2,160
questions
2
votes
2
answers
128
views
Fourier transform of a delayed LFM chirp
I know that for a given signal $s(t)$ and a given delay $ \tau $, by the shift theorem:
$$ \mathcal{F}\{s(t-\tau)(f) \} = e^{-j 2 \pi f \tau} \mathcal{F}\{s(t)(f) \} \tag{1} $$
However, when I try to ...
- 21
0
votes
0
answers
52
views
Derivation of 9 point Laplacian filter
I'm reading a paper on how construct isotropic laplacian filter, and perhaps because it's an old paper, the notation in it really bothers me a lot. So can someone please explain it to me? For example, ...
- 1
1
vote
0
answers
20
views
Is the amount of zero valued minors of a size n discrete Fourier transform matrix dependent on the amount of divisors of n?
This is a repost from Mathematics Stack Exchange due to lack of answers.
A minor is a determinant of a square matrix formed from a bigger square matrix by removing rows and columns. A minor having ...
- 221
0
votes
1
answer
95
views
Decoupling two signals with FFT
I have an audio signal $g(t)$ composed by the sum of my original signal $f(t)$ and a delayed copy of itself:
$$g(t)=f(t)+f(t+\varepsilon)$$
My goal is to recover the original signal $f(t)$ knowing:
$...
- 103
3
votes
1
answer
236
views
Convolution and Fourier transform for 1D signals
My problem is the following, I have 3 curves/signals (1D) , the measure, the signal and the resolution of my detector: $\mathcal{M},\mathcal{S},\mathcal{R}$, knowing that : \begin{equation}\label{eq:...
- 75
0
votes
0
answers
44
views
pffft equivalent of fftwf_plan_dft_r2c_1d function from fftw
I am trying to convert my project from using FFTW to pffft. I only need to call the following two functions:
...
- 25
0
votes
0
answers
89
views
Phase Vocoder Pitch Shift Phase Artifacts (Embedded C++)
I'm working on a phase vocoder pitch shifter running in C++ on an embedded microcontroller platform. I've successfully written the phase vocoder using the optimized FFT library, and it appears to be ...
- 111
2
votes
0
answers
53
views
Extended CORDIC for general Lie groups and algebras via representations
CORDIC is a well-known method for quickly computing exponentials and logs, including trig functions and their inverses by decomposing the angle into conveniently computable increments and then ...
- 111
0
votes
0
answers
25
views
How to approach signal reconstruction with sampling frequency not equal to reconstruction
I'm trying to figure out what kind of equations i can use in a situation like this:
I know the relation between $x(t)$ and $x[n]$ is :
but then $x[n]$ is multiplied by a pulse train, with a ...
- 27
2
votes
1
answer
110
views
2D Fourier transform of an element-wise product of two matrices
I wonder if there is any known formula to describe a 2D Fourier transform of an element-wise product, i.e., Hadamard product, of two matrices. Let $\odot$ is the Hadamard product operator, and there ...
- 53
2
votes
3
answers
727
views
How can I find the following Fourier Transform without directly using FT pairs?
The question is to find the CTFT of $$x(t) = e^{-t}u(t)\cdot \sum_{n=-\infty}^{\infty} \delta\left(t-\frac{n}{2}\right)$$
Now I know that multiplication in time means convolution in the Fourier Domain ...
user67157
2
votes
2
answers
299
views
The uncertainty principle - Why does it imply that we can't localise
The uncertainty principle states that if you have a signal which is very concentrated in time, then its Fourier transform will be rather outspread and vice versa. However, I don't really understand ...
- 129
0
votes
0
answers
102
views
Calculate Phase Shift Using FFT
I'm not a specialist in this field and learnt FFT fairly recently.
I want to calculate phase difference of between 1 MHz signals sampled at 4 MHz. The sample counts are both 144. I think the ...
2
votes
1
answer
134
views
Proof for the energy correction factor of DFT
I am looking for a mathematical proof for the energy correction factor in conteext of windowed discrete fourier transform.
In Spectrum and spectral density estimation by the Discrete Fourier transform ...
- 151
0
votes
0
answers
37
views
Confusion about convolution [duplicate]
I'm facing confusion about the definition of the convolution between two discrete periodic signals.
Basically, the definition of convolution between s and ...
- 53
1
vote
1
answer
80
views
Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?
Suppose you have a function that can be described as $$f(s) = \sum_{n=0}^{\infty} a_n e^{f_n s}$$ where each $f_n$ is a complex number. I am looking for a transform $T$ to act on $f$ which produces a ...
- 121
1
vote
1
answer
68
views
How do I determine stationarity from a set of 50 complex values collected every 10 minutes?
I am trying to determine stationarity from a somewhat stochastic process. Every 10 minutes, I collect a set of 50 FFTs, i.e., 1 trial over $50$ seconds, so an FFT occurs every time second. I ...
- 19
2
votes
1
answer
94
views
Does subtracting a phase from the frequency components of a DFT output result in rotation?
I'm currently reading a paper (Page 23 of the PDF) about the application of the Fourier transform to standardize some climatic data to easily compare them.
I have the following text :
2.3 ...
- 53
2
votes
3
answers
772
views
Why does spectrum magnitude decay away from DC for positive signals?
I would like to understand why the second frequency component usually has the greater magnitude within the range [1, (N/2)], i.e why (I remove the DC component and ...
- 53
0
votes
2
answers
170
views
Is it possible to predict the peak value of a time-domain signal from its frequency-domain spectrum?
As the question states, is it possible to predict the peak value of a time-domain signal given its frequency-domain spectrum?
Since the time-domain signal is just the sum of the individual sinusoids ...
- 296
0
votes
0
answers
67
views
FFT of frequency bands and limited amplitude modulation
In this paper they preprocess a cent spectrum of an audio file.
For comparison of audio files they create the Logarithmic Fluctuation Pattern(LFP)(p.3).
For this I have to use a FFT on each frequency ...
- 25
1
vote
0
answers
61
views
Identifying frequency components only
I have a real world system of a rotating back and forth motion and the time domain data suggests that the data is a random signal (not a deterministic signal). I recorded discrete data points at a ...
0
votes
0
answers
30
views
non-integer phase estimation after dft(using psf)
I'm studying PSF function and the way to get the most accurate phase estimation at the non-integer locations.
My professor showed me a slide in lecture.
Rotate some integer coordinate in fourier ...
- 33
1
vote
1
answer
132
views
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 ...
0
votes
0
answers
73
views
How many samples are needed to compute an DFT?
Given a signal $x(t) = \frac4{10}\cos(800πt) + \frac12\cos(820πt) + \frac1{10}\cos(880πt)$ and knowing that the sampling frequency is $4000$ Hz.
How many samples are needed at least to represent the ...
1
vote
2
answers
403
views
Can someone explain the phase spectrum of a sinc function?
The Fourier transform of a sinc function will result in a rect function. Suppose I have a discrete time-domain sinc function with a frequency of $\omega_0 = 0.1$ Hz and amplitude of $A = 10^{-3}$:
If ...
- 296
4
votes
2
answers
361
views
Fourier transform of a propagating Dirac delta
I have a spatio-temporal signal $f(x, t)$ that propagates at a constant velocity $v$. To represent that propagation I'm reading in multiple papers that we can represent it in the Fourier domain with ...
- 141
0
votes
1
answer
69
views
Why can't I use the differentiation property of the Fourier transform?
I have some question about the function in frequency domain and I'd like to know its inverse fourier transform (IFT)
$$G(jw) = \dfrac{jw\cdot (jw+1)}{(2+jw)(3+jw)}$$
I know that:
$$\dfrac{d}{dt}x(t)\...
- 49
2
votes
1
answer
130
views
Why is there a difference in the phase when using fft versus a manual DFT on a cosine signal?
Apologies if this is a duplicate, but I can't find a good answer anywhere.
If I have a time-domain cosine signal of the form:
$$x(t) = A\mathrm{cos}(\omega_0 t)$$
Then this will result in an Fourier ...
- 296
-1
votes
1
answer
41
views
How to compute the ifft of a constant value?
I am clearly missing something obvious here because I am trying to do something that ought to be very simple: compute the ifft of a continuous signal.
My understanding is that the ifft of a continuous ...
- 296
1
vote
1
answer
53
views
Effect of BIBO-Instability on the frequency response of a ideal LPF
I recently came across this post stating that the continuous ideal LPF is BIBO-unstable since the impulse response is not absolutely integrable, and this post stating some examples.
I have been trying ...
- 95
2
votes
2
answers
112
views
How would you compute Fourier transform of a real world signal where the signal keeps getting updated (not a static one)?
Crossposted at Electrical Engineering SE
A very naive question: How do we use Fourier transform for real world signals - for which you have the information only up to the present instant (and the ...
- 153
5
votes
3
answers
351
views
What is the proper way to compute a real-valued time series given a continuous $1/\sqrt{\omega}$ spectrum?
I have never fully been able to wrap my head around Fourier transforms, so I apologize if what I am trying to do is trivial or violates basic theory in some way.
What I have is a "made up" ...
- 296
0
votes
1
answer
79
views
How can sound waves be modeled in a manner that distinguishes individual voices but also recognizes words?
More specifically, I'm curious how we can represent sound waves in a way that would both distinguish between individual voices and also recognize, e.g. that recordings of different people saying the ...
0
votes
1
answer
44
views
Displaying and analyzing an audio file in MATLAB
I was given the following problem at my university:
We are given an audio file which we have to download. Following that we have to create a MATLAB code that can create a discrete-time graph of the ...
1
vote
0
answers
30
views
Unbiased estimation of the bispectrum
There are many methods of computing estimations of the bispectrum, and in particular regarding methods to give unbiased estimations of this quantity. I was wondering whether if, given a complex-valued ...
- 11
1
vote
1
answer
277
views
Fourier transform identity not working in Matlab
$F^\ast(x(t))=F(x^\ast(-t))$
I'm trying to use this identity in Matlab. I expect this should translate to:
conj(fft(x)) == fft(conj(flip(x)))
It doesn't work out. ...
- 95
1
vote
2
answers
384
views
DFT of a sine, closed form solution and insights
I seek to calculate, mathematically, the Discrete Fourier Transform,
$$
\texttt{DFT}\{x\}[k] = \sum_{n=0}^{N - 1} x[n] e^{-j2\pi k n / N}
$$
of any arbitrary real-valued sine: any frequency, duration, ...
- 8,805
-1
votes
1
answer
109
views
Why does my irFFT function have a small discrepancy distributed through the entire output?
Since I've last posted on dsp@stackexchange, I have been working on my algorithms and recently came across a useful radix-2 implementation which delivers performance as good or better than that of ...
- 27
1
vote
1
answer
99
views
Getting different results when fourier transforming in python vs mathematica?
I am interested in troubleshooting why I get a very different answer when doing fourier transforms of my data in Mathematica vs Python. The version in Mathematica is well behaved, yet all versions of ...
- 11
0
votes
1
answer
165
views
Phase Spectrum of Signals
I did fft of a fish's trajectory, because it looks periodic and I tried to find the frequency. However, I can't understand what does the phase spectrum below represent. Does this lower left to upper ...
0
votes
1
answer
92
views
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 ...
- 1,850
1
vote
1
answer
68
views
Implementation of dispersion compensation of lamb waves
I am trying to implement the method from Paul Wilcox paper "A rapid signal processing technique to remove the effect of dispersion from guided wave signals" on data from a lamb wave ...
- 46
2
votes
2
answers
142
views
Fourier Transform Of Cosine on Finite Interval
First of all, DSP is not my expert area. I didn't take any DSP course and don't know DSP in detail but I have a question regarding Fourier Transform confusing me.
Well, suppose that we wanted to take ...
1
vote
1
answer
86
views
Power of filtered Bernoulli process
I have some doubt about this exercise.
The Bernoulli random process $X(n)$ with means $p=0.5$ is sent in input to a LTI system with impulse response $h(n)= \cos(\frac{\pi n}{3}) R_3(n+1)$ , where $$...
- 75
0
votes
0
answers
69
views
The distribution of peak and rms of response in time domain
I am trying to model the pdf of the peak and rms of the time domain response $y(t)$ in a reverberation chamber. The system is stimulated by pulsed linear chirp $x(t)$ for 200 ns that goes linearly ...
- 91
1
vote
1
answer
86
views
Fourier Mellin Transform
I'm working on a Fourier-Mellin transform on images to find angle and scale.
In most cases when I have scaled and rotated an image, the Fourier-Mellin transform gives me the almost exact angle and ...
- 33
1
vote
0
answers
155
views
How to compute modular transfer function (MTF) from line spread function (LSF) with given discretization
I have an optical system, which is commonly characterized by its point spread function. Somehow by the method, which resemble slanted edge method, I have end up with discretized line spread function ...
- 111
3
votes
1
answer
191
views
Fourier transform of a time discrete signal
I would like some help to better understand the Fourier transform of a discrete time signal. My doubts are:
The sampling of a signal can be seen as $x_s(t)=x(t) \cdot
\sum_{k=-\infty}^{+\infty} \...
- 75
0
votes
1
answer
103
views
Why does the discrete bode plot look like the following and if possible explain the black vertical line at the end for an averaging filter
Why in the attached image for a simple 3 point moving average that has been converted into a TF (z domain) is there a wired dip? It seems that when I change the sampling time, the dip shifts to the ...
- 103