Questions tagged [fourier-transform]
The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
1,305
questions
-1
votes
0answers
20 views
Time Domain Behaviour of Thermal Noise
Let's consider the thermal noise (or Johnson–Nyquist noise): It is white noise, that means that its power spectral density does not depend on frequency.
Now my question is: Which is a typical time ...
0
votes
1answer
32 views
Understanding the FFT phase spectrum with a simple example
I'm trying to compute the DFT using scipy's functions. I don't understand why the phase spectrum of a simple sine wave with 2 Hz frequency doesn't show $\pm\pi/2$ at the $\pm 2Hz$ frequencies. Instead,...
0
votes
1answer
38 views
Is it possible to reduce the complexity of radix-2 FFT if the input vector contains identical elements?
my question is about reducing the complexity of radix-2 FFT when the input vector has a specific structure.
For an input vector of x with N elements, the complexity is given by O(N log2 N).
My input ...
0
votes
0answers
32 views
Approximation with DTFT question
Let's suppose $x(t)$ has its Fourier Transform so that $ \hat{x}(f) = 0 $ when $|f| > 16$.
This function is sampled with $f_m =64$ and the only samples saved are those $x(\frac{n}{f_m})$ with n = ...
0
votes
1answer
53 views
Orthogonal Basis for a 2D Signals (Compressive Sensing)
I have a 2-D signal that is (1536x128) and that is sparse in the Fourier domain (after applying fft2).
I want to apply compressive sensing to recover the signal using fewer random elements, but I am ...
1
vote
1answer
49 views
Complex output after inverse FFT of a real signal
I have a real one dimensional signal s (light absorbance in a flow cell), which has significant noise and some periodic noise after performing a deconvolution of $S$ from $S_o$. Basically fft($S$) was ...
0
votes
1answer
37 views
Advantages of the Rotation Translation Operation Before Doing FT Smoothing
I was reading a relatively old paper from the 1970s on smoothing by FT methods (chemistry applications), where the authors show that if we do rotation translation operation on the signal (y- values) ...
0
votes
1answer
39 views
Finding the impulse response of a system
I have the following transfer function.
$$ H(j\omega) = \frac{1+0.5 e^{-j\omega}}{1-1.8 \cos(\frac{\pi}{16}) e^{-j\omega}+0.81 e^{-j2\omega}}$$
I'm trying to find the impulse response of the system. ...
0
votes
1answer
45 views
How To Find The Lowest Note of a Chord Being Played
The goal of my project is to find the lowest note in a signal coming from a guitar being played. I would like to do this programmatically and have sourced the equipment (raspberry pi, USB interface, ...
0
votes
0answers
25 views
Is it possible to recover the time-domain signal after manipulating it in the frequency-domain? [duplicate]
I've worked a fair amount with EEG signals, though I've never had formal training in signal processing, so please excuse my ignorance.
The problem is this: my signal has noise at many, many ...
0
votes
1answer
31 views
$x[n]$ after sampling of $cos(16\pi t+\phi)$ at 12kHz
I'm not sure what the question really means, so this is just guesswork.
I think options 1 and 4 can be ruled out as $w_0<\pi$.
The CTFT of $cos(16\pi t+\phi)$ has two spikes at $16\pi$ and $-16\...
1
vote
1answer
32 views
Discrete Time Fourier Transform (DTFT) cross correlation property
I came across this property of the Discrete Time Fourier Transform (DTFT) and I am having a tough time proving it.
In general, consider two real signals $x[n] \: \& \: y[n]$. If
$$ x[n] \...
1
vote
0answers
23 views
Find integral of DTFT after sampling (Graph of CTFT given)
So for the first question:
If this is sampled at 10kHz, then the amplitude is scaled by 10000. In the DTFT, the frequency 3.5kHz gets mapped to 3.5/10* 2pi=0.7pi. So this point lies outside the range ...
0
votes
0answers
18 views
Which frequency bins give the best interpolation for the derivative of a function?
A function $u:[0,2\pi]\to\mathbb R$ sampled over $N$ equidistant points $\theta_j=(2\pi/N)j,\, j = 0, \dots, N-1,$ can be interpolated by a set of functions $\{u_{k_0}\}$ enumerated by integers $k_0\...
2
votes
2answers
56 views
Why is a circular mask appropriate for Fourier filtering rectangular images?
Suppose I apply 2D DFT to an image with dimensions $H{\times}W$ where $H \neq W$, then shift the DC component to the center. Why does a circular mask capture the lowest frequency components, i.e. why ...
-1
votes
2answers
49 views
Derivation of Nyquist Frequency and Sampling Theorem
I have been looking through different sites and questions over the internet about Sampling theory, but couldn’t find the clear definition of how nyquist frequency condition is derived? It would be ...
0
votes
0answers
29 views
Fourier Transform of finite time series
I have some signal 𝑠(𝑡) which is real data i.e. finite.
The time runs from −𝑇 to +𝑇. The signal amplitude is large at 𝑡=0 and small (→0) at the ±𝑇 limits.
I can do a finite (discrete) Fourier ...
0
votes
1answer
18 views
What is the form of the spectral derivative in the all-positive-frequency notation in DFT?
The Discrete Fourier Transform (DFT) of a function $u:[0,2\pi] \to \mathbb R$ sampled over $N$ equidistant points $\theta_j = 2\pi j/N,\, j = 0, \dots, N-1,$ is defined by
$$
\tilde U_k = \frac1N \...
0
votes
0answers
41 views
Solving equation with convolution
I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$:
$$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$
where $\ast$ is the convolution.
I know $A(f)$, $B(f)$,...
0
votes
1answer
26 views
Inverse Fourier Transform Dirac impulse with scaled argument
Currently, I am dealing with the sampling problems and I don't understand how to calculate inverse Fourier transform of a scaling impulse function
$\textrm{IFT}\{\delta(\Omega T)\} = ?$, $T$ is ...
-1
votes
1answer
41 views
Sampling of frequency response
Let's consider any physical quantity depending on the frequency. For example, the impedance of a certain electrical component: $Z(f)$.
Now, imagine to measure it in a continuous interval of ...
0
votes
1answer
30 views
How to perform spectral inversion in the frequency domain to convert a low-pass filter into a high-pass filter?
To convert a linear-phase FIR low-pass filter into a high-pass filter with the same cut-off frequency, we can invert the sign of the low-pass filter's impulse response $h(n)$ and then add one to the ...
0
votes
2answers
47 views
Fourier transform of a periodic/aperiodic signal
Generally speaking, I know that periodic signals (continuous-time domain signals) with period 2pi/wo have a spectrum with equidistance Delta-impulses of distance w0.
My question is that, if we have ...
0
votes
1answer
20 views
Palmprint Identification - Why do we align the images before we use the Fourier Transform?
I have been reading the paper PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM by WENXIN LI, DAVID ZHANG and ZHUOQUN XU about identifying persons based on an image of their palm, one version of the paper ...
0
votes
0answers
60 views
Relationship between DFT and DTFT
Let $x[n]$ be an $N$-point sequence, i.e. $x[n] = 0$ for $n < 0$ and $n \ge N$.
Let $X[k]$ be the $N$-point DFT of $x[n]$.
Let $$y[n]= \left \{
\begin{array}{ll}
\displaystyle\sum_{l=-\infty}^{+\...
0
votes
0answers
18 views
FFT freqency bin center in R
I'm trying to do a spectral analysis in R. I learned it in Python from Allen Downey's ThinkDSP book.
What is the R equivalent of the Python numpy function, numpy.fft.fftfreq?
If you provide a window ...
0
votes
0answers
26 views
Two Consecutive Inverse Fourier Transforms [duplicate]
What happens to a function F(w) if you take two
consecutive inverse Fourier transform of it?
0
votes
1answer
31 views
How does one interpret an element of the “transfer matrix” used to calculate frequency domain granger causality (via VAR models)?
I am attempting to gain a better mathematical understanding for how autoregressive models can be used to infer frequency-domain granger causality. All freq. domain measures of causality that utilize ...
0
votes
0answers
48 views
Frequency Domain Signal to Noise Ratio
I am doing some research on low-cost air pollution sensors. I'm measuring the "ground truth" with a single low-noise sensor, and I'm trying to use it to calibrate a low-cost sensor that has high noise....
0
votes
1answer
49 views
If the cosine function is periodic, why does it have a Fourier Transform? [duplicate]
As far as I understand Fourier Transforms are for non-periodic signals and Fourier Series for periodic signals.
So why is it we can take the Fourier Transform of a cosine when it is a periodic ...
0
votes
1answer
39 views
How do I make sense of the cosine wave having Fourier Transform coefficients which have infinite magnitude?
To illustrate my question better, consider the Fourier Transform of an aperiodic (as a periodic cosine wave has a Fourier Transform not Fourier Series) cosine wave
$$f(x) =
\begin{cases}
\cos(2\pi ...
0
votes
1answer
40 views
How does minimum-latency partitioned convolution reverb work when you receive input samples in chunks, rather than one at a time?
I'm writing a reverb system where I receive an input block of samples 480 elements long, do some operation on them, and pass the block on to the next effect.
I've been reading up on partitioned ...
0
votes
1answer
41 views
DTFT of even and odd samples
Here to find DTFT of $h(2n)$ they have scaled omega, while in RHS to find DTFT $x(2n+1)$ they didn't, why is that?
0
votes
1answer
23 views
Inverse Discrete Time Fourier Transform of $1$
$\textrm{DTFT}(\delta[n]) =1$,
but $\textrm{IDTFT(1)} = \frac{\sin(\pi n)}{\pi n}$.
Why it is not equal to the unit impulse $\delta[n]$?
0
votes
1answer
33 views
What determines peaks in FFT?
I ran FFT on three audio files and found that the results for some have more peaks than the other. Could anyone give me any conceptual explanation as to what determines these peaks? Below are plots of ...
1
vote
1answer
35 views
Why zero padding the 2-d DFT interpolates images in spatial domain?
I was applying different image interpolation techniques and I came know to about interpolation in frequency domain. In this technique we first take 2d DFT of an image, padd it with zeros and take the ...
1
vote
1answer
50 views
Why the spectral coherence is unity for all frequencies between single-frequency time series and itself
In the example below, I am plotting the coherence between time series and itself. The time series do has one frequency.The coherence magnitude was one for all frequencies. I wonder why it is not zero ...
0
votes
0answers
39 views
How to find a Matched Filter Transfer Function from large signal sample
Lets say I have a system where I have a small sample of a signal with no noise $\hat{x}(t)$ and a lot of a similar signal with noise $y(t) = \hat{x}(t) + n(t)$, and from $\hat{x}(t)$ I want to create ...
0
votes
1answer
49 views
Signal processing using numpy python
To process a .wav audio file with numpy (using fast Fourier transform algorithm). I want to process an audio signal at a particular interval with a sampling frequency 44100hz and sampling rate of 20ms ...
0
votes
1answer
35 views
Fourier Spectra : Significance of the Negative Amplitude [duplicate]
For example, for an aperiodic gate pulse, the Fourier Transforms for the continuous time case is a sinc function, while the discrete time case gives a sine over sine periodic kind of a function. In ...
0
votes
3answers
30 views
Is there a version of Welch's method that doesn't look for power?
Welch's method splits a time signal, $x(n)$ into $M$ periodograms $P_m$,
$P_{x_m,M }(k) = \frac{1}{M}|F_k(x_m)|^2$
and averages them to give the Power Spectral Density (PSD),
$S_{x}(k) = \frac{1}{K}...
-2
votes
1answer
79 views
How do I decide which frequencies are signal and which are noise?
I have an arbitrary recorded digial signal, on which I have run a Fourier transform. I'm not sure what conventions are on a case like this, but I have 1024 frequency bins. Second bin is the highest ...
0
votes
2answers
28 views
Fourier Transform: interpretation of continuous spectrum at specific frequencies
B. P. Lathi in his book "Principles of Linear Systems and Signals" mentions in the Fourier Transform:
When $x(t)$ is periodic, the spectrum is discrete, and $x(t)$ can be expressed as a sum of ...
0
votes
2answers
151 views
Aliasing when interpolating with DFT?
I'm coming from an understanding of the continuous-time Fourier Transform, and the effects of doing a DFT and the inverse DFT are mysterious to me.
I have created a noiseless signal as:
...
0
votes
0answers
15 views
How to search for irregular signals: Fourier, DWT or k-means?
See my notebook here
I want to search for irregular time signals in a data set of ~3 500 000 time signals. By eyeballing I have found hundreds of flat and oscillating signals, but just a few that are ...
0
votes
1answer
39 views
What is Imaginary in Fourier transform?
How to plot graph of $e^{-t}$ in frequency domain. What would be the axis? If its Fourier transform is $1 /(1+j\omega)$, then how can we plot imaginary on frequency domain (amplitude vs frequency ...
2
votes
2answers
113 views
Explain Auto-Tune in a simple way
I have to do a presentation about Auto-Tune and its relation to the Fourier transform. What is a good explanation on how does Auto-Tune work?
1
vote
1answer
23 views
Impulse response of a 3x3 PSF - how to find analytical expression for fourier transform of a 3x3 matrix?
I have a filter $\mu[n_1, n_2]$ with taps:
$$ (1/8) (1/4) (1/8)$$
$$ (1/4) (1/2) (1/4)$$
$$ (1/8) (1/4) (1/8)$$
How do I find an analytical expression for $\hat\mu(w_1, w_2) $?
Since it looks so ...
2
votes
2answers
76 views
STFT on time varying signal with good time and frequency resolution
I am trying to determine the main frequency of a noisy signal that varies in frequency over time. Ideally I want to detect changes in the frequency as rapidly as possible - say 50Hz update rate, but I ...
11
votes
6answers
5k views
Is there any practical application for performing a double Fourier transform? …or an inverse Fourier transform on a time-domain input?
In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
