Questions tagged [fourier-transform]
The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
1,828
questions
0
votes
1answer
76 views
+50
How to interpret a 1D-DFT of an image with a sinus grating/gradient compared to its 2D-DFT outcome?
For getting a better understanding on how the 2D-DFT works I was playing around with sinus gratings in grayscale. I tried to compute the 1D-FFT first and compare it with the 2D-DFT to get a better ...
0
votes
0answers
18 views
Calculate Nyquist frequency
I have a question about finding the Nyquist Frequency of the following Functions:-
a) $\frac{dX_a(t)}{dt}$
b) $X_a(2t)$
c) $X_a^2(t)$
d) $X_a\cos(\Omega_0*t)$
The question only says find the Nyquist-...
1
vote
2answers
155 views
Time domain to frequency domain conversion of audio signals to extract 1/3 octave frequencies
I am writing first time in this forum and I am not expert in programming and FFT. We have developed an android app (Noise Tracker) for noise measurement using smartphones. It displays noise levels in ...
2
votes
0answers
2k views
Power spectral density vs. Fourier Transform
I am trying to understand the difference between the Power Spectral Density and the Fourier transform. Specifically, I am trying to understand why the power spectral density is useful and in what ...
5
votes
1answer
76 views
Minimum statistics noise estimate - how to calculate the underestimation factor?
I have implemented a basic noise estimator using the minimum statistics method. Noise power estimate is obtained as a minimum of the short time power estimate within a window of subband power samples. ...
0
votes
2answers
58 views
aperiodic sum of periodic signals
Asumme that a continous signal is a finite sum of sinusoid. If the signal "begins" at $-\infty$ and "ends" at $\infty$, using Fourier transform, one can find the frequency, the ...
1
vote
1answer
185 views
Fourier Transform of the full Morlet wavelet
In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below:
Fourier Transform of Morlet wavelet Function?
However, it was the approximated Morlet wavelet not written with the ...
11
votes
2answers
5k views
Effect of windowing on noise
I understand that truncating a signal in time 'smears' the frequency response depending on the window chosen. In general, the shorter the signal duration, the more 'flattened' the frequency response, ...
3
votes
1answer
4k views
2D DFT in image processing in python
I try to compute 2D DFT in a greyscale image with this formula:
I write the code bellow with python
...
0
votes
1answer
85 views
transform signal
Hello everyone I need help solving a Fourier transform for the given signal, I know it will be a frequency convolution for the first function it will be a window function and for the second function I ...
2
votes
1answer
560 views
Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?
Let
$$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$
Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure
what will the frequency domain for $Y(\nu)$ look like for a ...
1
vote
1answer
478 views
Why is the arithmetic mean the same as the DC component of its fourier transform?
When we define $$\overline{\left|x\right|} = \frac1T\int_0^T x(t) dt$$ as the arithmetic mean of a signal we can see that it is the same as its dc component in the fourier transform.
Why is this the ...
0
votes
1answer
24 views
Spectral function value of a frequency above the nyqist limit
this was the question on my today's exam on signals and systems:
*We have a continuous function $f(t)$.
Its value of the spectral function at an angular frequency of $8000\pi\ rad/s$ is $\frac{1}{...
1
vote
2answers
57 views
Mixing with Deformed Local Oscillator Signal
I've decided to build up an AM receiver which is intended to capture sound signals from a nearby broadcasting station that is operating at 954 kHz. I've completed the system design and started to test ...
0
votes
1answer
40 views
Inverse Fourier transform of complex exponential with frequency dependent shift
In the case of a constant delay $\tau$, we have the following equality:
$$\begin{align}\mathcal{F^{-1}}\left\{e^{-j\omega \tau}\right\}=\delta(t-\tau)\end{align}$$
If the delay is frequency dependent $...
0
votes
1answer
32 views
Why doesn't the magnitude of Fourier Transform change when signal is shifted (i.e when a time shift is introduced)?
I understand that a time shift in the time domain produces a corresponding phase change / phase shift in the frequency domain. But I don't understand why the magnitude is unchanged (I am referring to ...
0
votes
1answer
31 views
Partial column approximation error
Can someone help me understanf how to plot the next partial column in MATLAB:
while N=2001
|M|<700
ak =
0
votes
1answer
34 views
Unexpected result with custom FFT implementation
To fully understand the Fourier Transform I have been working on a rather standard implementation of the FFT algorithm. I tried generating a 440 Hz sin wave and passing it through the algorithm, ...
2
votes
2answers
63 views
2D Spatial Fourier Tranform on a pressure field
I'm doing some research on Fourier Near-field Acoustic Holography (NAH). The basic theory behind Fouerir NAH is that you take a sound pressure field measurement in a 2d plane p(x,y), 2d spatial ...
0
votes
1answer
24 views
What transformation preserves first term and averages the opposite conjugates?
I can't figure not find any reference on what is this transformation (what $X$ represents in relation to $A$).
If $A=[a_1+jb_1, a_2+jb_2, a_3+jb_3, ..., a_n+jb_n]$, $X$ is defined as:$$X=\left[j b_1, \...
3
votes
2answers
678 views
Calculating the Norm of Each Sample of the DFT Transform
Given a discrete signal $ \left\{ x[n] \right\}_{n=0}^{N-1} $ and its Discrete Fourier Transform $ X[k] = DFT \left\{ x[n] \right\}[k] $.
I'd like to effectively compute the norm of each sample of ...
0
votes
1answer
53 views
Why does the 2D-DFT of a sinus gradient not show energy along the diagonal straigh lines and only vertical/horizontal from the diagonal point?
I have been experimenting a little bit with simple examples of the 2D DFT to get a better sense for it's interpretation.
For this purpose I have been using sinus gratings with the following code:
<...
1
vote
1answer
40 views
Ft and DTFT of negative frequency
I have a question that might sound silly but if I have a real and even signal x(t) can I define the FT and DTFT of the negative frequency if I can show:
$$X(-\omega) = \int_{-\infty}^{\infty} x(-t)e^{...
0
votes
2answers
39 views
Can you quickly find the inverse Fourier Transform using the duality property?
Cheers, in an exercise of mine I reach the point that I have to find the $F^{-1}\{Λ(ω)\}$ (where $Λ(ω)$ is the triangle function, with $1-|ω|$ for $|ω| \leq 1 $ and 0 elsewhere. Using the duality ...
0
votes
1answer
52 views
Doing the inverse of the fourier on EEG data?
I have EEG data.
I have 51 values(complex numbers) that are supposed to represent the frequency.
I plot the absolute values.
They have negative values and have an imaginary component as well:
...
0
votes
2answers
29 views
Fourier Transform of the signum function, using the integral property
Cheers, I am trying to find the fourier transform of the signum function, which is
$$ \operatorname{sgn}(t) \triangleq \begin{cases}
1 \qquad & t>0 \\
0 \qquad & t=0 \\
-1 \qquad & t<...
1
vote
1answer
24 views
Find fourier transform given the graph of a function
Cheers, I am given the following graph for $x(t)$:
and I am asked to find the fourier tranform by using the integral property and knowing that $F(Π(t)) = sinc (\frac{\omega}{2\pi})$
The solution I ...
1
vote
1answer
53 views
Zero padding affects the DTFT?
I wanted to understand better how zero padding affects a signal:
Which is just N ones. where $ N > 0$ is an Integer
$$ X[n] = 1, 1, 1, ... 1 $$
Zero padding it gives:
$$ X[n] = 1, 1, 1, ... 1, 0, 0,...
1
vote
0answers
65 views
Error in the computation of PSF?
I am in trouble computing a PSF of an optical system in optical turbulence.
Background
The optical transfer function (OTF) for an imaging system in optical turbulence can be modeled as the product of ...
2
votes
1answer
374 views
Phantom harmonics when using cosine windows why do they appear and how to avoid them?
Given an $L$ order cosine window, it is possible to show that the width of the main lobe is given by:
$$\omega_w = \frac{2 \pi L}{(2N+1)}$$
Where $L$ is the order of the window, $N$ is the maximum ...
0
votes
1answer
246 views
Fourier transformed acceleration from Fourier Transform of velocity and position using Omega arithmetic
Let's say the position of an object is given by simple sine function. By elementary calculus, I can calculate the acceleration in the time domain and find its Fourier transform.
I can also calculate ...
0
votes
1answer
69 views
Output of LTI (in time and frequency $\omega$ domain) : when input goes through LPF
I would like to raise a mathematical question :
Let's say we are been given :
$$x(t) = \begin{cases} \cos(\pi t) & |t| \leq 0.5 \\
0 & \textrm{otherwise} ...
0
votes
1answer
76 views
I'm having problems simplifying this discrete-time fourier tranform
I have this problem, and I can't get to the solution.
$$X(e^{j\omega}) = \sum_{n=-\infty}^{\infty} {(0.6)^{|n|}[u(n + 10) − u(n − 11)]}e^{-j\omega n}$$
The solution is
$$X(e^{j\omega}) = \frac{0.64 − ...
0
votes
2answers
99 views
Questions about MP3 bitrate conversions
I was trying to analyse the lossy compression of MP3 audio files through their Spectrograms and the results were something like this (where the upper is 80Kbps and lower is 128Kbps).
It is obvious ...
0
votes
1answer
26 views
iFFT and extracting dw
I have a trivial fourier transform question. I have a correlation function, C(t), with complex components in the time-domain, and dt. I would like it in the frequency domain, C(w), like from ...
0
votes
1answer
68 views
Is there an order to apply time shifting and frequency shifting to signals in DTFT?
For instance in one question applying frequency shifting first and then applying time shifting yields a different answer wrt applying time shifting first. Please elaborate i am clueless.
if i use ...
0
votes
2answers
777 views
Detection of Troughs and Notches in a PPG Signal
I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below...
I'm having problem in finding the troughs and dicrotic notch for ...
2
votes
1answer
74 views
inverse fourier transform coefficients
Context
I want to implement (real) cepstrum on stock data (for example MSFT stock) and achieve cepstral coefficients of this time series.
as noted in "Cepstral-based clustering of financial time ...
0
votes
1answer
3k views
Calculating the magnitude spectrum and phase spectrum
From a window function $x(t)=u(t+2)-u(t-2)$, we can get the Fourier Transform $X(j\omega)=\frac{2\sin(2\omega)}{\omega}$.
Then, I want to calculate its magnitude spectrum and phase spectrum.
The ...
1
vote
1answer
625 views
Relation between two k-spaces phase-frequency and spatial frequencies in
When I see MRI explained, two types of 2D k-space images seem to be described as if they were the same.
Axes are the two spatial frequencies. This images is directly fourier-transformed into the ...
1
vote
2answers
49 views
Filter filters out more than needed
I am currently coding a school assignment. I have a 1.5s recording of someone's speech that has 4 rogue cosines mixed in. With sampling rate 16000Hz, I divided the recording into frames of 1024 ...
0
votes
0answers
11 views
Phase Correlation with Mask for Translation-Invariant Log-Polar Registration
At the moment, I have implemented a registration method utilizing the mask in the log-polar domain, which consists of the below steps:
Algorithm 1
Transfer Image, Template, and Mask into Log-Polar ...
1
vote
2answers
274 views
Problem identifying the analytic expression of such determined signal
I came across this problem
I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal.
The teacher suggests that I should consider ...
6
votes
1answer
2k views
2-d circularly symmetric low-pass filter
For a square pixel grid, the ideal 2-d low-pass filter with a horizontal and a vertical cut-off angular frequency $\omega_c$ in radians has an impulse response (kernel) $h_{\small\square}(x, y)$ that ...
0
votes
1answer
61 views
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 ...
7
votes
4answers
2k views
Is interpolation of an audio signal to increase frequency resolution possible?
I apologize if some of what I ask is not entirely correct, I'm new to this field, but extremely interested.
I have an Audio signal of sample rate 44.1 kHz that I want to segment into 30 frames, and ...
0
votes
1answer
105 views
Unfortunately, my self-written Fourier transformation is not that good
In my question yesterday I said that I have a self-written Fourier transform and have to get to the data of the sound card. I have the latter now. I've already answered my question from yesterday. (...
2
votes
1answer
68 views
Palmprint Identification - Why do we align the images before we use the Fourier Transform?
I was 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.
The first step in their ...
0
votes
0answers
21 views
Recovering phase of harmonics in an arbitrary pulse train
I want to recover the phase of the harmonic components of a pulse train.
There's a lot of cool resources out there that talk about recovering power spectra from signals in several ideal and non-ideal ...
0
votes
0answers
22 views
What's the base and height of triangle obtained by FT{$\operatorname{sinc}^2(7\pi t)$}?
I'm a little confused about the $\operatorname{sinc}^2(7\pi t)$ function. How do you know the base and height of the triangle produced in the frequency domain only looking at the $\operatorname{sinc}^...
robert bristow-johnson
16.2k3 gold badges29 silver badges68 bronze badges