Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

Filter by
Sorted by
Tagged with
0
votes
0answers
13 views

FFT for Arbitrary time history

I have two Time-Speed histories one is real ( real measurements) the other is synthetically generated using formula. I need to compare both in the frequency domain using FFT given that: the time step ...
-2
votes
0answers
45 views

Find x3[n] if DFT of x3[n] is given by X3(k)=X1(k)*X2(k) where X1(k) and X2(k) are 4 point DFT of x1[n]={1,2,-2} and x2[n]={1,2,3,-1} respectivel [closed]

How do I solve this question? Can you tell me if I am right or wrong? First find $X_1(k)\; then\; X_2(k)$ using any technique. Multiply $X_1(k) X_2(k)$ Find IDFT. I am confused because IDFT is not ...
0
votes
2answers
64 views

Units of a Fourier Transform (FFT) and Spectrogram [closed]

I am very interested in analyzing signals in the frequency domain. Units of a Fourier Transform (FFT) when doing Spectral Analysis of a Signal 1.In the previous question, answer the unit for the ...
2
votes
1answer
38 views

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 ...
1
vote
1answer
57 views

Prove Convolution Property for DFT using duality

If $x_1[n]$ and $x_2[n]$ are finite length sequences of length $N$ $$\mathcal{DFT}(x_1[n] \circledast x_2[n]) = X_1[k]X_2[k]$$ where $X_1[k]$ and $X_2[k]$ are the DFTs of$x_1[n]$ and $x_2[n]$, ...
1
vote
1answer
198 views

Compressed Sensing -- reproducing simple 1-D example [python]

Context Attempting to reproduce an illustrative example of compressive sampling from Candes-Wakin 2008. Specifically, the L1 recovery of a sparse signal shown on pg 5 in Fig. 2. Using my code (below), ...
1
vote
1answer
79 views

How to interpret the Fourier Transform 𝑋(𝜔) (Foundational Questions)

The motivation behind the fourier transform is to somehow represent a non-periodic signal as a sum of sinusoids just as we do with the fourier series for periodic signals, correct? With the Fourier ...
1
vote
0answers
31 views

Discrete Fourier Transform of 2-D Images

I'm a high school student doing an essay on the applications of the Fourier transform on signal processing, but I haven't been able to find much information when applying the discrete fourier ...
1
vote
1answer
27 views

Frequency mixer shows 2 FFT spikes

I'm attempting to use a frequency mixer to shift one frequency range to another. Right now, I have a complex sine wave at $43\ \rm kHz$. My imaginary value on the complex object is 0. If I output a ...
0
votes
0answers
23 views

Gabor uncertainty and time-frequency resolution

I have a question about Gabor's uncertainty theorem, and how it relates to time and frequency resolutions. As I understand it, Gabor's uncertainty theorem states that the standard deviations of a ...
0
votes
1answer
78 views

Fourier coefficient to power

When doing a FT on a 4kHz and on a 8kHz signal (both 0dB amplitude), the Audition spectrum view shows 0dB for both freqencies as expected. But the calculated fourier coefficients for both frequencies ...
0
votes
1answer
27 views

Fast fourirer transform - Even and odd numbered elements

I'm trying to understand some optimizations on DFT. So in this step, there is a note like the following: The next step involves the mathematical observation that the even-numbered elements can be ...
1
vote
0answers
69 views

Wrong amplitude in the FFT for 10 seconds measured signal

I measured a signal with the Osziliscope that I generated with a signal generator. The signal is a pure sine wave with a frequency of 1 kHz and a peak amplitude of 2.5 V, I measured the signal for ...
0
votes
0answers
51 views

How to get the phase of a 2D sine wave?

I am trying to find the phase of a generic 2D sine wave with the 2D FFT. The formula for the phase is arctan(im/re). So I made 22 sine waves with phases ranging from 0 to 2 pi (by cropping the ...
0
votes
0answers
76 views

Symmetries of discrete analytic signals

Defining "analytic" as $x_a[n]$, where $X_a[k] = \text{DFT}(x_a[n])$, and $$ X_a[k < 0] = 0, \tag{1} \label{1} $$ what time-domain properties, such as symmetry or norm, are guaranteed for ...
0
votes
0answers
29 views

I have two signals, recorded from the same device. How do I standardize/normalise them?

I essentially have two signals X and Y, recorded with PPG devices. These have been filtered already. I want to standardize(z-score) or min-max scale them but I don't know if I should do this on each ...
0
votes
1answer
18 views

Dirichlet sufficient conditions satisfiability checking

I have 4 signal functions like this: $1.\ e^{-2t}u(t)$ $2.\ e^{-2|t|}$ $3.\ (1-\frac{|t|}{2014})(u(t+2014)-u(t-2014))$ $4.\ u(t)$ I know the answer would be the third option since the other ones have ...
0
votes
0answers
36 views

Recovering from exponential discrete-time signals

The spectrum of the discrete-time signal $x(n)=e^{-2n}$ is sampled at frequencies $2\pi\frac{k}{2014}$ for $k=0,1,\ldots,2013$. Can the signal $x(n)$ be uniquely recovered from these 2014 samples? ...
0
votes
1answer
39 views

Fourier transform of an aperiodic discrete-time signal

I have a signal of the form $x^{*}(-n+2)$. To derive the signal's Fourier transform I use The following properties of DFT: $x^{*}(n)=X^{*}(-\omega)$ and $x(n-k) = e^{-j\omega k}X(\omega)$ so the ...
2
votes
1answer
46 views

Correlation and the Fourier transform

In the book Fundamentals of Music Processing: Audio, Analysis, Algorithms, Applications by Meinard Müller, the coefficients $d_\omega$ and $\phi_\omega$ are defined as where $\cos_{\omega,\phi}(t) = \...
1
vote
1answer
34 views

What does not happen if we limit the duration of this sequences to 2014 samples?

I am confused with this multiple-choice question: Assuming that $x(n) = e^{-2n}u(n)$, what does not happen if we limit the duration of this sequences to 2014 samples? A. The signal power leaks out ...
1
vote
0answers
41 views

Remove Noise from Discrete Signal with given Noise Model

I am interested in finding the true signal $p \in \mathbb{R}^D$ of an observed discrete signal $t \in \mathbb{Z}_{+}^D$. I know that each observed $t_{i}$ with $1 \leq i \leq D$ is the result of a ...
0
votes
3answers
51 views

Why Matlab Spectrogram of slow and rarely sampled signal shows high frequencies

I have a signal, which was measured for 14.4 minutes (= 864 seconds). There are 192 measurements, so one measurement was done in every 4.5 seconds, which results in a 0.22 Hz sampling frequency if I ...
0
votes
0answers
14 views

compressed sensing versus Lomb-Scargle

Say I have a signal that's the sum of only a few sine/cosine waves, and some noise, which has been measured at random times. I would like to find the frequencies of the waves. With this goal in-mind, ...
2
votes
0answers
49 views

Multiple 1D gaussian filter

Given $$ \begin{cases} &f_0(x)=1 \\ &f_{n+1}(x)= (\varphi*(f\mathbb{I}_{[a_n,b_n]}))(x)=\int_{-\infty}^{+\infty}\varphi(x-t)f_n(t)\mathbb{I}_{[a_n,b_n]}(t)dt = \int_{a_n}^{b_n}\varphi(x-t)f_n(...
5
votes
1answer
414 views

Deblurring 1D Data Using Direct Inverse Filtering

In my assignment I have been given recorded temperature over a period of time (193 Values) and the Impulse Response (5 Values with n=0 corresponding to the middle value). data : data.csv | h = [1/16 4/...
0
votes
0answers
22 views

Average Power Spectral Density (1D and 2D) of multiple images of different sizes in python

I am trying to calculate avg 1D and 2D PSD of multiple image with different sizes. Any idea how can I do this? Current I'm calculating 1D psd using this function. The problem here is that each image ...
0
votes
0answers
10 views

Numpy 2D FFT produces corona that is not uniform around center

Tldr: Numpy FFT creates non uniform output when output is wanted to be uniform. I want the output to be a uniform corona. I am trying to eventually run a Gerchberg-Saxton phase retrieval algorithm. I ...
2
votes
1answer
61 views

Fast computation of a convolution integral with Gaussian kernel

Given a convolution integral with gaussian kernel $$ g(y) =\int_a^b\varphi(y-x)f(x)dx=\int_{-\infty}^{+\infty}\varphi(y-x)f(x)\mathbb{I}_{[a,b]}(x)dx $$ where $\varphi(x)= \frac{1}{\sqrt{2\pi}}\exp{\...
2
votes
3answers
52 views

What does the intensity values on wavelet transform mean? Amplitude or power?

So when applying wavelet transform, we get a 2d plot. Each point in that 2d plot has a color, showing intensity of something. But I cannot understand if it is an amplitude or power?
0
votes
1answer
56 views

Can FFT tells us existance of same frequencies with different phases?

So I know that applying FFT on a time-domain signal, shows which frequency components exists and what amplitudes each frequency signal has. My question is, suppose the signal contains same frequency ...
0
votes
1answer
22 views

Sparse FFT of ramp using zero padding

I would like to sparsely represent a linear function/ramp in the Fourier domain. In an attempt to improve the sparsity, I have zero padded it. With this padding, it is possible in the example I tried ...
0
votes
1answer
34 views

Extracting different frequency bands (alpha, beta, gamma) from MEG source estimated data

I have a dataset that consists of source estimated data of MEG brain signals. I need to extract the different frequency band features (i.e., alpha, beta, gamma, etc) from them. What steps/procedure ...
0
votes
1answer
24 views

Inverse discrete Fourier transform or inverse Fourier transform of composite function?

I collected spectrometric data which produced a graph with the intensity of each frequency of light. What more do I need to perform an inverse fourier transform of this data? Should I attempt an ...
0
votes
1answer
35 views

Solving Fouriertransform exercises without explicitly doing the transform

Hey there in the signal processing course I am studying there is an excercise that reads: The sequence $x(n)$ is given $x(n)=\{-1\quad2\quad \underline{-3}\quad 2\quad -1\}$ and the fouriertransform $...
0
votes
1answer
51 views

Polar Fourier Transform and its similarity to the Z-Transform

The DFT is given by $X_{\mathcal{F}}(k) = \sum_{n=0}^{N-1} x_n e^{-j 2 \pi k n / N}$ Knowing that complex numbers can also be represented using a polar form $A \angle\theta$, I was looking for a ...
-2
votes
2answers
82 views

DFT modulus property?

We know fft(cos), and abs(cos) is just positive cos with halved period, so seems there ...
0
votes
1answer
54 views

Why is the Fourier transformation full of spikes with 12.5 Hz frequency steps?

I am performing a fourier transformation in matlab for time signal data with monitoring points for pressure extracted from a simulation. What I get at the end is a spectrum as shown below: I am ...
2
votes
1answer
61 views

ringing artifacts using FFT-based gaussian blurring

I'm trying to do an FFT-based gaussian blur on a grayscale image, and it works, however it seems to introduce ringing artifacts to the result when compared to the expected direct filter. What can I do ...
1
vote
3answers
80 views

Inverse Fourier transform: where am I going wrong?

I am studying a course in signal processing, currently we are examining Fourier transforms. I got stuck on an exercise with an inverse Fourier transform. I am supposed to find the inverse Fourier ...
0
votes
2answers
88 views

Why does my amplitude change upon inverse Fourier Transform when I am only randomizing the phase of the fourier transform using Python numpy?

I am trying to make a surrogate time series of a discrete data series using python, basically I wish to keep the amplitude same and change the frequency I take a Fourier Transform of the data I ...
3
votes
0answers
55 views

real time - active noise control

I am trying to implement an adaptive filter for system identification and active noise control for realtime signal processing on an FPGA using Labview. For system identification, I implemented the ...
4
votes
4answers
130 views

One-sided waveforms in both time and frequency?

Can a complex signal be one-sided (causal in time and positive only spectrum in frequency) in both domains? I understand that a function can't have finite support in both domains, but what if both ...
1
vote
3answers
119 views

Some signals whose Fourier transform are a particular rotation of its self

Let $N\in \mathbb{N}$. I am looking for a non-zero scalar $\lambda$ and a nonzero vector $$f=(f(0),f(1),\cdots,f(N-1)) \in \mathbb{C}^N$$ satisfying the following equations for $l=0,\cdots,N-1$: $$\...
3
votes
1answer
120 views

Generate a Gradient Operator for a Fourier Transform

I came across this equation while trying to process an image $z$, $$ \mathcal{F}\left(\mathbf{D}^T \mathbf{D}\right) \mathcal{F}\left(z\right), $$ where $\mathcal{F}$ is the 2-D Fourier transform, and ...
1
vote
1answer
74 views

Compare two Fourier transforms of two signals by calculating the coherence

My overall aim is to compare the edges of two images by comparing their Fourier Transforms (FFT) and to calculate one number as a key performance indicator that describes how much they are similar to ...
0
votes
0answers
35 views

filtering large wiggles in signals

I am trying to filter out large wiggles showing in a signal. Those wiggles are happening due to many signal processing layers and a final sine Fourier transform (no phase) Here's the python code i am ...
1
vote
1answer
27 views

Differentiate betwee sibilant "sssh" voice sounds and instruments like hi-hat?

How would I differentiate betwee sibilant "sssh" voice sounds in a music track and a similar sounding instrument sounds like hi-hat or cymbals?
2
votes
2answers
57 views

Meaning of Rect and Train of Rect Spectra

The Fourier transform of $x(t)=\operatorname{rect}(t)$ is $X(f)=\operatorname{sinc}(f)$ The Fourier transform of a periodic train of rectangular pulses $x(t)=\sum\limits_{n=-\infty}^{\infty}\...
1
vote
3answers
69 views

Can we generate signals in reality that have non symmetric magnitude spectrum in the Fourier domain?

I am reading communication systems, and have a doubt: Is it possible to generate signals in reality that have a non-symmetric magnitude spectrum in the Fourier domain? For example, if I have a signal $...

1
2 3 4 5
36