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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Which is more powerful Laplace transform or Fourier transform?

In undergraduate, in some books, we study the first Laplace after Fourier and vice versa. there is the type of signal for which we found the first Laplace and we put jw in place of s and find Fourier ...
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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 ...
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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? ...
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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 ...
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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) = \...
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27 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 ...
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31 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 ...
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interpreting wavelet transform of brain siganls

I have created wavelet transform of my signal using the following code: ...
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UWB signal modulation [closed]

Consider a baseband signal (Blackman filter), multiplied by $\cos(\omega_0t)$, where $\omega_0$ is small enough so the modulated signal is UWB. How can I find the relation between the bandwidth of the ...
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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 ...
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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, ...
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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(...
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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/...
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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 ...
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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 ...
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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{\...
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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?
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51 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 ...
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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 ...
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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 ...
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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 ...
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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 $...
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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 ...
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DFT modulus property?

We know fft(cos), and abs(cos) is just positive cos with halved period, so seems there ...
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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 ...
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1answer
51 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 ...
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77 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 ...
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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 ...
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51 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 ...
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128 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 ...
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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 $l=0,\cdots,N-1$: $$\...
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101 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 ...
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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 ...
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29 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 ...
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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?
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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}\...
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3answers
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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 $...
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Where can I get the file l1eq_pd.m?

To recover the original signal when compressive sensing is used, we get an error, to avoid the error, we need to modify the l1eq_pd.m file. How to go about it? Where can I get this file in Matlab?
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How do I get this Fourier transform?

In the image, the signal is a pseudorandom sequence with values oscillating between -1 and +1. It is periodic (in this case with period 0.001). I don't see how the sequence yields a fourier transform ...
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57 views

can $e^{j\phi_0}$ be incorporated into the sine and cosine terms?

This is from "communication system" by Carlson fifth edition page 109: If transfer function of a channel be like this: $H(f)= Ae^{j\phi_0}e^{-j2\pi ft_g} $ and input to this system be: $x(t)=...
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31 views

Different “zoom” after reconstruction from Radon transform using Fourier Slice Theorem

I have implemented the procedure to reconstruct an image from its Radon transform involving the Fourier Slice Theorem (FST). After application of the FST, the data is transformed from polar ...
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47 views

Use Fourier Transformation to compare 2 short audio files [duplicate]

I want to use Fourier Transformation to compute the similarity of 2 audios. I am dealing with small audios having the same size: 1 second length, mono channel. My question is how can I use the Fourier ...
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1answer
55 views

Fourier Transform of $u(t)$ [duplicate]

I am just unable to find the correct Fourier transform of these signals (unit step, sine and cosine functions) which are containing delta functions in their Fourier transform. For unit step function, ...
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1answer
77 views

How to take into account phase differences when doing Fourier Transform?

I apologize if the title seems very vague, I don't really know how to put it a different way. From what I understand, the Fourier transform is essentially just doing a dot product between multiple ...
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Possible RF Mixing for Increasing Frequency of a Pulse Train

I am planning to build a low-power DC/AC inverter circuit along with MOSFETs and the full-bridge configuration. The MOSFETs are going to be controlled via two 4047s on the both side of the inverter. ...
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Frequency domain filtering: must filter coefficients always be conjugate symetric?

While trying to do frequency domain filtering of audio signals using windowed overlap-add methodology, I came across some pre-calculated frequency domain coefficients. I noticed that the coefficients, ...
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4answers
73 views

Meaning of frequency and bandwidth of a signal, despite the fact that we do not know the signal

First of all, I am completely new to the domain of signal processing. As far as I know, a signal can be represented with an infinite integral of infinitesimal complex exponentials, which is known as a ...
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1answer
74 views

Adding phase noise to a signal results in amplitude variation on a constellation - whats the mistake? *plots inside*

I am attempting to add phase noise to a modulated signal. I am doing this by taking a phase noise mask (single sided 0 Hz to 1 MHz), which shows dBc values away from central value or reference value. ...
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1answer
96 views

Calculation of inverse impulse response in the frequency domain

I want to calculate the inverse impulse response of a LTI system in the frequency domain. I generate a simple impulse response $g$. For this I generate a vector of 100 zeros. I set the value of the ...
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1answer
31 views

Find response of discrete time LTI system given input and impulse response

For this question the guide says to use $Y(e^{j\omega}) = H(e^{j\omega}) X(e^{j\omega})$. I have been able to find the discrete time Fourier transform of the impulse function as $$H(e^{j\omega}) = \...

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