Signal Processing

Questions tagged [fourier-transform]

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

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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 ...
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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 ...
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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 ...
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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 ...
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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 $x_2[n]$, ...
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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), ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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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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/...
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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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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{\...
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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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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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1answer
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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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1answer
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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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1answer
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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
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 ...
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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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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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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 ...
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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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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 ...
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1answer
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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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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 ...
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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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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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