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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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555 views

Finite and Infinite support in time and frequency domain

It's known that signals with a finite support in time has an infinite support in frequency (talking about Fourier Transforms). A common example that is given for the claim is the triangle function ...
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330 views

Why is the second half of the FFT negative frequencies

There are lots of questions here about what the negative frequencies in fft mean, but I'm confused on why the second half of the fft calculation is the correct calculation for a negative frequency. ...
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324 views

Why MATLAB fft cos makes imaginary parts?

The cos fourier transform has no imaginary parts, but in this code it has imaginary parts that little big. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(7); fs=128; t=-4*pi:1/fs:4*pi-1/fs;...
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58 views

Bilateral Laplace transform and existence of Fourier transform

I was reading from Athanosios Papoulis' "The Fourier integral and its applications." and they referenced the bilateral Laplace transform and Fourier Transform as: $$F(p)=\int_{-\infty}^{\infty}e^{-pt}...
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448 views

Cosine Fourier Transform and Phase

If we do FT of cosine wave, then sine wave will be orthogonal. So, the imag parts of FT will be 0. This is my think. But, the result isn't show that. Like this. Figure 1. Real and Imag parts (Y label ...
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159 views

Finding the Period of a Signal by Its DTFT Data

find period of DTFTs where vertical lines represent Dirac deltas
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43 views

Properties of DTFT to Infer the Inverse DTFT of Altered Data [closed]

Given a signal $ x \left[ n \right] $ and its DTFT $ X \left( {e}^{j \omega} \right) $. Which property of the DTFT allows you to easily compute the inverse DTFT of $ \frac{4 X \left( {e}^{j \omega} \...
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540 views

Calculate the Inverse DTFT of the DTFT Derivative in Terms of $ x \left[ n \right] $

Consider the signal $ x \left[ n \right] $ and its DTFT transform $ X \left( {e}^{j \omega} \right) $. Assume $ X \left( {e}^{j \omega} \right) $ is differentiable. What is the Inverse DTFT of: $$ j ...
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78 views

Orthonormal Dictionaries for Band Limited Signals

If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
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1answer
148 views

Understand Inverse DFT (FFT)

I was reading this article to understand the fft https://jackschaedler.github.io/circles-sines-signals/dft_walkthrough.html I understand that the fft takes a block (256 or 512) of the signal, ...
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1answer
818 views

Numpy fft2 frequency shift

I don't understand how to make frequency shift in fft2 or higher dimensions. Could anyone explain it, please? import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import ...
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302 views

Relation between the DTFT and CTFT in sampling- sample period isn't as the impulse train period

I will quote an answer of Matt L. from this post (I didn't comment there because I can't) If you have a continuous-time signal $x(t)$, then the two signals you're talking about are $$\begin{...
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208 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 ...
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1answer
47 views

FFT for distance-limited sum of pairwise products

I have a sequence of fixed length $N$ input arrays ($x_0$, $x_1$, ..., $x_{n-1}$), and my goal is to compute output arrays as such: $$d_{00}[l] = \sum_{i = 0}^{N - l} x_0[i]x_0[i + l]$$ $$d_{01}[l] = ...
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55 views

What to do for the right FFT in Matlab (two peaks and incorrect amplitude)?

This is the FFT I'm using. But two peaks (did not expect the one in the beginning) are occurring and the amplitude is not as specified (expecting a value of 2). Any help is much appreciated! ...
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4answers
906 views

Why does the frequency in the DFT have to be an integer?

I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ...
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21 views

How does a cross-looking error profile arise in discrete fourier transform?

I am numerically computing a 2D NxN complex Hermitian matrix using a discrete fourier transform operation on an 2D MxM complex Hermitian matrix. The phases of the output 2D NxN matrix elements are ...
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1answer
56 views

how to guess what the interference source it could be

At work, we are in an industrial area, and there is always a signal that I receive inside my office which interferences with my tests. This signal is in the 433 MHz and when I see the spectrum, ...
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21 views

Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
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1answer
96 views

I want to get impulse response of causal system

I want to get impulse response of this causal system on first photo. So I got frequency response on second photo from this system. and now I am trying to transform this frequency response to impulse ...
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207 views

PHAT filtering for cross-correlation yields wrong results while simple cross-correlation does OK (Python)

I work with two signals, the second being perfectly delayed and attenuated, with no reverberation. I implemented cross-correlation algorithm, which yields me these results: Here is my code for these ...
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120 views

Graph signal processing

What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
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4answers
773 views

DFT (FFT) of a Real Even Function Doesn't Yield Real Only DFT Signal

There are a lot of similar questions already, but I can't find one answering this problem. I used the following MATLAB code to perform the FFT on a Lorentzian input signal ...
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1answer
59 views

Accuracy of time domain signal when one frequency is absent

Suppose the known frequency spectrum of a signal is: $$ G(n\Delta f)=9,4,3,5,1,6,... $$ where $n=0,1,2...$ and $\Delta f=1$ Hz If, for some reason, we cannot sample $G$ at $n=0$ (i.e. $G(0)=9$ is not ...
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91 views

In a periodogram, why is the modulus squared of the DFT taken rather than the DFT itself? [duplicate]

Why can't you just take the DFT itself? And how accurate is this method in spectral density estimation? Are there cases in which it is very accurate?
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41 views

How to Calculate the number of DFTs taken in a STFT

Given variables of window size (W), overlap (O), and length of the Signal (S) (in my case, length of a song) and I am trying to determine an equation that gives me the number of DFTs that would be ...
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1answer
246 views

Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
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1answer
1k views

STFT amplitude normalization, librosa library

So librosa.core.stft returns a complex single sided spectrogram. My question is: What normalization of the amplitude values should I perform afterwards? I believe I have to multiply the amplitude ...
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1answer
99 views

Question about time shifting property

I know that time shifting property of discrete-time Fourier Transform states that $x[n]\leftrightarrow X(e^{j\omega})\implies x[n-n_0]\leftrightarrow e^{-j\omega n_0}X(e^{j\omega})$ So given a signal ...
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1answer
169 views

Bandwidth of Information Signal

I have trouble finding the bandwidth of a signal. Say I have an info bearing signal m(t)=sinc(2t/pi). I found the fourier transform of the sinc function and found that the angular frequency was 1/pi. ...
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64 views

Discretization of Sinusoidal Signals

How do I should sample two continuous sinusoids of $f_1$=1/4 Hz and $f_2$=1/2 Hz at a 1 Hz rate? Can i recover both if i bandlimit after sampling at a 1/2 Hz limit?
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239 views

Should scipy.signal.coherence be 1 for single input and output signals?

I am trying to calculate the coherence between input and output signals. I thought I could work with a single input and a single output time series and calculate the coherence $\gamma^2$ between them. ...
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1answer
170 views

Signal squared in time domain

In some publication I have found a formula that for some reason squares signal in time domain. I am analyzing it now. What should be the Fourier transform of a signal that was squared in time domain? ...
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1answer
121 views

CMV: COLA constraint is not necessary

In the literature on the short-time Fourier transform (STFT) it is often stated or implied that the constant overlap-add (COLA) constraint must be satisfied in order for the STFT to be invertible. ...
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1answer
289 views

How to calculate a delay between two signals in frequency domain?

Calculation of a delay between two signals is generally done by finding the maximum in the cross-correlation of the two signals (in time domain): $$ \tau_{delay} = \arg\max_\limits{t}(f(t) \star g(t)) ...
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573 views

Hilbert transform of unit step function

How to calculate Hilbert transform, if it exists, of the signals like $u(t)$, $sgn(t)$. What properties should a function satisfy for existence of Hilbert transform. Absolute integrability of a ...
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2answers
73 views

How does sampling rate of $x[n]$ relate to sampling rate in frequency domain after DFT transformation?

I've got an analog signal $x(t)$ sampled at frequency $F_s$ to obtain samples: $$ x[n] = x(t) \bigg|_{t=n/F_s} $$ I transform this signal with DFT defined as: $$X[k] = \sum_{n=0}^{N-1}x[n]e^{-i2\pi ...
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Wikipedia equation for DFT seems to be bad?

I was writing a simple fourier transform implementation and looked at the DFT equation on wikipedia for reference, when I noticed that I was doing something differently, and after thinking about it ...
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0answers
85 views

Find cepstrum of a function with dirac function

$$x[n] = d[n] + a\cdot d[n − N_p]\ ,\ \ |a| < 1$$ I need the complex and real cepstrum of this function as well as what would happen for $N=N_p/6$ for the DFT approximation $$x_p[n] = \frac{1}{N} ...
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1answer
153 views

Uncertainty Relation between time and frequency

Typically, humans can hear sound waves in the frequency range 20 Hz to 20 kHz. If one wants to make digital record of sound such that no audible information is lost, what is the longest time interval ...
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621 views

Why is the Fourier transform valid only for absolutely integrable signals?

Why is the Fourier transform valid only for absolutely integrable signals? For example, why can't we do the Fourier transform of exponential order functions?
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2answers
369 views

Amplitude of signal and PSD peak height

So, suppose you have a superposition of cosines of the same magnitude: $\sum_{i}\cos[\omega_i t]$ When you take the Fourier transform, theoretically you'd expect to find $\delta$-like peaks of the ...
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1answer
99 views

Inverse DFT to a real signal when only odd harmonics are present

There is an old paper by L.R. Rabiner, "On the Use of Symmetry in FFT Computation" which describes (among other things) an optimized method to calculate the DFT of a real signal $x_n$, $n=0,\dots, N-1$...
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1answer
6k views

How to find the phase spectrum of a rectangular pulse? (Fourier Transform)

How to find the phase spectrum of a rectangular pulse? The Fourier transform of a rectangular pulse $$ x(t) = \begin{cases} 1, & \text{for $|t| \le \tau /2$ } \\ 0, & \text{otherwise} \end{...
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1answer
971 views

Understanding Magnitude Spectrum of Images [closed]

I am facing problem in reading Fourier domain of a given image. I don't understand what to interpret from it. For instance, consider this image. Ok, so there is a dot in the middle, with some ...
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3answers
103 views

Demonstrate that $x(t)$ and $\hat{x}(t)$ are orthogonal

I have to demonstrate that a function $x(t)$ and his Hilbert's transform are orthogonal, it is said: $$\int^{\infty}_{-\infty} x(t) \cdot \hat{x}(t) dt = 0$$ I have tried the exercise using Parseval'...
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2answers
1k views

Why is the size of the output of the FFT of a signal is same as the size of the input signal?

I am kind of new to the DSP domain. I was trying to get the frequencies associated with a signal by performing FFT over it. I used numpy.fft.fft for this. ...
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2answers
171 views

Understanding where the constant $2/N$ comes from in Fourier transformation

I'm implementing Fourier transformation in my analysis and I wanted dig a bit deeper on the reasons why the absolute value of Fourier transformation is usually multiplied by the constant $2/N$ to get ...
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186 views

output shape of STFT

I cant figure out why our output image is 257 * 32 , 32 I know why , but 257 I cant understand ? this is the exact word of this paper wich applied STFT on 3 channel of eeg signal : Short time Fourier ...