Skip to main content

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
1 vote
1 answer
121 views

beam pattern are fourier transform of the beam weight, is it true ? if it's true how?

what i understood is the equation of AF looks similar to DFT equation as we are multiplying with exponential term
Thouhidul Islam's user avatar
2 votes
0 answers
125 views

The Discrete Fourier Transform (DFT) decomposes any signal into four orthogonal signal components

Let $F=\frac{1}{\sqrt{n}}(w^{kl})_{k,l=0}^{n-1}$ be the discrete Fourier matrix of size $n$ where $w=\exp^{-\frac{2\pi i}{n}}$. It is a well-known that $F_n^4 = I_n$ where $I_n$ represents the ...
ABB's user avatar
  • 387
-1 votes
2 answers
90 views

Orthogonal signals basics [closed]

Suppose we have 2 orthogonal signals $x_{1}(t)$ and $x_{2}(t)$ and we add them up. Can we always say that the resulting signal will be of this form: $$x_{3}(t)=x_{1}(t)+jx_{2}(t)$$ ? If that is true ...
Root Groves's user avatar
1 vote
1 answer
196 views

Constraints on choosing the frequency axis when Fourier transforming non-uniformly sampled data?

Does anyone have a reference that specifically discusses choosing the frequency scale for a simple 1D data for non-uniformly sampled time-domain data when performing the discrete Fourier transform. In ...
AChem's user avatar
  • 569
6 votes
2 answers
873 views

How to know if a continuous function can be represented by a finite sum of sinusoids?

I have a lack of mathematical knowledge, and notably in mathematical vocabulary, so maybe a similar question exists but with a different wording. What I want to know, is actually how to know if a ...
endyx's user avatar
  • 63
1 vote
1 answer
77 views

How to feed multi-channel spectrograms to Deep Neural Network?

I am using a 14 channel EEG device. To do away with the need for any handcrafted features, I wish to implement an ML classification task with the EEG data collected using deep neural networks (such as ...
Anantha Krishnan's user avatar
1 vote
0 answers
69 views

Debug the difference between two Frft implementations

I need help to understand the difference between two fractional Fourier transform implementations. On this website two different implementations for the fractional Fourier transform are presented (...
Laszlo Korte's user avatar
1 vote
1 answer
224 views

Are complex exponentials real thing?

Is there any physical significance of complex exponentials. I mean can we produce them like how we can produce sinusoidal signals using a signal generator? OR are they just pure mathematical ...
amoghfyi's user avatar
1 vote
3 answers
106 views

How are the results of a fourier-transform interpolated to cover the entire frequency range?

Say we have an audio signal and we do a Fourier transform with block size 2048. Now the outputs correspond to 1024 different frequencies. A spectrum analyzer however doesn't just display 1024 discrete ...
Potheker's user avatar
0 votes
1 answer
224 views

Can someone explain me how the phase spectrum of trigonometric fourier series is related to phase spectrum of exponential fourier series of a signal?

Suppose we take a periodic signal and perform fourier analysis over it . Now we have two ways of representing the fourier series of this particular signal , one is trigonometric fourier series and ...
amoghfyi's user avatar
3 votes
1 answer
459 views

(graphic) Relation between FFT and complex signal

I have a complex signal with a frequency between 0 and 16 (16 not included). I have made four plots (in python) to show four examples. For each example I provide the signal, its FFT in both real, imag ...
Mart's user avatar
  • 195
1 vote
1 answer
90 views

Why do singularities on the imaginary axis affect the Fourier transform differently than the Laplace transform?

(Please note that I'm aware there are already several questions asking about the difference between the two transforms. However, none of them that I could find touch on this specific issue of the ...
Mikayla Eckel Cifrese's user avatar
0 votes
1 answer
52 views

Radix-4 DIT Inverse Transform Reordering Issue

I am trying to implement a radix-4 DIT FFT. It looks like the forward transform is working correctly, but the backward transform output is not in the correct order. I'm pretty sure that the ...
Tobias Hienzsch's user avatar
1 vote
4 answers
130 views

why fourier transform multiplies $e^{-i\omega t}$ not $e^{i\omega t}$?

I think that difference between $e^{-i\omega t}$ and $e^{i\omega t}$ is only the direction of rotation. Is there any reason why Fourier Transform multiplies $e^{-i\omega t}$ and Inverse Fourier ...
백종윤's user avatar
0 votes
1 answer
96 views

Does the length of DFT points (duration of a signal) affect the "amplitude" of the power spectral density?

For example, performing a DFT on a 10-second-long and 20-second-long signal with the same sampling frequencies will change the "amplitude" of the power spectral density (PSD) at each ...
Tom's user avatar
  • 3
2 votes
1 answer
112 views

Fourier Transform of $|t|$

I was going through Papoulis' book (The Fourier Integral and its Applications) when I came across the Fourier Transform for $|t|$. To find it he writes $|t|$ as (I am not sure how): $$|t| = -\frac{1}{\...
Ahsan Yousaf's user avatar
  • 1,548
2 votes
1 answer
139 views

Window function with no sidelobes

I found the Hann–Poisson window on Wikipedia. It has no sidelobe for $\alpha \ge 2$. I am interested to know more examples of such window function with no sidelobes and what they are useful for. I ...
anonymousRabbit's user avatar
1 vote
1 answer
129 views

What are the *undesirable* effects of windowing in Fourier space?

My goal is to split a periodic signal into two (or more) signals. The first signal would contain the low-frequency information, and the later signals, the higher-frequency information. These signals ...
user572780's user avatar
1 vote
1 answer
89 views

How To Calculate Length Of Sequences And A Suitable N?

I have been struggling to understand how to calculate the length of a sequence and also the minimal N to choose in order to avoid aliasing. Most sources tell me to take the (last non-zero value - ...
Sugi's user avatar
  • 11
1 vote
2 answers
337 views

What exactly is a frequency component, and what is the phase shift from the argument of the Fourier Transform relative to?

I'm an EE undergrad that struggles heavily with the intuition behind the Fourier Transform (most likely due to a shoddy mathematical foundation). Specifically: From what I understand, the real part ...
Philip's user avatar
  • 13
0 votes
1 answer
148 views

Calculation of frequency correlation function based on power delay profile

We know that the frequency-domain correlation function and the power delay profile appears as a Fourier transform pair, i.e., $$A_{c}(\Delta f) = \int_{-\infty}^{\infty}PDP(\tau) \cdot e^{-j2\pi \...
Vic's user avatar
  • 113
0 votes
0 answers
24 views

Compare Discrete Fourier Transform for multiple signals

I have heart rate data from a wearable sensor (no ECG). I want to perform Discrete Fourier Transform to see if some patterns are present. I have over 200 signals, as each individual has heart rate ...
TRM's user avatar
  • 1
1 vote
1 answer
71 views

What is the Fourier Transform integral equation for a 1D signal and how can it be expanded into 2D, 3D, and 4D?

I know that is the 1D Fourier Transform (FT), and the 2D FT is and 3D FT is , but I am not sure whether these expressions are in fact Fourier transform integral equations for a 1D signal, expanded ...
LiuXiu's user avatar
  • 13
1 vote
3 answers
115 views

FOURIER TRANSFORM: How can i find the index of data points

I am a senior in high school and am currently trying to conduct an exploration of Fourier Analysis, specifically using the Discrete Fourier Transform to analyse a chord played on my piano. Basically, ...
Ralph Khouri's user avatar
0 votes
2 answers
48 views

Estimating acoustic sound signal energy radiated

Im recording sound generated by a drilling machine against an object. I have the recording of following : Ambient noise with drilling machine switched off. Drilling machine on+ambient noise Drilling ...
V.M Sypher's user avatar
0 votes
1 answer
34 views

Relationship between IDFT and discrete Fourier series?

I want to know how IDFT $$x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k\cdot e^{\frac{i 2 \pi}{N} k n}$$ is related to discrete Fourier series (Eq. 3) $$x_{_N}(n) = \sum_{k=-N}^N C_k \cdot e^{\frac{i 2 \pi}{...
Ray Siplao's user avatar
0 votes
1 answer
90 views

Decomposing a signal so that the magnitude spectrum of the decomposed signals lie in some specific amplitude range

Suppose I have the following signal: I can compute its power magnitude spectrum: PSD = np.abs(np.fft.rfft(signal)) Now I would like to pick a specific amplitude ...
user572780's user avatar
0 votes
2 answers
2k views

How to normalize the FFT?

I want to normalize my FFT signal. From this page it says that we can normalize it by dividing the FFT result by the lenght of the signal in time domain. On the other hand, my supervisor told me that ...
Apinorr's user avatar
  • 125
0 votes
1 answer
108 views

Fourier Transform of a triangle function [duplicate]

Good afternoon, I am having a question regarding the following function : Let $g(x)$ be : $$\begin{cases}\pi + \frac{\pi}{2}x \text{ if } -2 <x < 0\\ \pi - \frac{\pi}{2}x \text{ if } 0 <x &...
Ravinala's user avatar
0 votes
1 answer
50 views

Understanding symmetry in DFT magnitude plot

I am trying to intuitively understand the mystery of why the DFT of a complex vector with real values produces apparent symmetry in the magnitude plot (see the second plot here for example). In DFT $X[...
John Davies's user avatar
0 votes
1 answer
95 views

Scaling plots after FFT

I have multiplexed 32 signals into 1 signal with python. Now I want to plot that signal in time domain and to plot it's amplitude spectrum. Professor gave us his plots so we can look up to it. These ...
3d014's user avatar
  • 15
2 votes
1 answer
116 views

Reconstructing the original signal from its DFT

Hi I am a newbie to signal processing and I am trying to better understand how inverse DFT works under the hood. Consider this signal and its DFT: (Source) For the sake of this post, let's assume ...
John Davies's user avatar
4 votes
2 answers
162 views

Why is the CT inverse Fourier Transform also an integral?

Intuitively it seems that to get a function back that was integrated, you would take the derivative. Instead, with the Fourier Transform we take an area under a curve of a modified function, and to ...
Yulia's user avatar
  • 61
1 vote
0 answers
56 views

Spectrum and Fourier transform of a sine wave

Take for example: $x(t)=A\sin(2\pi f_0t)$. The Fourier transform of this signal is $\hat{s(f)}=\frac{A}{2i}(\delta(f-f_0)-\delta(f+f_0))$. If we want to represent the spectrum of the signal we would ...
fi-xgamex do's user avatar
13 votes
4 answers
3k views

Why is the time domain low-pass filter the "sinc" shape?

Consider: I'm looking at low-pass filters, and I see that the time domain representation of an "ideal" filter resembles the shape above whereas the frequency domain is a box. I also get the ...
thepman's user avatar
  • 133
1 vote
1 answer
101 views

Fourier transform magnitude of the sum of two signals

Let $$\mathscr{F}\Big\{x_1(t)+x_2(t)\Big\}=X_1(f)+X_2(f)$$ I think that in general $$\big|X_1(f)+X_2(f)\big|^2\leq\big|X_1(f)\big|^2+\big|X_2(f)\big|^2$$ but I was wondering if $$X_1(f)X_2(f)=0,\qquad\...
giannisl9's user avatar
1 vote
1 answer
81 views

Frequency content of a noisy signal

To find the frequency content of a noisy signal (PSD), there are two methods below: #1 Take the fourier transform of its power signal (square the noisy signal) #2 Find the autocorrelation function of ...
scc28adi's user avatar
2 votes
1 answer
199 views

Finding Discrete Fourier Transform (DFT) for different DFT size

$N$ is an even integer, $x[n]$ is a finite length signal over the interval $n \in [0,N-1]$, and $X[k]$ is the $N$-point DFT of $x[n]$. Analytically find the DFT of sequence below in terms of $X[k]$. ...
nexxterp's user avatar
1 vote
1 answer
74 views

Relationship between fourier transform and fourier series

Let $$x(t) = A\sin(2 \pi f_0 t + \alpha)$$ its Fourier transform is given by $$ X(\omega) = \frac{A \pi}{i}(e^{ia}\delta(\omega-2\pi f_0) - e^{-ia}\delta(w+2\pi f_0)). $$ the Fourier series complex ...
MOHAMED SALHI's user avatar
1 vote
1 answer
75 views

Is it useful to think of a Fourier Transform as writing out a signal in terms of a basis?

The (modified) trigonometric functions $\{0, \cos(kx), \sin(kx)\}$ serves as a basis for periodic function. I have also seen (but not rigorously) that the Fourier transform can also be seen as an ...
AyamGorengPedes's user avatar
0 votes
2 answers
89 views

Alternative way to find fourier transform

Let $$x(t) = A \text{rect}_T({t-\tau})$$I calculated its fourier transform through the direct way: $$X(\omega) = Ae^{-i\omega \tau} \int_{-T/2}^{T/2} e^{-i \omega t} dt = Ae^{-i\omega \tau} \frac{\sin(...
MOHAMED SALHI's user avatar
1 vote
0 answers
69 views

Is `fft` always the best choice?

I hope this is the right place to ask this question since it is partially a note which might help others. Until recently, I always used the fft-algorithm ...
TheIdealis's user avatar
1 vote
0 answers
41 views

Calculating k-space coverage from antenna positions

I work with radar and I want to understand which spatial frequencies I can measure, i.e. the k-space coverage, given a set of coordinates of transmitter-receiver combinations. The ideal coverage for a ...
DominikR's user avatar
1 vote
0 answers
60 views

How to identify square wave in audio signal

I'm interested in identifying a square wave signal from recorded audio. This subject may be a complex problem so I would like to present the problem where I'm currently stuck at. I recorded the audio ...
Lim Meng Kiat's user avatar
0 votes
0 answers
58 views

Fourier Transform and Music Analysis

I am a senior in high-school and am currently trying to conduct an exploration on Fourier Analysis, specifically using the Discrete Fourier Transform to analyze a chord played on my piano. Basically, ...
Ralph Khouri's user avatar
1 vote
0 answers
37 views

CFO Estimation in LoRa Chirp Signal (Preamble part)

I am trying to estimate CFO in LoRa chirp signal (preamble part). I have seen the discussion about CFO on this forum but it is mainly related to CFO estimation in OFDM. I want to estimate the CFO in a ...
Mogambo0001's user avatar
0 votes
1 answer
97 views

Why is the DC component of discrete fourier transform not the same as the signal's arithmetic mean?

In this question we have a mathematical proof that the DC component of normalized discrete Fourier transform should be the same as the signal's arithmetic mean. However, in the following example I ...
Cloudy's user avatar
  • 111
3 votes
1 answer
99 views

Why does multiplying a real signal by a random complex phase term result in "spreading" in the Fourier domain?

Suppose I have some real-valued signal $x\mapsto f(x)$. The amplitude of its Fourier transform $\mathcal{F}[f]$ then looks like a peak around the DC-term, decaying as we move towards higher ...
user2983473's user avatar
2 votes
1 answer
166 views

Fourier transform of $|x_\mathrm{a}(t)|^2$

Let $x_\mathrm{a}(t)$ be the analytic signal for real signal $x(t)$. I want to find an expression for $\mathscr{F}\{|x_\mathrm{a}(t)|^2\}(f)$ in terms of $x(t)$. The analytic signal can be written as $...
S.H.W's user avatar
  • 726
0 votes
1 answer
33 views

Why does applying Fourier Transform on point Spread Function yield h(t) which is complex-valued

I wanted to understand why this text talks about applying the Fourier transform on H(f) to obtain h(t). I view Fourier transform as moving from the time or spatial domain to the frequency / spatial ...
Hari's user avatar
  • 93

1
2
3 4 5
45