Questions tagged [fourier]

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Comparing custom Welch periodogram with Julia's Welch periodogram

I wrote my own PSD struct in Julia for practice purposes. It involves two type of constructors: a "direct" PSD and a <...
lafinur's user avatar
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Ignoring Negative Frequencies from FFT on Real Time Series Seems Inconsistent With Time Series

I ran an FFT on real financial monthly time series data. If I plot the FFT frequency domain output on the interval $[0, f_s)$, the dominant frequency pair peaks occur at $f_{A1}$ $\approx$ $0.02 \ ...
Data2Dollars's user avatar
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Binning and Frequency for FFT on Financial Time Series Data

I'm trying to analyze financial market time series data, so are there any particular concerns in using FFT for that kind of data? The data seems to be relatively covariance stationary. My sampling ...
Data2Dollars's user avatar
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Fourier transform processing of iq data

I want to perform fourier transform on the iq data that is taken from spectrum analyzer. The purpose is to estimate phase noise from iq data.
Komal's user avatar
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1 answer
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Minimum amount of data needed for low pass filter on real time sensor data

I need to apply a low pass filter up to a period of 10 hours to my data. My sensor has a sampling rate of 1 sample every 5 minutes. I need to know how much data I at least need to have to be allowed ...
TRM's user avatar
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Result of complex exponential fourier series approximation and trignometric fourier series approximation are not exactly same in MATLAB?

I have a signal and i am trying to observe its approximations using complex exponential fourier series and trignometric fourier series but i am not getting exactly same result(graph of trignometirc ...
Engr's user avatar
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1 answer
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what will be the DC component of this function? [closed]

My answer is that the signal can be splitted into 2 regions, and cancel out the negative and positive areas under the integral, based on the definition Needed some validation on this analysis Thanks.....
Wireshark's user avatar
2 votes
2 answers
108 views

What is the difference between the DFS (Discrete Fourier Series) and DTFS (Discrete-Time Fourier Series)

I'm looking at two different books written by Oppenheim. In Discrete-Time Signal Processing (source 1) he defines the DFS to be: where, $W_N=e^{-j(2\pi/N)kn}$ , while in Signals and Systems (source 2)...
eball's user avatar
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1 answer
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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
1 vote
2 answers
178 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
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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
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3 answers
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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
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1 answer
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Does upsampling require a low-pass filter?

I am currently wondering about the frequency spectrum when performing upsampling using linear interpolation. As far as I know, linear interpolation corresponds to a $\text{sinc}^2$ function. If I ...
hajo's user avatar
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13 votes
4 answers
2k 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
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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
2 votes
1 answer
93 views

What's the meaning of the amount of frequency 0 in the Fourier Transform?

In the Fourier series, I knew that the coefficient $a_0$ represents the DC value, shifting the signal up and down by the amount. Then, what's the actual meaning of the amount of frequency $0$ in the ...
Hao Wu's user avatar
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1 answer
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How can I plot a sinc function correctly?

I am generating a rectangular pulse using a piecewise function on Matlab. I have listened to some advice to use a normalization coefficient and the amplitude appears correct now. However, my issue is ...
Arcadius's user avatar
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How to adjust the length of the window of the Fourier transform with respect to the length of the signal in Python

I ran the following code in Python, setting the window length to 5s, but he reports an error as the window length does not match the signal length. How should I adjust it please? code: ...
BaiYueChu's user avatar
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Having problems with convolution in Fourier space

First attempt: I tried convolution in Fourier space. step: transform grayscale image ==> (real1,imag1) step: transform kernel (a simple box filter) ==> (real2, imag2) step: multiply (complex) ==...
Gianni's user avatar
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5 votes
2 answers
429 views

Integer multiples of fundamental period in sine wave

I have a simple question. Suppose I have a signal : $f(t)=\sin(2\pi \, 25t)$ We know that it's CTFT(continuous time fourier transform) will result in 2 delta's at +- $2\pi\,25$ [rad/sec]. Or ...
Sammy Apsel's user avatar
1 vote
1 answer
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Finding a discrete signal using some information about its Fourier coefficients

I'm struggling to solve the following question. I've solved it partially, but I can't get complete it. We have the given information about a signal of the form ...
Danialz's user avatar
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1 answer
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What is the symbol for angular frequency?

I am reading the book Signals and Systems Laboratory with Matlab Book by Alex Palamides and Anastasia Veloni I was going through chapter 6 (Fourier transform) and I came across a confusing thing ...
DSP_CS's user avatar
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1 vote
1 answer
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Removing zero frequency peak in fourier spectrum

I have been looking at the FFT (in python) of various simple functions. Everything was working as expected, except when I take the Fourier transform of the function: $$ f(t) = e^{-\gamma t}\cos^2\...
Angus's user avatar
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2 votes
1 answer
702 views

Real and imaginary parts of the Fourier transform of a pure cosine wave

My understanding of the Fourier transform is that the FT of a cosine wave should be non-zero in the real part and all zero in the imaginary part. This follows from the orthogonality of sine and cosine:...
Joseph's user avatar
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1 answer
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Representation of Sampling Frequency in the Fast Fourier transform

I have 21600 data in the time domain. What Sampling frequency should I use? can someone explain the effect of showing the result by selecting different sapling frequencies? Cheers
IMAN RAMZANPOOR's user avatar
3 votes
1 answer
154 views

How to get DFT spectral leakage from convolution theorem?

I have an issue, where my numerically calculated leakage from a DFT of a simple cosine does not match the theoretical prediction from the convolution theorem. I will try to present the example using ...
xaberus's user avatar
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pulsating current in the PWM amplifier vs. the RMS current of the fundamental sine wave after the filter

I want to know how calculate pulsating current on FET switches in a PWM class D amplifier versus RMS current of the fundamental sine wave after the filter. It depends on the positive and negative ...
German Correa's user avatar
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1 answer
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Can a large drop in the PSD indicate the presence of a periodic noise?

I was wondering if a large drop in the plot of the PSD of a sensor measurement could indicate the presence of a periodic noise. Here is my PSD: Thank you.
Fred vh's user avatar
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0 answers
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Discrete Fourier transform of a 2D exponential decay

The Discrete Fourier transform of a 1D discrete decay function $d[n]=e^{-a n}$ is simply computed as the sum of a geometric series: $$\tilde{d}[k] = \sum_{n=0}^{N-1}e^{-a n}e^{2 j \pi n k/N} = \frac{1-...
that_guy's user avatar
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Finding $A_k$ coefficients

I was able to demonstrate that for a signal $x(t)$ real, we can write the truncated Fourier series as: $x_N (t) = A_0 +\sum\limits_{k=1}^{N}A_k\cos(kω_0t + \varphi_k)$, but now I've been given the ...
Anna Smith's user avatar
2 votes
1 answer
105 views

For a real-world system of oscillating mechanical components, what kinds of frequencies should I seek in DFT?

I have a real world system I am analyzing consisting of actual mechanical components that oscillate by rotating back and forth in a fixed axle (kind of like those finger fidget spinners but my system ...
LobsterMan123's user avatar
1 vote
0 answers
59 views

Combining audio and image filters in matlab

I am trying to write audio and image filtering together code in my project. Purpose: The main aim of this project is to combine audio with image filters; like for example passing low frequencies of an ...
CompA's user avatar
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What happens if you use the Fourier transform of the autocorrelation of a non-WSS process to compute power spectral density?

The Wiener–Khinchin theorem states that the power spectral density of a wide-sense stationary stochastic process can be obtained through the Fourier transform of the autocorrelation of the signal i.e. ...
Tommy Wolfheart's user avatar
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2 answers
132 views

How can I use the FFT in MATLAB to get the time domain equation representation of an image? [duplicate]

My goal is to take any image and break it down to obtain its time-varying equations so it can be redrawn and store the picture as two equations. One for $x$ and one for $y$. As I understand, MATLAB's ...
ijustwannalearnrobot's user avatar
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2 answers
173 views

Proof that DFT is symmetric

I am working through the proof that the DFT is symmetric from Lyons - Understanding Digital Signal Processing I don't quite understand the use of the $N$ variable. My understanding is that in $X(N-m)$,...
Joseph's user avatar
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How to generate a sound closer to a saxophone using sinusoids after Fourier Transform?

Generate a sound wave of saxophone frequency and compare it to the original sound clip and play both to listen to if there is a good match. I am trying to generate a sound closer to a saxophone using ...
Adrian Surani's user avatar
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1 answer
194 views

Trying to find the Fourier Series Representation of a sum of Sinusoids

Given a signal: $$x(t) = -5\cos{(93.6\sqrt{2}\pi t - 2\pi/3)} + 3 \cos{(135.2\sqrt{2}\pi t + \pi/13)}$$ I am confused about the right process to take or if there is an easier way than following all ...
user64544's user avatar
0 votes
2 answers
120 views

Problem with transforming a tophat to obtain a sinc?

I have observed that the Fourier transform of a tophat function is a Sinc-like function with higher peak sidelobes than an actual Sinc. However, the Fourier transform of a Sinc is a tophat-like ...
visco's user avatar
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1 vote
3 answers
236 views

Sample Frequency does not matter if it is sufficiently large

I'm not able to convince a colleague on the following topic. Statement: If, and only if, the sample frequency is sufficiently large and above the Nyquist frequency it does not matter what fs is as ...
pimovietc's user avatar
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1 answer
37 views

perform fourier-type integration using DFT misunderstanding

I need to perform the following integral ($i^2 = -1$) (with a fixed value of $m$): $ \int_{\phi=0}^{\phi=2\pi} \psi(\phi) e^{-im \phi} \hspace{0.7mm} d\phi $ for all values of $m$ in $\{-N_{\theta}, -...
velenos14's user avatar
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1 vote
1 answer
157 views

sampled FT of Continuous time LTI output

I am trying to compute the sampled Fourier Transform of a Continuous Time LTI system output. $x(t)$ is the input of LTI and $h(t)$ is the impulse res. $y(t)$ is the output. we know that $$ y(t) = \...
jeff yan's user avatar
1 vote
0 answers
195 views

Fourier transform of a top-hat function in the Faraday Measurement synthesis context

I'm currently trying to calculate the Fourier transform of a top-hat function in the context of Faraday Measurement Synthesis. This is pretty straightforward, however, I cannot understand why I cannot ...
Miguel Cárcamo's user avatar
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How to calculate DFT of signal which occurs from 3 to 8?

How can I calculate discrete fourier transform of this signal? I'm confused as in the normal cases signal always start from 0 to N-1 but in this case it starts from 3 to 8 instead. So what would be ...
hana's user avatar
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1 answer
280 views

Given the Fourier Transform of a continuous signal how can I sketch the sampled signals discrete time fourier transform

I am given the frequency response for a continuous time signal $X(j\omega)$ = 2 at $\omega=0$ and 0 at $\omega = -10000\pi$ and $10000 \pi$. Looks like a triangle. I am told to sketch $X(e^{jw})$ ...
Caleb Burke's user avatar
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What can I do to improve the sound of a signal?

I want to improve the sound of my signal, I know I can do it by increasing or decreasing the amplitude of the signal itself. Are there any other ways to do this? How can I apply the Fourier transform ...
Luca Leone's user avatar
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1 answer
192 views

What's the difference between male and female voice? [duplicate]

If I record the voice of a man and a woman, what are the main differences I get in the various spectra and harmonics in Fourier analysis?
Luca Leone's user avatar
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43 views

What happens if I register my entry?

Taking as an example that I want to record my voice. How does it appear in the frequency spectrum? Can I also view it on other spectra?
Luca Leone's user avatar
1 vote
1 answer
231 views

Computing the frequency response using fourier transform of an unstable LCCDE system

Given LCCDE system. Is it possible to calculate the frequency response using Fourier transform?
Ibrahim Ali's user avatar
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1 answer
77 views

Continuous Inverse Fourier Transform [closed]

How to find inverse Fourier transform of: $ X(j\omega) = \frac{cos(3\omega) \cdot cos(\omega)}{\omega^2} $ The answer to this question is: $ x(t) = \frac{1}{2} y(t + 1) + \frac{1}{2} y(t - 1) $ where $...
0jas's user avatar
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0 answers
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Fourier Transform: $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$

I'm currently studying Fourier Transforms and do not understand the Fourier Transform of $x(t)=2\sin(2\omega_0t)\cos(3\omega_0t)$ My solution states that it is $X(\omega)=\frac{2}{2\pi}(-j\pi[\delta_0(...
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