Questions tagged [fourier]
Anything related to Fourier series, Fourier transform and similar mathematical tools used to analyze the frequency content of a signal.
338 questions
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Uncertainty principles and signal recovery (Donoho and Stark)
I am trying to reconstruct a signal that has missing samples using the methods proved in the title paper. The paper is readily available (https://web.stanford.edu/dept/statistics/cgi-bin/donoho/wp-...
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Interpretation of Laplace Variable
Through my study of circuits and signal processing, it is my understanding that the complete response of an LTI system is the sum of a transient response and a steady-state response. When analyzing ...
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Rectangular wave to pure sine wave of fundamental frequency
This is a follow up of my previous question...
Lets say my input produces a square waveform. By playing with the Fourier series simulator of Falstad, I noticed that you only have odd harmonics, but ...
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How does half wave symmetry cancel out even harmonics?
Can someone simply prove the above statement. I am at a complete loss. I am told that even harmonics are not found in functions with half-wave symmetry. Yet, why do functions like cosine(2t) and ...
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Complex Fourier series coefficients of a perturbed switching waveform
I am trying to recreate the analysis from a paper published in 2008. I will try to provide a detailed understanding of what I was able to comprehend from the paper so that the readers don't need to go ...
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Parseval's Relation Fourier Transform Question
This is an example from Oppenheim's Signals and Systems book, the example continues but i couldn't understand how we found 5/8 for E as book suggests. I tried to apply the formula but i obtained a ...
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3
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Why do we need phasors for analysing signals and systems?
Phasor includes a real part as well as an imaginary part, in real domain the intuition is more clear, i.e we can use vectors instead to represent things, but to imagine a signal in a complex domain ...
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Input of RC low pass filter from the output
In general, for an RC low pass filter, the output signal is related to the input signal by
$$
Q_{out}(\omega) = H(\omega) Q_{in} (\omega),
$$
where the \$Q\$s are the Fourier transforms of the time ...
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How does DC converter switching cause broadband noise in this case?
As per Source1:
"a broadband disturbance is defined as an electromagnetic disturbance which has a bandwidth greater than that of a particular measuring apparatus, receiver or susceptible device.”
...
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MATLAB Fourier: Why do I see less harmonics the more I increase the sampling frequency?
I made MATLAB calculate the Fourier transform of these square wave pulses which have a frequency of 60Hz. I do not understand why, the more I increase the sampling frequency, the less visible the ...
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Why is \$e^{-j2\pi f ~t_0} \$ instead of \$e^{-j2\pi f ~(t - t_0)} \$ for time shifting in the Fourier transform?
In signal processing and the study of Fourier transforms, the time-shifting property is a fundamental concept. This property describes how a shift in the time domain of a signal affects its Fourier ...
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How do I calculate THD?
I want to calculate the total harmonic distortion of the signal using this graph and formula.
The formula is taken from this page: Calculating harmonic distortion
First Question: So my problem is to ...
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How to use Fourier analysis for a daily sound? [closed]
Consider I want to set up a device to record any sound near my resident. It will be, of course, record all sounds, including humans sound, birds, cats, dogs, cars, motors, building constructions, wind ...
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Fourier series complex to real
I have to find the Fourier series of this function in complex form and transfer it to real:
\$f:(-\pi;\pi]\to \mathbb{R},\;\;\;f(x)= \begin{cases} x & -\frac{\pi}{2} \leq x \leq \frac{\pi}{2} \\ 0 ...
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Fourier circuit analysis of a RLC circuit
I was trying to calculate output voltage across the inductor in the RLC circuit below. I had used the Fourier transform to convert input signal \$V_{i}(t)\$ which is a single rectangular wave pulse in ...
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FFT of a real sequence
I know there are many questions (almost the same as this one) on this forum and I am sure I have read most of them, however, I still cannot answer this question:
I use the RFFT function of ARM CMSIS (...
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FFT basic concepts
This is my first time studying the Fourier transform. I can't understand some basic and somewhat more "practical" concepts from the formulas .
EXAMPLE: I have a 1kHz sinewave with 1ms period....
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Discrete Fourier transform for musical analysis
I am a senior in highschool 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 I'...
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Equation for a Triangle wave shape, x(t) ,a0, an and bn
How do I write the function \$u(t)\$ for a given graph, and what steps should I follow to derive expressions like \$\frac{4U_M}{T}\$, \$2U_M - \frac{4U_M}{T}\$, or \$-4U_M + \frac{4U_M}{T}\$?
I have ...
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Can an entire signal with transients be reconstructed from an inverse Fourier transform?
If we have a long signal (say some music) that contains a lot of transients at different frequencies (i.e. the relative "volume" of each different frequency changes over time) and we take a ...
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Why does MATLAB show a pole in bode plot of an underdamped second order system at natural frequency?
I am using the sisotool in MATLAB to obtain the bode plot of the following transfer function:
MATLAB marks a pole at wo which is approximately 11.18
What is the meaning of this? How would you even ...
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Sketching fourier transform after sampling
I'm having trouble understanding how this system is supposed to work. My sketch (all my sketches are for fourier transforms) for \$X_b(jw)\$ are two pyramids centered at 7pi and -7pi with height 1/2. ...
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Why don't we use the third harmonic in power transmission?
For some high power high voltage lines DC is used with the advantage that sinus wave AC obviously doesn't use the line to it's maximum capacity at all times. To correct this, we could use square wave ...
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DC bus capacitance design for SPWM inverter
I am working on a 5kW grid-connected inverter where I need to find the DC bus capacitance value. I understand that the capacitor serves 2 purposes: 1) to provide a low impedance path for the high ...
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Frequency spectrum in PLECS for CM noise measurement
I am performing a simulation to measure the common mode noise in a buck converter. I have three models, an ideal buck, a non-ideal buck with parasitic capacitors, and a CM equivalent circuit to ...
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How to properly take the discrete Fourier transform of a signal as well as calculate the power spectral density of the DFT?
I'm getting conflicting answers on how to properly represent a DFT and normalize the results as well as calculate the normalized PSD of the time series. For background, I typically work with voltage ...
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How would you compute Fourier transform of a real world signal where the signal keeps getting updated (not a static one)?
A very naive question: How do we use Fourier transform for real world signals - for which you have the information only up to the present instant (and the present time keeps moving continuously)?
The ...
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Need help on signals and systems, Fourier representation of a signal
I've got a homework question for my signals and systems class.
In the question, we're given the graph of the magnitude and the phase of a continuous signal. Here are the graphs:
I have to find the ...
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Fourier Transform of Voltage Readings
I am working on developing a Fourier transform for voltage readings. The goal is to determine voltages at different frequencies (frequency domain). I am taking readings at 100Hz and am measuring both ...
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FFT analysis in LTSpice is giving wrong results during partial execution of time domain simulation (Details in body)
In LTspice, while computing FFT using waveform window (View-> FFT), the results seems to be wrong if FFT is computed after partial execution of simulation ( eg: if simulation is paused in between)...
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What is the structure and type of harmonics generated by a very differentiated square wave (i.e bipolar spikes)?
this question is in two parts.
Firstly, can you please tell me what the structure and amplitude distribution is of harmonics generated by a differentiated square wave of 50% duty cycle, where the time ...
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Calculating inverse fourier transform and graphing it
Recently I stumbled upon Fourier transforms which means I am very new to it. I've been given a question from my professor to find the inverse Fourier transform of a frequency spectrum which is given ...
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FSK Modulation in Python
I am currently writing a script that uses I/Q data to do FSK modulation.
My question is about the FFT plot. I expected to have a peak at 1Hz and 2Hz which are the frequencies that represent binary 0 ...
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A DFT-based phasor estimation
I have the sample set of ideal and real secondary current during CT saturation, need to apply the DFT analysis to samples and estimate the fundamental phasor (magnitude and phase angle) of samples (...
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Fourier series from the graph
I am trying to find the power spectral density, autocorrelation function, and power content of a periodic signal. In order to do this I need to find the Fourier series coefficients.
I am trying to ...
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Fourier transform plot
A continuous-time signal x with bandwidth \$\frac{20π}{3}\$ rad/sec is
sampled with sampling period \$T_s = 0.1\$ seconds to obtain a
discrete-time signal \$x_s[n] = x(nT_s)\$ for all n. The discrete-...
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Time period for analysing an instantaneous sound wave and then converting it to the frequency domain?
I am confused about how a signal is analysed in the frequency domain after being recorded in the time domain instantly.
Does the spectrum of frequencies that are displayed based on a previous period, ...
user306683
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Confusions regarding Laplace transform
We know that Laplace transform has two parts, \$\sigma \$ and \$ j\omega\$.
\$\sigma\$ is the real part
while \$ j\omega\$ is the imaginary part.
Is it okay to say that the term \$\sigma \$ is a ...
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Mathematical difference between FFT and STFT
Can a FFT be recreated by performing STFT on the smaller time intervals and then summing them up. My doubt is that FFT is a usually a amplitude vs frequency data and STFT has a x-axis in units of time....
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Transfer function of two frequency spectra
When you have two amplitude frequency spectra (fourier spectrum), in this case of a torque ripple, how do you define the transfer function (or the ratio) between both? How do you "divide" ...
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How does this modulation cause sidebands?
The following figure is an excerpt from this paper: Input Differential-Mode EMI of CRM BoostPFC Converter by Fei Yang.
Q#1 (first highlighted sentence): How does the modulation line frequency cause ...
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A half-wave rectified sinusoidal waveform has a peak voltage of 10V. What are its average value and the peak value of the fundamental component?
I know to to find average value: 10/pi
What does "peak value of fundamental component" mean?
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Signal Dimensions in Simulink
I'm using R2022a, in Simulink I can not find the Display tab to access Signals & Ports>Signal Dimensions. Could someone point me in the right direction please?. Also, in the figure below the ...
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Downconversion Intermodulation Frequencies - Where do they come from?
I recently came across this video which discusses the downconversion of a signal (referred to as IN) to an Intermediate Frequency (IF) using a Local Oscillator (LO). I'm assuming that all of these ...
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Confused about the similarities between Fourier Series and Fourier Transform
My understanding of Fourier Series was, it is a method that decomposes a periodic signal into sum of signal given by infinite number of sines and cosines. And in case of Fourier Transform it was, that ...
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Why does a cosine function have a non-infinite Fourier coefficient?
I took my signals class a long time ago and have gotten used to using Fourier tables for a lot of things. I'm reading a textbook on communications and I stared at the Fourier transform equation for a ...
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Why is this signal considered odd when v(t) is not equal to -v(-t)?
In the solution of a problem, that asked to find the Fourier Series of the waveform, shown below. The coefficient of cosine part an is taken taken 0, because it is ...
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Signals and systems - Find the inverse Fourier transform of a RLC circuit
I was analyzing the following RLC circuit:
And applying the Fourier transform on the circuit, I ended up with the following transfer function:
$$
H(\omega)=\frac{V_c(\omega)}{V_i(\omega)}=\frac{1}{1+...
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Why do we have two separate transforms for transforming a time domain signal to the frequency domain? [duplicate]
I know that Laplace transform and Fourier transform are not exactly equal; they will be equal when alpha = jω.
But according to my understanding, both transforms convert a time domain signal to the ...
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Why am I getting linear phase?
I'm trying to plot the phase of Fourier transform of the function below:
\begin{gather*}
x[n] = 2e^{-0.9|n|} \: \: n \in [-5,5]\\
x[n] = 0 \:\: n \notin [-5,5]
\end{gather*}
which is equal to the ...
