Questions tagged [fourier]

Anything related to Fourier series, Fourier transform and similar mathematical tools used to analyze the frequency content of a signal.

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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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1 answer
128 views

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....
0 votes
1 answer
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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" ...
3 votes
2 answers
310 views

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?
1 vote
1 answer
74 views

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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1 vote
1 answer
54 views

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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1 vote
2 answers
105 views

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 ...
2 votes
0 answers
66 views

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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0 votes
1 answer
111 views

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 ...
1 vote
3 answers
190 views

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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1 answer
109 views

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 ...
1 vote
0 answers
97 views

Numpy giving the wrong Fourier transform of sine functions

I'm using numpy's FFT to calculate the Fourier transform of \$\cos(\omega_0t)\$ and plot it. By using the definition we can derive its Fourier transform as below: \begin{equation} X_3(j\omega) = \pi (...
0 votes
1 answer
131 views

Phase of Fourier transform when it arrives at \$ \pi \$

I'm trying to calculate the phase of "rect" which is like below \begin{equation} f(x)=\begin{cases} 1 & \text{if }256<x<768,\\ 0 & \text{otherwise}. \end{cases} \...
2 votes
2 answers
139 views

Fourier transform and what it represents

Suppose we have a sine voltage supplied to a resistive load. When I perform a Fourier transform to this signal in the frequency domain what do I get? All values of g(a) will be 0 except for the ...
1 vote
0 answers
57 views

Frequency domain analysis when sampling a switched (gated) integrator

I would like to use AC analysis (e.g. in spice) on a non-ideal op-amp integrator where the reset switch is open, and then apply a shaping function to the result of the AC simulation (in the frequency ...
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0 votes
0 answers
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How to use DFT to find harmonic content of an AC waveform?

I am kind of new to this coding and simulation environment. For my first project I need to take samples of current signals from power line and find out the harmonic contents using DFT. I haven't done ...
2 votes
2 answers
149 views

Bandwidth of a signal

I have found that the convolution of two rect(f) functions (f=frequency) gives a triangular pulse of width 2 centred at 0 Hz. Can anyone tell me what the bandwidth of this pulse is? Is it F or 2F? My ...
0 votes
3 answers
104 views

.FOUR command doesn't give the required output

This netlist for a full wave rectifier was actually written for PSPICE. When I type the same netlist in LTSpiceXVII, the log file doesn't show the proper output. I have replaced ...
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1 answer
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Fourier Series - Double Check Work

I was solving this Fourier series problem from my book, but was not able to find a solution to it to double-check my work. This is the problem: My work: \$T=4+2=6 sec\$ \$C_{n}=(\frac{1}{T})(\int_{t_{...
2 votes
5 answers
2k views

Does the DC component of any signal also carry information?

Every signal carries some types of information in it. Mathematically we Know from Fourier series that these signals can be represented as a sum of its DC component and all the harmonics of fundamental ...
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10 votes
3 answers
2k views

Why is a signal that is finite in time domain, infinite in its frequency domain?

Why does every single band-limited signal in frequency have an infinite time domain and vice versa (As it's a symmetric relation, inf in one is finite in the other). I understand how a digital signal ...
0 votes
2 answers
130 views

Inverter Fourier analysis

I have an inverter circuit like below: I will use bipolar control method to produce sine wave. Our teacher said us prove basic harmonic of inverter is equal to multiplying of modulation index and Vd, ...
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1 answer
58 views

OFDM IDFT implementation

i have some doubts with the implementation of the IDFT in OFDM systems. The question concerns the expression of the IDFT of the OFDM signal. During the symbols period \$T_s\$ we have the following ...
3 votes
0 answers
52 views

Finite-duration signal in the time domain, means what exactly in the frequency domain?

I'm trying to understand exactly what restrictions a finite duration time domain signal has on its Fourier transform. I found a helpful table in The Fourier Transform and its Applications by Ronald ...
0 votes
0 answers
68 views

Circuit analysis problem involving Fourier series

Please help me with this problem I can not solve this. It is about Fourier series. It is so hard.
2 votes
2 answers
273 views

Amplitude Spectral Density from a Fast Fourier Transformation

I want to calculate the Noise-equivalent Power (NEP) of a photodetector. Hereto, I have to measure the Amplitude Spectral Density (ASD) of the detector and divide the result by the Responsivity: The ...
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2 votes
0 answers
245 views

Pulse Doppler radar system simulation using MATLAB

How to code this project in MATLAB I'd tried coding this project (prob. 3-2, third paragraph) in MATLAB through this tutorial : https://www.mathworks.com/help/phased/ug/doppler-shift-and-pulse-doppler-...
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2 votes
0 answers
73 views

Representation of Fourier transform

I have a problem interpreting 2 different representations of Fourier transform and proving their property. In some texts Fourier transform is represented as: $$ \begin{align*} x(t) = \frac{1}{2\pi} &...
0 votes
1 answer
102 views

How to calculate THD using only the first harmonic?

How can I calculate THD using only the first harmonic? How can I implement in C code DFT voltage formula in order to calculate THD?
0 votes
4 answers
126 views

how to calculate the fourier transform of this input?

I have been trying to find a relation between dominant frequency and the time period 'T'. The input is a digital ramp with an increase of 1mV per step. And each step has a time period 'T'. Will I get ...
0 votes
0 answers
37 views

how to define a relative bandwidth for the signal with the equation K/w^2

I have a straight line with a slope. Thus its fourier transform is K/w^2. I wanted to estimate its relative bandwidth(Wont it be dependent on the slope?[1st question]). If the answer for 1st question ...
0 votes
0 answers
30 views

Relationship between two differently sampled Fourier coefficients

Assume a periodic signal \$s(t)\$ with fundamental period \$T_0\$. If one were to use the period \$kT_0\$ to find the Fourier series coefficients, how would they be related to the standard Fourier ...
2 votes
5 answers
896 views

What are the applications of the Fourier transform in communications?

I have learned about the Fourier transform, but I do not have a deep understanding of it. I heard that it is used in radios, butI don't know how and why. Can anyone explain it in a very detailed ...
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1 answer
121 views

Differences between downsampling and upsampling

Explain why the amplitude of the Fourier transform of a sampled signal changes when downsampling, but not when upsampling.
1 vote
0 answers
67 views

Fourier transform of the electrical conductivity function

In this pdf https://studylib.net/doc/18704299/chapter-1 the author writes that the Fourier transform of the current density is: $$ \Delta j_{i}(\mathbf{k}, \omega) \equiv \frac{1}{(2 \pi)^{2}} \iiiint ...
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0 votes
1 answer
171 views

Explanation and Draw of Line Impedance Stabilization Network (LISN)

I am trying to learn about LISN circuits. As far as I see, there are standards for LISN. But the point is everybody is applying standards, I would like to know why these values are chosen or why there ...
1 vote
2 answers
81 views

The Fourier transform

The Fourier transform is just an operation on certain functions. When the functions are signals, why is it that the variable chosen (w) has to correspond to the frequency of the signal, when it is ...
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partially periodic function and fourier series representation

I am thinking about this for a while but I could not reach a conclusion. If I have a periodic signal let's say a square wave but it is only non-zero for t<100 and t>-100. the function is ...
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0 votes
1 answer
471 views

Converting PDM Data to analog

I have researched about PDM Data and I have seen this sentences on wikipedia: In section of Digital-to-analog conversion "The process of decoding a PDM signal into an analog one is simple: one ...
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1 vote
1 answer
380 views

RC filter impulse response is exponential decaying but inverse Fourier is Sinc function

As we all know that the inverse Fourier transform of a frequency domain unit pulse/rectangular function (which looks like low pass filter) is Sinc function. So, I was under the impression that any low ...
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0 answers
56 views

can fourier transform be used in circuit design?

If I formulize the input voltage that I am planning to give to a circuit and if I formulize relative output voltage that I expect to see with respect to input voltage, I can take their fourier ...
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1 vote
1 answer
91 views

Labview inverse Fourier transform: Why can't I visualize Gibb's effect (or ringing)?

I am studying electrical engineering and have an assignment which I have been working on for couple weeks, but can't solve. I have a discontinuous function as shown below and applied a FFT on it, ...
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2 votes
2 answers
439 views

How do causality and stability affect the response of a linear time-invariant system?

Suppose that there's a linear time-invariant system with the following transfer function: $$H(s) = \frac{1}{3(s-2)}-\frac{1}{3(s+1)}$$ If the system is causal and stable, I can determine \$h(t)\$ by ...
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0 votes
1 answer
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Phase-shift a Broadband Time-Domain Function

Suppose we have an operator \$A_\phi\$ which phase-shifts a sinusoid by \$\phi\$: $$A_\phi[\cos(\omega t)] = \cos(\omega t + \phi)$$ In phasor domain, \$A_\phi = e^{+j\phi}\$ is a complex constant. I ...
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2 answers
306 views

Electromagnetic radiation from spark gap

I am an electrical college student. I learned from some papers, sites online, including this forum that lightning discharge or any electrical arc emits wideband radio frequency because the odd integer ...
1 vote
2 answers
537 views

Bucketing FFT into one-third octave bands

I'm trying to understand how to take the results of an FFT calculation and bin them to one-third octave bands. As my questions aren't about the code but about fundamentally understanding the arguments ...
0 votes
1 answer
188 views

find current, voltage and power at each branch using fourier series analysis

Question: find current, voltage and power at each branch using fourier series analysis Update - here is my solution attempt:
1 vote
1 answer
133 views

Using FFT to calculate derivatives of polynomial

I know that there are several posts about FFT and derivatives, but I don't get it. I also tried in mathematics but no answer. The formula is: $$ f(t)→\hat{f}(ξ),f′(t)→2πiξ\hat{f}(ξ) $$ First, I don't ...
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