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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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 ...
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298 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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44 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.
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42 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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42 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 ...
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2answers
57 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 just ...
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28 views

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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1answer
45 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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1answer
97 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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43 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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28 views

Circuit analysis using fourier series equations

I need to find the current and voltage at each of the brach and also power at one of the branch but I am stuck on how to solve this question with the non-sinusoidal voltage source. And how to ...
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1answer
39 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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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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52 views

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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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 ...
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1answer
92 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:
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1answer
85 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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12 views

Integration of PSD (Doppler Spectrum)

The expression for received signal PSD corresponding to a simple cosine wave (frequency fC) being transmitted is given as: \begin{equation} S_r(f) = \mathcal{F}[A_r(\tau)]=\begin{cases} \frac{...
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1answer
58 views

Fourier Transform Time Scaling Property using f (frequency) or w (omega - angular frequency)

The time scaling property for a fourier transform is as follows: My book shows this property in terms of \$f\$; however, my instructor likes to use \$\omega\$. I have also seen this property written ...
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1answer
61 views

Power and Energy Computations in the Frequency Domain

How do you calculate the power and energy of a signal given only the frequency domain form of the signal function? For the purposes of this question, please do not assume that it is possible to find a ...
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What is the physical meaning of reactive power in non-sinusoidal steady-state (with harmonics)?

In sinusoidal steady-state (linear loads, no harmonics), I understand what is reactive power \$Q = V_{\text{rms}} I_{\text{rms}} \sin{(\theta)}\$ where \$\theta = \theta_v - \theta_i\$: its absolute ...
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1answer
30 views

Equation for square law circuit modulator

For DSBFC AM (double side band full carrier amplitude modulation ) the message signal m(t) must be multiplied by carrier maybe $$ Ac*cos(\omega_c(t)) $$ (For modulation) This modulation is done in ...
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146 views

Why is there a low pass filter in a DSBSC demodulator?

In analog communication, DSBSC (double side band suppressed carrier) is way of modulating signal. In this the carrier is simply multiplied with the message signal. At the demodulator, the carrier is ...
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Why do sampled signals repeat in the frequency domain?

I do understand it mathematically, that multiplying a signal with a Kronecker(T) is the same as convolving it with Kronecker(1/T) in the frequency domain, and that makes sense. But is there an ...
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1answer
60 views

If interharmonics are defined for periodic signals, aren't interharmonics misleading?

Before explaining my question, I'm going to assume that 1) interharmonics, just like harmonics, are sinusoids; and 2) to analytically represent the interharmonics of a signal, we sum them to the ...
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44 views

Absolute values of fourier transform of noise-charged RLC circuit

I am doing time-domain simulations of currents in a parallel RLC circuit charged by thermal noise. In detail in pseudo-code: ...
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2answers
133 views

When a signal has an interharmonic, is the signal periodic or non-periodic?

I have some questions regarding interharmonics. What I'm going to do is first ask just a few, and then as people answer them I would expand this post or create a new question. Harmonics are sinusoids ...
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1answer
39 views

How to isolate coefficiets from complex fourier series?

I have to find yn/xn ratio. From the circuit analysis i found out transfer function Uout//Uin = . I am having hard time trying to isolate two coefficients of two complex fourier Series. Any help is ...
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2answers
38 views

Validity of superposition when summing powers from each harmonic

In Boylestad's Introductory Circuit Analysis 13th edition page 1176, there's an example about working out the total power dissipated by a circuit fed a nonsinusoidal signal. The signal is decomposed ...
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3answers
42 views

Why do we use a wide-band amplification in order to reproduce a sharp pulse without distortion?

I was reading some content with regards to the Fourier Transform and the uncertainty principle. In the book I was reading that Due to the uncertainty principle, in electronics we use a wide-band ...
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3answers
108 views

Generation of triangular wave from passive networks

I wanted to generate a triangular wave from a pure sine wave using only passive networks (RLC circuit only.) I wanted to realize such a network and at first I thought maybe the Fourier transform (of ...
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257 views

Low Pass Filter to Isolate DC component

I have a question based on low pass filtering. If I input a signal to this low pass filter, why does the output file have an AC (of very low frequency). The input signal is$$ v_i(t) = 2 + sin(2*pi*...
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1answer
61 views

RC circuit not ideal sampling

I have this circuit and I have to find \$x(t)\$, starting from \$ x_c (t) \$ I know that, at \$t=0\$, the switch is closed, so the capacitor is charged and, at the moment \$ x(n)T_c \$ the switch is ...
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105 views

Importance of Sine Waves And Maxwell's Equations

Sine waves, by a huge margin, are the most important waveform in electronics - we measure a circuit's frequency response with sine waves and represent all other signals through sine waves, with the ...
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227 views

Are there ICs that allow extracting a selected frequency component from a signal? [closed]

In many applications, what you need is just extracting one frequency from a signal (that is, to know its amplitude). I was dreaming about an IC that allows selecting a frequency of interest, perhaps ...
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1answer
113 views

Inverse Fourier transform of a shifted cos

I am preparing for an exam. I found this signal I want to inverse transform using the Fourier transform: The problem is that when I try using the general formula for inverse Fourier transform I get ...
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1answer
74 views

Fourier transform of an integral

I am preparing for an exam. I found this problem : I am trying to use the properties then use a pre-transformed function from the table but I couldn't find one. I saw a solution on web : I think he ...
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17 views

Difference Amplifier to retrieve sine wave

I have built the following summing amplifier circuit from a Fourier approximation of x(t)= 0.143 + 4/π ∑((sin⁡(2π(2k-1)ft)/(2k-1)). I am now trying to retrieve a sine wave from the output of the ...
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2answers
56 views

Fast method to calc th Fourier transform

exist a fast method to calc the Fourier trasform (in both sense, t -> f and f->t)? When I use the table and the properties of the Fourier transform, sometime I have difficult to calc this... Any help ...
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1answer
48 views

I need help with Fourier Series

I am having problems analyzing this sketch of a continuous Fourier series as it can't find a single known function
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1answer
95 views

plotting dirac delta function using inverse Fourier transform

I was trying to plot shifted dirac delta function in Matlab. $$\begin{align}\mathscr{F}\left(\delta(t-t_0)\right)&=\mathcal{F}(\omega)=e^{-j\omega t_0} \\ e^{-j\omega t_0}&=\cos\omega t_0-j\...
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Interpreting Fourier transform of Images

I'm new to image processing and am learning about the Fourier transform. I've read that FT decomposes a function to its constituent frequencies. However, I'm not sure how to tell which is a low ...
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1answer
117 views

Relationship between harmonic's amplitude and square wave's Tr and Pw

I started reading this TI guide on high speed layout guidelines and had some question on the theory of clock signals (pages 2 and 3). From the image below it's clear that the amplitude of the first ...
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1answer
83 views

Why opamps honor fourier series but not other series, for exmaple, power series?

A periodic function can be represented as an infinite sum in many bases. I know at least one other series apart from fourier: Power series: \$\sin(t) = \sum\limits_{k=0}^{\infty} \frac{(-1)^kt^{...
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3answers
115 views

Aperiod vs Period waveform Fourier Transform: How does nature understand which is the case?

Today I reviewed the theory behind the Fourier Transform, and I asked myself a question that I couldn't answer to in the process. Theory: A periodic waveform has a Fourier series which can be seen ...
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137 views

How to find the Fourier series of an output given input and transfer function

I have an input rectangle pulse, \$f(t) = rect(t/\tau) \$ and a transmission line whose transfer function depends on frequency. The transfer function of the t.l. is the transmitted wave divided by the ...
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Raspberry Pi and FFT (Fast Fourier Transform) — Using MCP3208

EDIT: I've made adjustments based on your answers, while I couldn't get it to be evenly spaced, I managed to get a better curve with more samples per cycle. Turns out I need to remove the print ...
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3answers
73 views

Fourier Series Concept

Hello, I am learning about the Fourier Transform, and I can do the math, but I'm having trouble with the fundamental concepts. From my understanding, the Fourier transform allows us to see the ...
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2answers
39 views

Instantaneous and active power in an ideal switch powered by real source and squared wave

This is a somewhat theoretical question, but one that has some impact on power theory. The circuit in the figure is composed of a real DC source (with non-negligible internal resistance) and feeds a ...
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1answer
78 views

What is the type and frequency of x(t)

This is a Fourier waveform question that I am struggling with. $$x(t) = \frac{8}{\pi}\left(\sin(8000\pi t)+ \frac{1}{3}\sin(24000\pi t) + \frac{1}{5}\sin(40000\pi t) + \frac{1}{7}\sin(56000\pi t) + \...

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