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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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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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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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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46 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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35 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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1answer
108 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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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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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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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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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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70 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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58 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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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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222 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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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
71 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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15 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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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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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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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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73 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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81 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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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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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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How do I get specific values that caused peaks in a Fast Fourier Transformation?

I want to detect peaks from a periodic signal with a Fourier transformation. A simple example looks as follows. This signal in picture 1 is an array with the values 10 and 0: [ 0, 0, 10, 0, 0, 0, ...
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71 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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38 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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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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Frequency Domain Analysis with Transistors

I have some doubts about how some circuits with transistors are described in electronics textbooks. Let's see an example (taken from Thomas H.Lee, The Design of CMOS Radio-Frequency Circuits). This ...
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88 views

How can I calculate the amplitudes of this signal's harmonics?

How can I calculate the amplitude's of the harmonics? This signal is the voltage of a capacitor bank. There is a few amperes of current on the capacitors in form of PWM. On the signal the 200mV Jumps ...
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329 views

Why convolution in time domain is multiplication in frequency domain? [closed]

I am trying to understand intuitively why convolution is multiplication in frequency domain. I started at the mathematical derivation of this, but didn't understand what is happening intuitively. This ...
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43 views

Software to detect certain sounds?

I’m trying to incorporate into an arduino, some programme to light up an LED when it hears certain sounds. Basically Shazam. This app uses the fourier transform to break down songs into frequencies ...
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Parabolic wave equation, electric and magnetic field definitions

The split step solution for Parabolic Wave Equation (PWE) applied to the tropospheric propagation problem is: $$u(x+\Delta x, z)=e^{ikM(z)10^{-6}\Delta x}\mathfrak{F}^{-1}[e^{\frac{-ip^2\Delta x}{2k}}...
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47 views

Electric Power in Frequency Domain

Let's consider an impedance Z inside a certain circuit. Let's suppose that we are working with a generic non periodic signal (so it is possible to analyze the circuit with the Fourier Transform). How ...
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113 views

Voltage Measurement through Spectrum Analyzer

I have done some measurements with a Spectrum Analyzer of a square wave of 100kHz and amplitude equal to 1V. The resulting power spectral density is here shown: The highest peaks represent the odd ...
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1answer
53 views

Fourier Series of Convolution of Periodic and and Aperiodic Signals?

The impulse response of an LTI system is aperiodic and I pass in a periodic signal. Now I need to find the Fourier series representation of the output. Since Convolution in time domain is ...
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61 views

Fourier Coefficients

I have no idea how to solve the following exercise, can you help me, please? Find the periodic function whose Fourier coefficients are $$C_{k} = \frac{sin^{2}(\pi k T)}{(\pi k T)^{2}}$$ I think ...
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Apparent lack of rigor in Phasor domain analysis of steady state AC circuits

so I have encountered a hitch in my understanding of analyzing steady state AC circuits. I have looked everywhere for the answer to my question and I can find nothing. Usually when we analyze ss AC ...
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1answer
80 views

Finding a Fourier series of a Burst Fired sine wave having consecutive 2 cycles on & 2 cycles off?

I have been trying to find the solution of the following problem but with no luck. I have a system that generates a waveform of sinusoidal type with the only difference being that this wave has 2 ...
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203 views

Vanishing of Gibbs Phenomenon in MatLab

I was trying to represent a square wave with its Fourier series in Matlab. But as I increased the number of terms in Fourier series expression, the Gibbs phenomenon vanished and the edges of the ...
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How to determine the transient response of a circuit to causal periodic inputs?

As you know, analyzing a circuit with phasors provides only the steady-state response, and is only useful for sinusoidal signals and DC signals. Fourier series allow us to analyse a circuit with ...
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87 views

If I look at a signal in its frequency domain, are there some guidelines by which I can tell how that signal looks in the time domain?

I was studying the Laplace transform and the Fourier transform, and I can't figure out if there is some intuitive way of finding out how a signal looks in the time domain if we know its frequency ...
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55 views

Spectral lines vs Envelope of PWM wave

On the wiki page of 'Duty Cycle' there is a nice animation that shows the frequency spectrum of PWM wave as its duty cycle is modulated from 0 to 100%. The animation shows the 'spectral lines' as ...
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Find the exponential Fourier coefficients

I am confused as to what the periodic function, Vin, is! I know the slope is 2/pi, but what about the vertical line? I am also unsure about its relation to Vo.
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Phase, Frequency and Laplace transform

I have a doubt on the relationship between phase and frequency. We know that the definition of angular frequency is: ω(t) = d(\$phi\$(t) / dt, where \$phi\$(t) is the istantaneous phase of our ...
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201 views

Filtering a Square Wave into a Sine Wave

I am trying to Filter a +-4V odd inverted square wave into a sine wave. How should I go about doing so? So far I have computed the Fourier series of my particular input signal to be: Which I ...
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66 views

Real time spectrum analyzer and Fourier Transform

I am studying spectrum analyzers and a doubt came to me about real time spectrum analyzers. Suppose you have a signal in the time domain: in order to calculate the Fourier Transform, you need to know ...

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