Electrical Engineering Stack Exchange
Electrical Engineering Stack Exchange

Questions tagged [fourier]

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

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

Fourier series and transform are named after French mathematician Jean Baptiste J. Fourier (1768-1830), who gave great contributions to trigonometric series theory while he was studying heat transfer in solid bodies.

See also Wikipedia on Fourier series and Fourier transform.

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Would a triangle wave have finite or infinite sinusoidal components?

A discontinuity causes a signal to have infinite sinusoidal components, but a triangle wave is continuous, I was taking a class in which an instructor said that since the triangle wave is continuous it can be represented by a finite number of sine…
Syed Mohammad Asjad
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Scaling FFT output by number of points in FFT

When computing the N-point FFT of some signal, the result is always divided by N. I can understand why this is the case for a summation over the N points, but often the result of the FFT operation is a vector of length N rather than a summation. Why…
john
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Fourier Transform and the Delta Function

The Fourier transform of cosine is a pair of delta functions. The magnitude of both delta functions have infinite amplitude and infinitesimal width. What I thought this meant: The cosine function can be constructed by the sum of two signals of…
Chris-Al
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RL voltage across inductor differential equation

I have a simple RL circuit such as the one shown below and I want to derive the differential equation relating the input and output voltages. I want to take the output voltage as the one across the inductor. So far I have done the following but I'm…
milongo
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plotting dirac delta function using inverse Fourier transform

I was trying to plot shifted dirac delta function in Matlab. $$\begin{align}\mathscr{F}\left(\delta(t-t_0)\right)&=\mathcal{F}(\omega)=e^{-j\omega t_0} \\ e^{-j\omega t_0}&=\cos\omega t_0-j\sin\omega t_0\end{align}$$ Using Trigonometric form of…
PG1995
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DC level in Fourier series

From this answer: The Fourier series: \$ V_t = \dfrac{a_0}{2} + \displaystyle \sum_{i=1}^{\infty}[a_i sin(i \omega_0 t) + b_i cos(i \omega_0 t) ] \$ Why is the DC level written as \$\dfrac{a_0}{2}\$, and not \$a_0\$? stevenvh says it's…
Federico Russo
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Why are these Fourier transform values not as expected?

We are being taught Fourier Transform in our EE course this semester and I have several questions about it. The answers do not need to be rigorous and mathematical, all I need is an intuitive 'feel' of the Fourier Transform. I may be completely…
lakshayg
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How to apply the Fourier Transform to this?

I have the equation \$5\cos(t)e^{-3t}u(t)\$ and the Fourier Transform of it is $$\frac{5(3+j\omega)}{(3+j\omega)^2 + 1}$$ I can't figure out how to arrive at this answer. Using the FT pairs table, I have…
Ryan McClure
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Why are functions for the frequency domain expressed in terms of a whole complex number rather than just omega?

I don't understand why some formulas used in electrical engineering, especially why using fourier analysis, include static numbers in function inputs, rather than just the changing variable. For example, the formula for the Fourier Transform of…
Peter Moran
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Is probability theory useful in electrical engineering

I have a few days off after finishing this semester and I am hoping to study something. Ideally, I would like to be able to benefit from it in any upcoming courses I might take. I'm thinking of either Fourier Series or Probability Theory. Currently…
Mustafa
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Fourier Series Expansion of Periodic Signal

Why is it necessary for a periodic signal to be a power signal for its fourier series expansion to exist?
user36685
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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. With my microcontroller, in that 1ms period I sample the…
KaleM
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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 a variable?
Pranav
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Average of Fourier Transforms

I'm working on some acceleration data, looking at vibrations and at what frequencies they're occuring. The recorded periods are fairly long (~1 minute) and I was wondering, what's the difference was between doing a FFT on the whole 1 minute data set…
BeB00
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Fourier series and Fourier transform of signals which can be generated in real world

Let first remind on Dirichlet conditions: In mathematics, the Dirichlet conditions are sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at each point where f is continuous. Moreover, the…
etf
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