Tag Info

New answers tagged

1

In general, no you cannot. If you're told that the three source signals are all sinusoidal (for example), then Fourier analysis will give you the answer. But if, e.g., the three source signals are each a combination of various waveforms such as sawtooth or square, then there's no way to separate them unambiguously. I would like to warn you that there's no ...


1

What is color? Color has two possibilities. It is what our eye retina perceives as red, blue, yellow ... and its study belongs to biology. For example mixing blue paint and yellow paint gives the green color identified by our retina. In the rainbow each frequency is displayed according to the strength coming from the white light source, and our retina ...


5

Consider a single value of $m$. The Fourier series for just that $m$ gives $$a_m \cos(2\pi m t / T) + b_m \sin(2\pi m t / T) \, .$$ This can be rewritten as $$M_m \cos (2\pi m t / T + \phi_m)$$ where $$M_m = \sqrt{a_m^2 + b_m^2} \qquad \text{and} \qquad \phi_m = \tan^{-1}(-b_m/a_m) \, .$$ So, you can see that $a_m$ and $b_m$ are just the cartesian coordinate ...


2

I assume from your question, you are concerned with the Fourier transform of a scalar function of time (no space dependence): $$\tilde f(\omega) = \int_{-\infty}^\infty dt\, e^{-i\omega t} f(t)$$ With the inverse: $$f(t) = \frac{1}{2\pi} \int_{\infty}^\infty d\omega\, e^{i\omega t} \tilde f(\omega).$$ This symmetry is due to the fact, that your signal is ...


0

Expanding on the answer by @AndreaDiBiagio about the use of Fourier transforms to solve differential equations, specific applications I encounter occur in simulations of fluid dynamics, magneto-fluid dynamics (MFD), and plasma physics. Specifically, I have used Fast Fourier Transforms (FFTs) to significantly speed up the solution of a poisson problem for ...


0

By Fourier transforming a signal you indeed obtain frequency magnitude and phase information, and that can be very useful in a analysing experimental results. Another, related, extremely useful application of the Fourier Transform is in terms of solving differential equations. It turns out that many systems can be analysed pretty with differential equations ...


0

The Fourier Transform has many applications and you can find it in many places of maths and physics. I will show a pair of well-know examples; in Quantum Mechanics, the position space and the momentum space are linked by a Fourier Transform: $$\Psi(\vec{r},t)=\frac{1}{(2\pi \hbar)^{3/2}}\int_{\mathbb{R}^3} ...


0

However interesting, your question is probably too broad. When it comes to perception (so not just simple objective values), this topic is actually not perfectly understood in general. Always remember, that perception of any parameter of the sound is nonlinear and dependent on other parameters (e.g. you need to consider a pitch of the tone, when you ...



Top 50 recent answers are included