|WikiProject Statistics||(Rated Start-class, High-importance)|
|WikiProject Mathematics||(Rated Start-class, Low-importance)|
"Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency."
=> The Frequency Domain is used to understand the frequency content of mathematical functions and measured data.
Momentum space also redirects here, but there isn't any discussion of it. Fresheneesz 23:37, 30 April 2006 (UTC)
Yeah, why is that? It dosn't seem to make any sense when comming from [Wavefunction] What the hell does the frequency domain have to do with momentum space? Chad Okere
- Momentum space is the Fourier transform of the wavefunction in position space. It's an analogous relationship to time and frequency, but if it's not discussed here it shouldn't be linked here. Dicklyon 05:14, 19 June 2006 (UTC)
Momentum space is more of a physics concept used to explain Fermi energy levels, which uses wave function vectors that can also be called reciprocal lattice vectors in condensed matter physics. However I wish either separate articles are made for each of these definitions or that it be addressed that they are all basically the same concept.--Waxsin (talk) 03:06, 6 December 2007 (UTC)
Would be nice to see some graphs of examples of frequency and time domain functions. For example, a graph of a sound in each space. --jivy 18:53, 8 June 2006 (UTC)
"An example is the Fourier transform, which decomposes a function into the sum of a (potentially infinite) number of sine wave frequency components." this seems wrong to me, the fourier transform turns a signal in the time domain into its equivalent in the frequency domain. op seems to be talking about a fourier series which is completely different. only a 1st year undergrad though so might well be utterly wrong. —Preceding unsigned comment added by 126.96.36.199 (talk) 23:06, 26 February 2009 (UTC)
Wanted: Frequency Domains for Dummies
What follows is something of a cry for help, but I think it may also suggest how some Wiki pages might be made clearer - including this one. That's my excuse, and I'm sticking with it. :-)
I have been on a quest that took me to Wiki pages about transfer functions, the Laplace transform, filters, and audio crossovers. The object of the exercise was to write software to model loudspeaker systems. I finally got 'er done, up to a point, but there is one thing that is bugging me, and it has to do with the (frequency) domain of a transfer function, which is typically the ratio of two Laplace transforms.
It is clear that the domain of a transfer function includes pure imaginary numbers j*ω, where ω is a frequency expressed in radians per unit-time (seconds). It is also clear that the range of a transfer function consists of complex numbers whose modulus (aka absolute value, aka L2 norm) represents amplitude or gain, and whose argument (aka angle) represents phase. What is not at all clear to me is whether the domain also includes numbers that are not pure imaginary, and if so what they represent. Everywhere I go I see the formula σ + j*ω, without explanation. It seemed to me that σ represents phase-shift in the domain. I expected that when I used a complex number σ + j*ω with a non-zero σ as input to a transfer function, the amplitude output would be unchanged and the phase output would differ from the output for j*ω by σ. Not the case. If I make σ much different from 0, I get nonsense results.
So my question, which I think this Wiki page should clarify, is what specifically is the domain of a transfer function? Does it include only numbers of the form j*ω? If it includes numbers of the form σ + j*ω for non-zero σ, what do the those inputs and associated outputs represent?
[I posted essentially the same question on the talk page for "transfer function."]
- Yes, the whole complex space is the domain of Laplace transforms; the pure imaginary line reduces it to just Fourier transforms, which may be enough for you. The sigma represents the rate of growth or decay of the complex exponential (generalized sinusoid) exp(st). I have a draft book chapter that explains all this stuff better, imho; send me an email if you'd like to review it. Dicklyon (talk) 17:44, 17 December 2010 (UTC)
The disambiguation page Spectral analysis gives one meaning as:
Spectral density estimation, in statistics and signal processing, an algorithm that estimates the strength of different frequency components (the power spectrum) of a time-domain signal. This may also be called frequency domain analysis
If these indeed are just two different names for the same thing (or if frequency domain analysis can be adequately covered in the frequency domain article) the articles should be merged. Currently they aren't even cross-linked well; that's an alternative solution. -- Beland (talk) 22:17, 18 August 2012 (UTC)
- They are closely related concepts, but the frequency domain is useful for more than "analysis". Like for synthesis. The Spectral analysis disambig page link to various ways to get into the frequency domain. Dicklyon (talk) 00:00, 19 August 2012 (UTC)
- Spectral density estimation ~ frequency domain analysis
- Spectral density ~ frequency domain
Frequency Sub-domain Characteristics
Given that 99% of humanity does not have a degree, I would like to see a (low education) inclusion or reference to the characteristics or applications for various (all?) frequencies (DC to light) in various energy forms or media (acoustics, emf, population, behavior, history, physics, etc.). It might be possible to include some essay into the nature of wave forms (pulse, ICW, sign-waves, etc.) in practical behavior, technology, geology, physics, etc., but frequency is an important and pervasive influence on every reader, without an outline of that influence.
Frequency list (initial): 0: life of universe; 100 million years: climate oscillations; 10 million years: Earth's magnetic oscillations; ... 20 years: human generations; yearly: Earth's orbit around Sol; monthly: Moon's orbit around Earth; ... 3 Hertz: human blinks, ELF Submarine radio, ; 1-100 Hz: Human brain waves; 60/sec: earthquakes ; 50-400 Hz: commercial electric power transmission (Usu. 60 Hz); 15 Hz-20 Kz: human hearing; 0.5 Hz-300 Kz: animal hearing; 10 kHz (10 microseconds): Loran; ... 1 MHz: computer clock rate(appx); ...
I realize that pedagogically, this is a multi-dimensional challenge, and might not easily fit here (Frequency domain) without a great deal of cross-referencing. It would also be a backbone (link all above refs) for exploration of many other fields.