EM superposition [complete image synthesis?]

[C. Dopplebock]

Readers, please bare with me as I attempt to explain the reasoning of my question. Any help will be greatly appreciated.

Suppose I turn on my radio. And suppose one of my favorite songs happens to be playing, and that song happens to include the tried and true guitar, bass and drum trio. My understanding of Fourier analysis tells me that I should be able to mathematically 'separate' these instruments from the whole (the complex wave) and, furthermore, be able to break these singled-out instruments into even simpler pure tones. Likewise, with the proper parameters I should be able to recreate the entire song on the pure-tone level. All this keeping in mind that sound is linear as perceived by humans (assuming that one ear is covered) due to the mechanizations of the inner ear.

Now, as I type this, I am viewing a scene processed two dimensionally [when I close one eye]. Are the monitor, books, pencils, and other objects analogous to the instruments of the song from the radio? Could I pull these objects out, and break them down even further into a series of simple waveforms? Is it possible to *synthesize* a scene with a series of simple waveforms? The concept of the 'pinhole' camera suggests so. Where the light converges to a single point suggests that at that point an entire scene can be expressed as a single complicated wave [or a fraction of]. What type of equipment could generate these waves; say for transmission through optical fibers [the 'pinhole']?

Is any of this even possible?

 

[Tyger]

You can have Fourier transforms

in any number of dimensions. You could use such a transform to represent any part of a two dimesional image, but the problem is separating the image of a pencil from the image of a piece of paper. Even the one dimensional problem of separating tones is not as simple as you think it is. The one dimensional transform changes from a time representation to a frequency one, but our ears and brain don't really do a Fourier transform, they do one that is in between, some time and some frequency, so to speak.

 

[ravenprp]

Your question is a very interesting one and it brings up some important concepts in physics and signal processing. EM superposition, also known as the superposition principle, states that when multiple electromagnetic waves are present in the same medium, the total electric and magnetic fields at a given point are equal to the sum of the individual fields produced by each wave. This principle is essential in understanding how waves interact and how we can manipulate them for various applications.

In terms of complete image synthesis, the idea of breaking down complex waves into simpler pure tones and recreating the entire image is not a new concept. In fact, this is the basis of Fourier analysis, which is used in various fields such as image processing, audio engineering, and telecommunications. By breaking down a complex image into its individual components, we can manipulate and reconstruct it using simple waveforms.

However, it is important to note that this process is not as straightforward as it may seem. In the case of sound, our ears can only perceive a limited range of frequencies, so it is possible to break down a song into simple tones that we can hear. But in the case of light, our eyes are sensitive to a much wider range of frequencies, and it is not possible to break down an image into simple waveforms that we can see. Additionally, the concept of a "pinhole" camera is limited to a 2D representation of an image, whereas our eyes perceive a 3D world.

As for the possibility of synthesizing a scene with simple waveforms, it is theoretically possible but would require extremely complex and advanced equipment. The pinhole camera concept is a simplified representation of how light can be focused and manipulated, but in reality, it would require a combination of lenses, mirrors, and other components to accurately reproduce an image using simple waveforms. This is not currently practical or feasible with our current technology.

In conclusion, while the idea of breaking down complex waves and reconstructing them using simple waveforms is possible in theory, it is not as straightforward or practical in reality. The concept of EM superposition plays a crucial role in understanding how waves behave and interact, but it is limited by our current technological capabilities.