Jumbled up spectra of stars/glaxies

[terahertz]

When you look at the emission/absorption spectrum of a single element, you can clearly see various emission/absorption lines, which are characteristic of that element. However, radiation from stars/galaxies contains spectra of many elements. How do astronomers make sense of this jumbled-up spectrum? In other words, how do they know that an absorption line, for instance, comes from this element and not that, especially since the spectra are doppler-shifted?

 

[mfb]

Doppler-shift does not change the fractions of wavelengths. Typically a few elements are dominant in the spectrum, once you identify at least one of them (via those ratios) you know redshift and can adjust the whole spectrum. Afterwards you can look up all lines in tables.

 

[Bandersnatch]

Since spectral lines of each element are unique, there is actually no room to mistake which line comes from which element. Similarly, Doppler shift doesn't pose a problem, since it always affects the whole spectrum, preserving the line patterns.

E.g.
Imagine we've determined absorption lines of elements A, B, C and D in a lab. Their lines have positions:
A = 2, 5, 9, 14
B = 4, 6, 11
C = 3, 12
D = 1, 7, 13

If you then observe a spectrum with the following lines:
2 4 5 7 8 12 13 14

There's only one way to fit the elements in there (and determine how Doppler shifted it is).

 

[terahertz]

Thanks a lot for your enlightening response. Your simple example clarified a lot of things!