Multiplication of the time-dependent signal data by an exponential function, exp(t/TC), where t is time and TC is a parameter called the time constant (in spectroscopy). The time constant can be chosen to either improve the signal to noise ratio (with a negative TC) or decrease the effective spectral line width (with a positive TC) in the resulting spectrum. The use of a negative TC to improve SNR is equivalent to line broadening by convolving the spectrum with a Lorentzian function of corresponding reciprocal width.

Convolution differentiation is a method of suppressing broad underlying spectral lines in order to emphasize narrower spectral lines. Strong smoothing of the spectrum (e.g., by severe negative exponential weighting of the time data) will suppress the narrow lines but minimally affect very broad ones; subtracting such a smoothed spectrum from the original will largely remove the contributions from the broad lines. This provides a means of baseline correction.

Every tissue in the human body has its own T1 and T2 value. This term is used to indicate an image where most of the contrast between tissues is due to differences in the T1 value.
This term may be misleading in that the potentially important effects of tissue density differences and the range of tissue T1 values are ignored.
If the machine parameters are chosen, so that TR less than T1 (typically under 500 ms) and TE less than T2 (typically under 30 ms), a power series expansion of the exponential functions and then neglecting second and higher order terms yields
Mxy = Mxy0 TR/T1
thus the expression becomes independent of T2 and yields the condition for T1 weighting. Therefore a T1 contrast is approached by imaging with a short TR, compared to the longest tissue T1 of interest and short TE, compared to tissue T2 (to reduce T2 contributions to image contrast). Due to the wide range of T1 and T2 and tissue density values that can be found in the body, an image that is T1 weighted for some tissues may not be so for others.
Lesions with short T1 are (bright in T1 weighted sequences):
fat (lipoma, dermoid)
sub-acute haemorrhage (metHb)
paramagnetic agent (Gd, pituitary)
protein-containing fluid (colloid cyst)
metastatic melanoma (melanotic).