What would be the effect of a dc component on the fft of a signal with time varying frequency content?
There will be an impulse at 0 frequency having amplitude equal to that DC value. which actually represent that DC.
As Bakht Zaman said above, there will be a big component at frequency zero. If you don't want that try to either high pass the signal prior to the FFT calculation or detrend it (remove best fit straight line):
">> help detrend
detrend Remove a linear trend from a vector, usually for FFT processing.
Y = detrend(X) removes the best straight-line fit linear trend from the
data in vector X and returns the residual in vector Y. If X is a
matrix, detrend removes the trend from each column of the matrix."
Do you mean a DC-offset, or a quasi-static component that is still periodic on very large time-scales? The latter refers to the cases where, when looking at short intervals, there appears to be a DC-offset but on longer intervals one realizes this to be false.
I make the distinction because a discrete Fourier transform can suffer from leakage, aliasing, etc. Leakage can occur if the signal is not periodic on the interval of interest, which has the similar effect of inserting step functions at the end of your time intervals. If you perform an FFT on the entire time series, then any discontinuity will add power to all Fourier components. In regards to a time series, any transition that occurs faster than the sample rate of your signal could produce a discontinuous result. This is usually easy to see by eye (e.g., an under-sampled sine wave can look like a triangle wave).
There are ways to mitigate both aliasing and leakage by using zero-padding and/or a windowing function (e.g., a Hanning window).
Useful references:
Harris, F.J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform," Proc. IEEE Vol. 66, pp. 51-83, 1978.
Also, D. Donnelly and B. Rust have five useful papers in Computing in Science & Engineering between 2005 and 2006.
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