New Approach to Sideband {

First we develop the theory of reduced instability in order to analyze stability of bifurcating solutions via the Liapunov{Schmidt reduction. Next, this theory is generalized to cover sideband instabilities using a Floquet ansatz. The method is applied to roll patterns in the Swift{Hohenberg equation which serves as a model for pattern formation. We analyze the stability problem of small rolls analytically by calculating expansions of the critical eigenvalues in terms of the sideband vector. Thus we recover the Eckhaus and the zigzag instability. Finally, we compare the results with the predictions of the Newell{Whitehead equation and obtain good agreement.