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This paper presents the first application of the virtually imaged phased array (VIPA) in a Fourier transform pulse shaper for programmable manipulation of optical pulse bursts using a spatial light modulator (SLM). Due to the periodicity of the VIPA spectral dispersion function, a periodic spectral phase function is automatically generated from a single-period spatial phase function. Experimental results and theoretical simulations were compared with quadratic, cubic, and m-sequence mask patterns. The data demonstrate programmable manipulations of the pulse envelopes, in good agreement with the theory.