Speckle is an inherent characteristic of coherent imaging systems. Often, as in the case of Ultrasound, Synthetic Aperture Radar, Laser Imaging and Holography, speckle is a source of noise and degrades the reconstructed image. Various methods exist for the removal of speckle in such images. One method, which has received attention for the removal of speckle from coherent imaging, is to use a temporally incoherent source. We create a novel digital signal processing technique for the reduction of speckle from digital holograms by simulating temporal incoherence during the digital reconstruction process. The method makes use of the discrete implementation of the Fresnel Transform, which calculates the reconstructed image for a range of different wavelengths. These different spectral components can be weighted to suit a temporally incoherent source and the intensities from each wavelength are added together. The method is examined using the speckle index metric..