Modern diagnostic ultrasound beamformers require delay information for each sample along the image lines. In order to avoid storing large amounts of focusing data, delay generation techniques have to be used. In connection with developing a compact beamformer architecture, recursive algorithms were investigated. These included an original design and a technique developed by another research group. A piecewise-linear approximation approach was also investigated. Two imaging setups were targeted -- conventional beamforming with a sampling frequency of 40 MHz and subsample precision of 2 bits, and an oversampled beamformer that performs a sparse sample processing by reconstructing the in-phase and quadrature components of the echo signal for 512 focal points. The algorithms were synthesized for a FPGA device XCV2000E-7, for a phased array image with a depth of 15 cm. Their performance was as follows: (1) For the best parametric approach, the gate count was 2095, the maximum operation speed was 131.9 MHz, the power consumption at 40 MHz was 10.6 mW, and it requires 4 12-bit words for each image line and channel. (2) For the piecewise-linear approximation, the corresponding numbers are 1125 gates, 184.9 MHz, 7.8 mW, and 15 16-bit words.