In this paper, we investigate the optimal ways to sample multichannel impulse responses, composed of a small number of exponentially damped sinusoids, under the constraint that the total number of samples is fixed - for instance with limited storage / computational power. We compute Crame #x0301;r-Rao bounds for multichannel estimation of the parameters of a damped sinusoid. These bounds provide the length during which the signals should be measured to get the best results, roughly at 2 times the typical decay time of the sinusoid. Due to bandwidth constraints, the signals are best sampled irregularly, and variants of Matching Pursuit and MUSIC adapted to the irregular sampling and multichannel data are compared to the Crame #x0301;r-Rao bounds. In practical situation, this method leads to savings in terms of memory, data throughput and computational complexity.