Frequency Response of Finite Aperture Sample-and-Hold Systems

Sampling systems frequently store the collected samples in the form of a series of numbers in the memory of a digital computer. Ideally, the stored number represents the magnitude of the sampled function at one instant of time. Practically, the stored number is the result of some weighted averaging of the sampled function during a finite time interval. As this acquisition time interval becomes a significant fraction of the sample period, the averaging process degrades the sample-system frequency response. The procedure is reviewed whereby one calculates the frequency response for the class of systems that are linear and time-varying or constant during the acquisition interval. The transfer function is calculated for a sampler that first acts as an RC integrator during the acquisition time, then transfers the accumulated charge to some holding circuit (for A-D conversion), and finally begins to acquire the next sample. Tradeoffs between overshoot and rise time in the design of the system transfer function are shown along with an example of how one can arrive at the desired transfer function by convolution of the samples with a proper waveform.