14.9 INTERPOLATOR STRUCTURES

An interpolator is a device that passes a low-rate input signal through a low-pass filter then inserts the filter outputs to get a high-rate output. The low-pass filter is sometimes referred to as an anti-imaging filter. The model of a 1-to-L interpolator is shown in Fig. 14.10 [94, 95]. The operating frequencies of the different com­ponents are indicated above the input and output lines. The sample periods are indicated below the input and output lines. The block on the left is an N-tap FIR digital filter with impulse response h(nT′), where T is the high-rate sampling period, and operates at the high sampling rate F. The 1-to-M upsampler, or sample rate expander, inserts M − 1 zeros between the input sample x(nT), shown as the block on the left of Fig. 14.10. The upsampler generates the signal u(nT′) and the low-pass filter generates the signal y(nT′). The upsampler simply inserts L − 1 zeros between the input sample x(n) to produce a signal at L times the data rate. This process is sometimes called “zero-stuffing.” We can write the following equations for the two output signals:

(14.27)

(14.28)

Figure 14.10 General 1-to-L interpolator system.