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FIGURE 23.12 Digital-to-analog conversion process.

FIGURE 23.13 Frequency response of the ideal reconstruction filter.
2
From statistical considerations, the noise power is found to be ∆ /12 watts. A common measure of the
performance of the ADC is the ratio of the signal power to noise power, and this is called the signal-to-
quantization noise power, which expressed in decibels (dB) is

SQNR(dB) = 1.76 + 6.02b

Digital-to-Analog Conversion 8–12
Reconstruction of the analog signal from its sampled form is closely akin to lowpass filtering of the
sampled signal. Figure 23.12 shows how an analog signal can be reconstructed by filling the gaps between
samples and holding the current value constant till the next sample is received. Consider an ideal
reconstruction filter with an impulse response function h(t), then its response is given by

∞
yt() = ∑ xnT s )ht nT s )
(
(
–
n=∞
–
Taking the Fourier transform of this equation gives
Yf() = Hf()Xf()

where X( f ) is the periodic spectrum of x(nT s ) as shown in Fig. 23.13 and h(t) = sinc(F s t). Note that h(t)
is noncausal; hence it cannot be used for real-time applications. Furthermore, since h(t) is not time-
limited, an infinite number of impulse responses must be used for interpolating between values in order
to obtain exact results. Consequently, alternative reconstruction filters such as zero-order hold (staircase),
first-order, or fractional-order holds are used in practice. However, the staircase reconstruction filter is,
by and large, the simplest and most widely used in practice. The impulse response of this filter is given

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