The application of the input code word results in a high-amplitude transient, called a “glitch”. This is especially the case when two consecutive code words to the A/D differ by several bits.

The reconstruction of the signal x (t) from its samples as an interpolation problem and have described the function:g(t)=\\(\\frac{sin⁡(πt/T)}{(πt/T)}\\).

An important parameter of a D/A converter is its settling time, which is defined as the time required for the output of the D/A converter to reach and remain within a given fraction (usually,±1/2 LSB) of the final value, after application of the input code word.

x(t) = \\(\\sum_{-\\infty}^\\infty x(nT) \\frac{sin⁡(π/T) (t-nT)}{(π/T)(t-nT)}\\) where the sampling interval T = 1/Fs=1/2B, Fs is the sampling frequency and B is the bandwidth of the analog signal.

The analog filter corresponding to the ideal interpolator has a frequency response:

The ideal reconstruction filter is an ideal low pass filter and its impulse response extends for all time. Hence the filter is noncausal and physically nonrealizable. Although the interpolation filter with impulse response given can be approximated closely with some delay, the resulting function is still impractical for most applications where D/A conversion are required.

W hen viewed as a linear filter, the S/H has an impulse response:

The usual way to remedy this problem is to use an S/H circuit designed to serve as a “deglitcher”. Hence the basic task of the S/H is to hold the output of the D/A converter constant at the previous output value until the new sample at the output of the D/A reaches steady state, and then it samples and holds the new value in the next sampling interval. Thus the S/H approximates the analog signal by a series of rectangular pulses whose height is equal to the corresponding value of the signal pulse.

The reconstruction of the signal from its samples as a linear filtering process in which a discrete-time sequence of short pulses (ideally impulses) with amplitudes equal to the signal samples, excites an analog filter.

D/A conversion is usually performed by combining a D/A converter with a sample-and hold (S/H) and followed by a low pass (smoothing) filter. The D/A converter accepts at its input, electrical signals that correspond to a binary word, and produces an output voltage or current that is proportional to the value of the binary word.