Page 208 - DSP Integrated Circuits

5.2 Parasitic Oscillations 193

5.2.3 Periodic Input Oscillations

Another type of phenomenon may occur when the input signal is periodic. The
cause may be either overflow or quantization nonlinearities. For example, instead
of a pure output tone for a sinusoidal input, the output may contain both harmonic
and subharmonic components. A subharmonic component has a period that is a
submultiple of the period of the input signal. Another periodic input phenomenon
is illustrated in Example 5.3.

EXAMPLE 5.3
The input to the second-order section just discussed is a sinusoid that itself does
not cause overflow. However, an overflow occurs when a small disturbance is added
to this input signal.
The output signal, shown in Figure 5.7, consists of two parts. The first is due to
the sinusoidal input and the second is due to the disturbance. The effect of the latter
would, in a linear stable system, decay to zero, but in the nonlinear system, with
saturation arithmetic, the sinusoidal part and the disturbance together cause a sus-
tained overflow oscillation. The output signal jumps between two different periodic
output signals. Thus, saturation arithmetic does not suppress overflow oscillations
in the direct form structure. This behavior is unacceptable in most applications.

Figure 5.7 Jump phenomenon resulting from overflow in a second-order direct form
section with saturation arithmetic

5.2.4 Nonobservable Oscillations
In some filter structures the overflow oscillation itself is not observable at the out-
put of the filter. The presence of an internal overflow oscillation may instead be