Page 236 - DSP Integrated Circuits

Problems 221

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PROBLEMS
5.1 A two's-complement number is multiplied by a factor 0.5 and then quantized
to the original word length. Determine both the average value and the
variance of the quantization error.

5.2 Show that the quantization scheme, discussed in section 5.4, will suppress
parasitic oscillations.
5.3 Show that the simplified scheme, discussed in section 5.4, will suppress zero-
input parasitic oscillations for second-order allpass sections with poles on the
imaginary axis in the z-plane.
5.4 Show that a two-port adaptor is pseudo-lossless.

5.5 (a) Scale the signal levels in the FIR filter shown in Figure P5.5. Use safe
scaling since the filter length is short. Two's-complement representation
shall be used.
(b) Also, scale the filter using L2-norms.

Figure P5.5 Direct form FIR

5.6 (a) Scale a direct form II second-order section using the safe scaling
criterion. The filter is a half-band filter of Butterworth type.
(b) Scale the filter assuming a narrow-band input signal.
(c) Scale the filter assuming a wide-band input signal.