Page 239 - DSP Integrated Circuits

224 Chapter 5 Finite Word Length Effects

(c) Determine the requirements for the anti-aliasing filters for the two
systems.
(d) Determine the required filter orders for the two anti-aliasing filters if a
Butterworth approximation is used. The audio signal has a bandwidth of
20 kHz.
5.19 An FIR filter with linear phase, i.e., symmetric impulse response, has the
frequency response:

where N = 2K+1 = 201. Determine the maximum deviation of attenuation in
the passband when the coefficients are quantized with an accuracy of Q = 2^.
Assume that the filter is realized in
(a) direct form
(b) linear-phase direct form

5.20 Show that the variance of the output signal of an accumulator goes to
infinity when the input is a zero mean Gaussian process.
5.21 A D/A converter in an early circuit for CD players (TDA 1540) manufactured
by Phillips has a resolution of only 14 bits while the digital signal has a word
length of 28 bits. Hence, 14 bits have to be discarded. In order to improve the
SNR, the following features are implemented:
1. The output sampling frequency before the converter is increased by
interpolation to 4 x 44.1 kHz. The unwanted images are attenuated by at
least 50 dB using a digital filter.
2. The analog output signal of the zero-order hold A/D converter is filtered
through a third-order Bessel filter with a 3 dB passband edge of 30 kHz.
3. The 14 bits that are discarded are added to the next output sample before
it is rounded to 14 bit precision.
Determine the improvement that is obtained in the SNR.