Hardware and Software for Digital Signal Processors - Digital Signal Processing: Fundamentals and Applications - page 434

We choose the S factor as S ¼ 16 and we choose A ¼ 2 to scale down the denominator coefficients by half.
Since the second adder output after scaling is
y s ðnÞ¼ 0:75
B

wðnÞþ 1:49
B

wðn 1Þþ 0:75
B

wðn 2Þ

to avoid second adder overflow we have to ensure that each coefficient is less than 1, along with the sum of the
absolute values:

0:7 B þ 1:4 B þ 0:7 B < 1

Hence B ¼ 4 is selected. We develop the DSP equations as
x s ðnÞ¼xðnÞ=16

w s ðnÞ¼0:5x s ðnÞ0:76wðn 1Þ0:32wðn 2Þ

wðnÞ¼2w s ðnÞ

y s ðnÞ¼0:1875wðnÞþ0:3725wðn 1Þþ0:1875wðn 2Þ

yðnÞ¼ðB SÞy s ðnÞ¼64y s ðnÞ

The implementation for cascading the second-order section filters can be found in Ifeachor and
Jervis (2002).
A practical example will be presented in the next section. Note that if a floating-point DS processor
is used, all the scaling concerns should be ignored, since the floating-point format offers a large
dynamic range, so that overflow hardly ever happens.

9.6 DIGITAL SIGNAL PROCESSING PROGRAMMING EXAMPLES
In this section, we first review the TMS320C67x DSK (DSP Starter Kit), which offers floating-point
and fixed-point arithmetic. We will then investigate real-time implementation of digital filters.

9.6.1 Overview of TMS320C67x DSK
In this section, a Texas Instruments TMS320C6713 DSK (DSP Starter Kit) shown in Figure 9.18 is
chosen for demonstration. This DSK board has an approximate size of 5 x 8 inches, a clock rate of 225
MHz, and a 16-bit stereo codec TLV320AIC23 (AIC23), which deals with analog inputs and outputs.
The onboard codec AIC23 applies sigma-delta technology for analog-to-digital conversion (ADC) and
digital-to-analog conversion (DAC) functions. The codec runs using a 12 MHz system clock and the
sampling rate can be selected from a range of 8 to 96 kHz for speech and audio processing. Other
boards such as a Texas Instruments TMS320C6711 DSK can also be found in the references
(Kehtaranavaz and Simsek, 2001; TMS320C6x CPU and Instruction Set Reference Guide, 1999). The