II. Background Method

A. Companding

The word "companding" stands for compression and expansion, which is a process to reduce the number of bits required to encode a voice signal. In telephony systems, compander is used to reduce quantization noise in speech coding and to reduce the number of bits required to encode a voice signal. There are two companding laws are used:

· Bell Mu-law for USA/Canada/Japan and the Philippines
· CCITT A-law for Europe and the rest of the world

The illustration of the compander is as follows.

These conversion technique differ only on some points, but the common purpose is to enhance signal-to-quantization noise ration preserving the 64 kbits/s standard bit rate (8 kHz sampling rate and 8bit coding). Since human speech has a dynamic range of 50dB and its intelligibility constraints lead to at least a 12 bit word length when linear quantization is used, which requires 96 kbit/s (12 bits * 8000 samples/s) bit rate. However, since this is much higher than the 64 kbit/s bit rate required in telecom application, in order to store a voice signal and retain all its information, the normal 4kHz voice channel must be sampled at 8kHz in accordance with the Nyquist sampling theorem. Therefore, 8 bit non-uniform (logarithmic) quantization has been defined to match both the bit-rate and the intelligibility constraints. It can be proven that the signal to quantization-noise ratio becomes independent from the signal level if the quantization function is a logarithmic function like: .

The size of the quantization step increases with the input signal value: small amplitudes are coded with fine granularity (more steps) then larger amplitudes. Signal to quantization-noise ratio becomes constant because each signal level is coded with the same relative precision.[Mal95]

In U.S. m-law companding, weak speech signals are amplified where strong speech signals are compressed. Let the speech voltage level into the compander be x(t) and the speech output voltage be F(x). Following

Where m is a positive constant and has a value typically between 50 and 300. The peak value of x(t) is normalized to 1.
In Europe, A-law companding is used , and is defined by

Sign returns a positive or negative value, the variable m or A defines the curvature law. For m-law, the function taken is quasi-linear for x small and quasi-logarithmic for x large. The compression rate, C, near the origin is given by:

For the A-law, the curve is approximated with its tangent near the origin, so the quantization is linear for small signals. The slope of the linear part, called the compensation rate, has been fixed to 16 and is given by:

As seen above, the only difference between Mu-Law approximation and A-Law approximation is near the origin, and the quantization function of Mu-Law approximation near the origin will be explained later in Coding section.

B. Texas Instrument's TMS320C30 Floating Point DSP

1. General

The Texas Instrument's TMS320C30 Digital Signal Processor is high performance CMOS 32-bit floating-point device in the TMS320 family of single-chip DSPs. It integrates both system control and math-intensive functions on a single controller and this system integration allows fast, easy data movement and high-speed numeric processing performance. Extensive internal busing and a powerful DSP instruction set provide the devices with the speed and flexibility to execute at up to 60 million floating-point operations per second (MFLOPS). The devices also feature a high degree of on-chip parallelism that allows users to perform up to 11 operations in a single instruction.[Usr97]

2. Serial Ports

The TMS320C30 has two totally independent bi-directional serial ports. Both serial ports are identical, and there is a complementary set of control registers in each one. It is possible to configure each serial port to transfer 8, 16, 24, or 32 bits of data per word simultaneously in both directions and the clock for each serial port can originate either internally, through the serial port timer and period registers, or externally, through a supplied clock. An internally generated clock is a divide down of the clockout frequency, f(H1). A continuous transfer mode is available, which allows the serial port to transmit and receive any number of words without new synchronization pulses. The receive/transmit timer-period register is a 32-bit register and bits 15-0 are the timer transmit period, and bits 31-16 are the receive period.[Usr97]

3. Data Formats of 'C30

The TMS320C30 Supports three types of formats, integer, unsigned-integer, and floating point format. There are two types of integer and unsigned-integer formats, short format and single-precision format. Short-interger format is a 16 bit 2s-complement integer format for immediate integer operands and sign bit (15) is extended to 31bit when the single-precision integer format is represented in 2s-complement where MSB is sign bit of the number. Unsigned-integer's short format has no sign bit and bit 16 - 31 is filled with zero and both short and single-precision format consist data form of unsigned binary number.
Different from integer and unsigned-integer format, the 'C30 supports three floating-point formats. A short floating-point format for immediate floating-point operands, consisting of a 4-bit exponent, a sign bit, and an 11-bit fraction, a single-precision format consisting of 8-bit exponent, a sign bit, and a 23-bit fraction, and lastly, an extended-precision format consisting of an 8-bit exponent, a sign bit, and a 31-bit fraction. The floating-point conversion will be discussed later in the appendix.