## Quantization and Discrete Amplitude Properties

The representation of the digital code can be given in different ways, as was discussed in Sec. 1.2.2. Generally, we can chose whatever representation or mapping function we want. In most cases, however, we use two different ways to represent the signal by uniform or non-uniform quantization. The quantization give rise to noise, so called quantization noise. If the number of bits is small, distortion components are also visible in the spectrum. In an OSDAC, where the number of bits often is...

## XDSL Standards

The telecommunication industry forms new standards to meet the requirements on higher speed and the demands from more and more users. Naturally, there is a large number of different standards for different applications. A few of them are described in this thesis, although it should be emphasized that several telecommunication standards still not have found their final acceptance as a standard and they only work as de facto standards. All xDSL techniques are intended to be used on the existing...

## Semi Digital FIR Filter

The FIR filter is of current-steering type 45, 63 . The principle is shown in Fig. 3-8, where the single-bit output, w(nT), from the modulator is fed into a shift register and the contents of the shift register is used to control the current switches. For each switch a current source with the weight Iunit is associated, where the s are the coefficients of the filter and T n is a unit current size. Figure 3-8 Current-steering implementation of a semi-digital filter with coefficient length K....

## Interpolated FIR Filter

The use of an interpolated FIR (IFIR) filter may be advantageous since the width of the transition band, DwT wsT- wcT , can be made larger and therefore the number of non-zero taps can be reduced (2-39), hence less current sources, chip area, etc. Assume that the original FIR filter, H0(z), has the following specification (2-39) wcT 2p 1.15 fN fs 2.30p OSR and wsT 2p 1.47 fN fs 2.94p OSR (3-18) With an attenuation in the stopband of approximately 17dB the number of taps is 219 (Sec. 3.1.3)....

## Influence of Output Impedance Variations

Using the current-steering DAC Sec. 2.2 , it is easily seen that the output impedance of the converter is signal-dependent, since any non-ideal current source has a finite output impedance. Dependent on what code is applied, different numbers of current sources are connected to the output. The whole DAC can briefly be modeled as a current source, shown in Fig. 3-3, where the output is terminated with a load resistance RL. Figure 3-3 Current source, I5X , with finite output resistance, Rs X ....

## Error Feedback Modulator

The error feedback modulator uses the quantization error to feed back 37 , as shown in Fig. 2-9. The quantization error, q nT _ y nT - w nT , is given by the LSBs of the input signal to the quantizer, w nT , and the output signal y n is the MSB of w nT . In the frequency domain, the quantization error signal is W z H z X z - G z Q z which gives Y z H z X z 1 - H z G z Q z Figure 2-9 Basic principle of an error feedback modulator. The signal transfer function, STF z , is STF z H z and the noise...

## Analog Smoothing Filter

The output of the semi-digital filter still contains images in the frequency domain due to the sample-and-hold elements. With an analog continuous-time lowpass filter CT LP , Fig. 2-12, the images and noise at higher frequencies above the original wanted bandwidth are attenuated. Figure 2-12 Images and noise are attenuated using the continuous-time filter Figure 2-12 Images and noise are attenuated using the continuous-time filter In addition, in front of the continuous-time filter, also an...