Pulse Code Modulation

The modulation methods PAM, PWM, and PPM discussed in the previous lecture still represent analog communication signals since the height, width, and position of the PAM, PWM, and PPM, respectively, can take any value in a range of values. Digital communication systems require the transmission of a digital for of the samples of the information signal. Therefore, a device that converts the analog samples of the message signal to digital form would be required. Analog to Digital Converters (ADC) are such devices. ADCs sample the input signal and then apply a process called quantization. The quantized forms of the samples are then converted to binary digits and are outputted in the form of 1's and 0's. The sequence of 1's and 0's outputted by the ADC is called a PCM signal (Pulses have been coded to 1's and 0's). Example: A color scanner is scanning a picture of height 11 inches and width 8.5 inches (Letter size paper). The resolution of the scanner is 600 dots per inch (dpi) in each dimension and the picture will be quantized using 256 levels per each color. Find the time it would require to transmit this picture using a modem of speed 56 k bits per second (kbps). We need to find the total number of bits that will represent the picture. We know that 256 quantization levels require 8 bits to represent each quantization level. Number of bits = 11 inches (height) * 8.5 inches (width) * 600 dots / inch (height) * 600 dots / inch (width) * 3 colors (red, green, blue) * 8 bits / color = 807,840,000 bits Using a 56 kbps modem would require 807,840,000 / 56,000 = 14426 seconds of transmission time = 4 hours. For this reason, compression techniques are generally used to store and transmit pictures over slow transmission channels. Quantization The process of quantizing a signal is the first part of converting an sequence of analog samples to a PCM code. In quantization, an analog sample with an amplitude that may take value in a specific range is converted to a digital sample with an amplitude that takes one of a specific pre–defined set of quantization values. This is performed by dividing the range of possible values of the analog samples into L different levels, and assigning the center value of each level to any sample that falls in that quantization interval. The problem with this process is that it approximates the value of an analog sample with the nearest of the quantization values. So, for almost all samples, the quantized samples will differ from the original samples by a small amount. This amount is called the quantization error. To get some idea on the effect of this quantization error, quantizing audio signals results in a hissing noise similar to what you would hear when play a random signal. Assume that a signal with power P s is to be quantized using a quantizer with L = 2 n levels ranging in voltage from –m p to m p as shown in the figure below.

preprint, April, 2005

The White Noise Hypothesis (WNH), introduced by Bennett half century ago, assumes that in the pulse code modulation (PCM) quantization scheme the errors in individual channels behave like white noise, i.e. they are independent and identically distributed random variables. The WNH is key to estimating the means square quantization error (MSE). But is the WNH valid? In this paper we take a close look at the WNH. We show that in a redundant system the errors from individual channels can never be independent. Thus to an extend the WNH is invalid. Our numerical experients also indicate that with coarse quantization the WNH is far from being valid. However, as the main result of this paper we show that with fine quantizations the WNH is essentially valid, in which the errors from individual channels become asymptotically pairwise independent, each uniformly distributed in [−∆/2, ∆/2), where ∆ denotes the stepsize of the quantization.

2011 24th Canadian Conference on Electrical and Computer Engineering(CCECE), 2011

ITU-T G.711.1 is a multirate wideband extension for the wellknown ITU-T G.711 pulse code modulation of voice frequencies. The extended system is fully interoperable with the legacy narrowband one. In the case where the legacy G.711 is used to code a speech signal and G.711.1 is used to decode it, quantization noise may be audible. For this situation, the standard proposes an optional postfilter. The application of postfiltering requires an estimation of the quatization noise. In this paper we review the process of estimating this coding noise and we propose a better noise estimator.

IEEE Transactions on Communications, 1976

The technique of nearly instantaneous companding (NIC) that we describe processes n-bit p-law or A-law encoded pulse-code modulation (PCM) to a reduced bit rate. A block of N samples (typically N zz 10) is searched for the sample having the largest magnitude, and each sample in the block is then reencoded to a nearly uniform quantization having (n -2) bits and an overload point at the top of the chord of the maximum sample. Since an encoding of this chord must be sent to the receiver along with the uniform reencoding, the resulting bit rate is fs(n -2 , + 3/N) bits/s where& is the sampling rate. The algorithm can be viewed as ?n adaptive PCM algorithm that is compatible with the widely used p-law and A:-law companded PCM. Theoretical and empirical evidence is presented which indicates a performance slightly better than (n -1) bit companded PCM (the bit rate is close to that of (n -2) bit PCM). A feature which distinguishes NIC from most other bit-rate reduction techniques is a performance that is largely insensitive to the statiStics of the input signal. ' In addition, we assume mid-tread bias and decision level assignment. Extensions are straightforward.

Digital Signal Processing, 2011

Eleventh Annual International Phoenix Conference on Computers and Communication 1992 Conference Proceedings, 1992

Multicarrier modulation is an efficient transmission sys-tem on interfered and frequency-selective channels. Es-pecially a discrete multitone transmission, a special type of multicarrier modulation, has been frequently used in systems where the signal is transmitted near the base-band frequency. One reason for the popularity of dis-crete multitone transmission is that the signal is con-structed with discrete Fourier transform for which sev-eral efficient algorithms exists. Implementation of the algorithms in fixed-point digital signal processor re-sults on limited accuracy of data samples. As a result, the quantization noise of the transmitted data symbols is increased. The magnitude of the noise can be taken into account in selection of the cost-optimal digital-to-analog and analog-to-digital converters.