Multimedia Systems and Applications Lecture 2: Digitization Process Introduction to Multimedia

Introduction to Multimedia Contents Digital Technology Sound (Wave) Representation Sampling Quantization Aliasing and Quantization Error Quantization Interval Sampling and Sampling Rate Sample Size Image Sampling & Quantization Continuous Image Representation of Digital Images Introduction to Multimedia

Introduction to Multimedia Digital Technology Everyday, we encounter many values that change continuously, for example, the voltage of the electricity that lights up our room varies continuously over time. These are also known as analogue signals. However, modern computers are built to deal with entities in completely different way. These are known as digital computers because they work with digits. Introduction to Multimedia

Introduction to Multimedia Digital Technology Because of this, when using a computer to process continuous signals, we first need to find a way to represent them so that the computer is able to handle them. Usually, this is a digital representation, i.e., we use a series of numbers to denote the continuous signals. Introduction to Multimedia

Introduction to Multimedia Digital Technology Then, we have to convert the continuous signal into the digital representation. This process is known as digitization. The first step in the digitization process is sampling which takes samples of the continuous signal. The number of samples taken during a time period is known as sampling rate. The second step is known as quantization where we restrict the value of the samples to a fixed set of levels. Introduction to Multimedia

Introduction to Multimedia Digital Technology Introduction to Multimedia

Sound (Wave) Representation Introduction to Multimedia

Introduction to Multimedia Frequency Frequency is expressed in cycles per second - 1 cycle = 1 hertz (Hz) the higher the frequency, the higher the pitch of the sound. For example, a violin = 2000 Hz, and a brass band = 100 Hz. A high quality system will produce sounds in the range 20Hz to 22,050Hz (Human range). Frequency: The rate (over time) that a signal varies from positive to negative voltages. Violin: كمنجة brass: النفخ Introduction to Multimedia

A Frequency of Sound Signal Introduction to Multimedia

Introduction to Multimedia Amplitude The amplitude of an analogue audio signal is measured in decibels (dB).     Introduction to Multimedia

An Amplitude of Sound Signal Introduction to Multimedia

Introduction to Multimedia Amplitude Introduction to Multimedia

(Analogue to Digital Conversion) Digitizing Sound (Analogue to Digital Conversion) Introduction to Multimedia

Introduction to Multimedia Sampling Readings of the analogue voltage are taken at uniformly spaced time intervals - this is called the sampling rate: the number of samples taken per second. In theory, the sampling rate must be at least twice the highest frequency in the range of analogue voltage values. Sampling rate = 2*f max; f : Frequency. Nyquist Rule For Human sound : 20Hz to 22,050Hz We take 2* 22,050 = 44,100 sample/sec Introduction to Multimedia

Sampling the Low Frequency Signal Introduction to Multimedia

Sampling the High Frequency Signal Clearly, the sampling rate for the high frequency signal is inadequate - it does not 'catch' every peak and trough - the rate would have to be increased. Introduction to Multimedia

Introduction to Multimedia Quantization After sampling has been completed, it must be remembered that the sampled data is still analogue in form. It must therefore now be turned into digital data. This is achieved using a process called Quantization. Quantization is the process of converting analogue values to digital values. Introduction to Multimedia

Introduction to Multimedia Quantization Introduction to Multimedia

Aliasing and Quantization Error If we under sample, i.e., taking less samples than as required by Nyquist sampling theorem, some of the frequency components will be mistakenly converted into other frequencies. This is known as aliasing. On the other hand, if we use too few levels to represent each sample value, there will be large amount of error for each sample. This is known as quantization error. These errors can be thought of as noise on the signal. Introduction to Multimedia

Quantization Interval When 8 bits are used, there are 28 = 256 bands, and also, therefore, 256 quantization intervals. The fewer the number of analogue bands, the wider each band must be, and thus the greater the range of analogue values which are translated to a single digital value. Introduction to Multimedia

Quantization Interval It is better to use a larger number of bits for each quantization interval. For instance, when 16 bits are used, the number of bands/quantization intervals is 216 = 65,536. Thus less coarse (and therefore more accurate) than 8-bit samples. 16-bit sampling is in fact the norm for sound digitization. The data rate of a stream of digitized data is calculated as: sampling frequency x bits per sample / 8, expressed in bytes/sec. Introduction to Multimedia

Sampling and Sampling Rate To record everything the human ear can possibly hear, we need to be sampling at a bit over 44kHz, or something like 44,100Hz, or 44.1kHz, which is what audio compact disks (CDs) are. By sampling at this rate, we effectively remove higher frequencies. For human listeners that's not a problem (since we cannot hear higher beyond 22kHz anyway). Introduction to Multimedia

Sampling and Sampling Rate For example, telephone samples at 8kHz (8000 samples per second), which effectively means that any frequency higher than 4kHz is wiped out. This is why on the phone we sometimes cannot tell the difference between certain letters (like "f" and "s"), and why we need to spell our names (s-as-in-Solid, and f-as-in-fast), and the listener still manages to make mistakes when writing it down. Introduction to Multimedia

Introduction to Multimedia Sample Size Another issue we have to care about when sampling sound is how big to make each sample. Basically, how many distinct values can a wave can take: * We want to record 0 dB – 60 dB (Normal Conversation) 60/8 = 7.5  8 bits needed * To record from 60 dB – 140 dB (Machines and Music) 140/8 =17.5  16 or 24 bits Most sound is encoded at 8-bit or 16-bit. Some (very rare) high end sound cards have 32-bit samples. Audio CD samples are 16-bit. Introduction to Multimedia

Introduction to Multimedia Sample Size For example, a 22kHz stereo sound, with 16-bit sampling will need to be sampled at 44.1kHz or 44,100 times per second. Each sample will be 16-bits, and we'll have 2 channels (one left, and one right---for stereo). Thus, we'll have 44,100 sample/sec * 2 bytes/sample * 2 channels = 1,411,200 bits/s = 176,400 bytes/s =173 kbyte/sec. Introduction to Multimedia

Image Sampling & Quantization Introduction to Multimedia

Introduction to Multimedia Basic Concepts To create a digital image, we need to convert continuous sensed data into digital form. This involves two processes: sampling and quantization Introduction to Multimedia

Introduction to Multimedia RGB Channels Introduction to Multimedia

Introduction to Multimedia Continuous Image This figure shows a continuous image, f (x, y), that we want to convert to digital form. To convert it to digital form, we have to sample the function in both, coordinates and amplitude. Introduction to Multimedia

Image Sampling and Quantization Digitizing the coordinate values is called sampling. Digitizing the amplitude values is called quantization. Introduction to Multimedia

Introduction to Multimedia This is a plot of amplitute (gray level) values of the continuous image along the line segment A B To sample this function, we take equally spaced samples along line AB. Location of each sample is given by a vertical tick mark in the bottom part of the figure. Introduction to Multimedia

Introduction to Multimedia However, the values of the samples still span (vertically) a continuous range of gray‑level values. In order to form a digital function, the gray‑level values also must be converted (quantized) into discrete quantities. Introduction to Multimedia

Introduction to Multimedia Quantization The right side of the above figure shows the gray‑level scale divided into eight discrete levels, ranging from black to white. The vertical tick marks indicate the specific value assigned to each of eight gray levels. The continuous gray levels are quantized simply by assigning one of the eight discrete gray levels to each sample. Introduction to Multimedia

Introduction to Multimedia The assignment is made depending on the vertical proximity of a sample to a vertical tick mark. Introduction to Multimedia

Representation of Digital Images The values of the coordinates at the origin are (x,y) = (0,0). The next coordinate values along the first row are (x,y) = (0,1). The notation (0,1) is used to signify the 2nd sample along the 1st row. Introduction to Multimedia

Coordinate convention used to represent digital images Introduction to Multimedia

A digital image of size M x N Introduction to Multimedia

Representing Digital Images The number of bits required to store a digitised image is b = M x N x k where M & N are the number of rows and columns, respectively and k is the number of bits /pixel. The number of gray levels is an integer power of 2: L = 2k where k =1,2,… It is common practice to refer to the image as a “k-bit image” Introduction to Multimedia

Introduction to Multimedia

Introduction to Multimedia Image Sampling Dense sampling will produce a high resolution image in which there are many pixels, each of which represents of a small part of the scene. Coarse sampling, will produce a low resolution image in which there are a few pixels, each of which represents of a relatively large part of the scene. Introduction to Multimedia

Introduction to Multimedia

High Data Volume of Multimedia Information Introduction to Multimedia