# Fundamentals Rawesak Tanawongsuwan

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Fundamentals Rawesak Tanawongsuwan ccrtw@mahidol.ac.th

Digital Data Bits are units of data that can only have one of two values. A byte is eight bits. Groups of bits can be interpreted as numbers to base 2, but can also be treated as characters, colours, etc.

Bytes to remember 1 byte = 8 bits 2 bytes = 16 bits 3 bytes = 24 bits 4 bytes = 32 bits.

Analogue and Digital Representation

Digitization Converting a signal from analogue to digital form – Analogue signal can vary continuously, digital is restricted to discrete values Two-stage process – Sampling – measure the value at discrete intervals – Quantization – restrict the value to a fixed set of quantization levels

Sampling and Quantization

The sampling rate is the number of samples in a fixed amount of time or space. The quantization levels are the set of values to which a signal is quantized.

Analogue vs Digital

Benefits of digital signals High fidelity Noise tolerance

Frequency Domain Any periodic waveform can be decomposed into a collection of frequency components – Each one is a pure sine wave The collection of frequencies and their amplitudes represent the waveform in the frequency domain – Compute the frequency domain representation (frequency spectrum) using the Fourier Transform – Higher frequency components are associated with abrupt transitions

Spatial and temporal signals Spatial and temporal signals are made up of pure sine wave components at different frequencies. The Fourier Transform operation can be used to compute a signal’s representation in the frequency domain. Higher-frequency components are associated with abrupt transitions.

Sampling Theorem If the highest frequency component of a signal is at fh the signal can be properly reconstructed if it has been sampled at a frequency > 2fh – Nyquist rate Undersamping leads to aliasing – Sound distortion, image 'jaggies' or Moiré patterns, jerky or retrograde motion

Aliasing Anti-aliased Aliased

Aliasing

Moiré Patterns

Too Few Quantization Levels Reducing memory requirements by using fewer bits for each value means fewer quantization levels are available Cannot distinguish between values that fall between levels Images: banding and posterization Sound: coarse hiss, loss of quiet passages, general fuzziness (quantization noise)

Image banding effects

Posterization

Digital Representation of Media There are established ways of representing images, video, animation, sound and text in bits. Media data may be represented as a textual description in a suitable language, or as binary data with a specific structural form.

Image Images are displayed as arrays of pixels and represented using an internal model. Generating the pixels from the model is called rendering.

Bitmaps vs Vector Graphics Images may be modelled as bitmaps or vector graphics. A bitmap is an array of logical pixels (stored colour values) that can be mapped directly to the physical pixels on the display. In vector graphics, the image is stored as a mathematical description of a collection of individual lines, curves and shapes making up the image, which requires computation to render it.

Good Things for Vector Graphics Often smaller than bitmaps Resolution-independent Scalable without loss of quality – only suitable for certain sorts of synthetic image, not photographs

Combining Vectors & Bitmaps Rasterize vectors – Lose all their vector properties Trace bitmaps – Difficult and can only produce an approximation (parameterized)

Layers Organizational device used in both sorts of graphics, especially useful in bitmaps – Permits separation and manipulation of different parts of a bitmapped image Digital version of clear sheets of acetate, stacked on top of each other – Areas without coloured pixels/graphic objects are transparent so lower layers show through Compositing – combine layers using different blending modes (digital collage)

Creatively Blending Layers http://www.carlvolk.com/photoshop15.htm

Creatively Blending Layers http://www.carlvolk.com/photoshop15.htm

Graphics/Image Data Types

RGB Components

Moving pictures, Videos, Animation Moving pictures can be created as live-action or animation. Live-action must be stored as video. Animation may be represented in other more flexible or efficient ways. Video frames require a lot of storage so video is invariably compressed for delivery.

Sound Sound can be represented as a sequence of samples after digitization. CD audio is sampled at 44.1 kHz, higher sampling rates are sometimes used. Audio delivered over the Internet is compressed, often using the MP3 codec.

Text A character set is a mapping from characters to character codes. Unicode is a character set capable of representing text in all known languages. A font is a set of character shapes, called glyphs.

Layout and Typography Many aspects of layout must be controlled when text is displayed.

Interactivity Interactivity is produced by executing a program in response to user input. In multimedia, programs are often written in a scripting language, such as JavaScript or ActionScript.

Compression Compression must often be applied to media data. Compression may be lossless or lossy. – Lossless – image can be reconstructed exactly from compressed version – Lossy – some information discarded, image can only be reconstructed approximately

Compression Different compression algorithms are applicable to different types of media data. Their effectiveness depends on the characteristics of the data itself.