4.5 Images and Sound

Representation of Images

• Meta Data describes data, like creation date, resolution, color depth, and GPS.
• Resolution is the pixel count in an image (width x height).
• Rasterization converts analog signals into a digital image.
• DPI (dots per inch) is the pixel density per square inch.
• Digital images are represented by binary code.
• Each color is represented by a unique binary sequence.
• Images comprise pixels, each a single solid color.
• Total bits per pixel depends on the possible colors.
• Bitmaps show the number of pixels and available colors.
• Total image storage is determined by bit depth and resolution.

Creating Digital Images

• Digital cameras split images into a grid of pixels.
• A light sensor measures each pixel's color intensity.
• Measurements convert to binary code using an analog-to-digital converter.
• More pixels increase bits and file size.
• Color values use hexadecimal representation for simplicity.
• Common bitmap formats include JPEG, PNG, JPG, GIF, BMP, TIF.
• One megapixel equals 1,000,000 pixels.
• Examples of pixel counts:
  • 385x385=148225=0.148 MP
  • 2438x2124=5178312=5.178 MP
  • 1435x1900=2726500=2.727 MP
  • 5128x4820=24716960=24.717 MP
• Resolution does not define the physical size of the image
• Raster graphics are bitmapped digital images.
• Resolution indicates the number of pixels in an image.
• A pixel is a small, single-color square forming a bitmap.
• Bit depth is the number of bits needed to store each pixel.
• X bits per pixel allows for 2^X colors.
• High quality images usually mean larger file sizes.

File Size Examples

• 1920 x 1080 x 16 ≈ 33.2 million bits ≈ 4.147 megabytes
• 2048 x 1768 x 24 ≈ 86.9 million bits ≈ 10.863 megabytes
• 1245 x 1020 x 8 ≈ 10.16 million bits ≈ 1.270 megabytes

Vector Graphics

• Bitmaps use pixels, while vector graphics use math.
• Vector graphics maintain resolution upon zooming, unlike pixelated bitmaps.
• Vector graphics use geometric objects and drawing commands such as:
  • Points in space
  • Lines or curves
  • Regular and irregular shapes
  • Commands that alter the graphic
• To define a rectangle, the attributes needed are:
  • The width
  • The height
  • A starting corner
  • Appearance
• To define a circle, the attributes needed are:
  • Radius
  • Centre position
  • Appearance
• Resolution independence means elements render consistently regardless of display resolution and can scale infinitely.

Bitmaps

• Bitmaps can be compressed and support varied file formats.
• Data about specific pixels is accessible.
• Bitmaps can be high quality but use considerable storage space.
• Enlarging bitmaps leads to quality loss.
• Transparency support is absent and the color palette is limited.

Vectors

• Vectors use resolution independence (no set scale).
• They result in smaller file sizes than bitmaps.
• Vectors are ideal for geometric designs but are complex to create.
• They are unsuitable for realistic images and have limited compatibility with other file formats.
• Specialised software is required to edit vectors.
• Vectors are suitable for website design, animation, and logos.

Representation of Sound

• Real-world sounds combine different frequencies, forming a sound wave.
• The sampling rate must be double the highest frequency to ensure accurate sound recordings.
• This concept, the Nyquist Theorem, can lead to memory wastage.
• MIDI (Musical Instrument Digital Interface) synthesises sounds instead of live recordings.
• MIDI relies on timed event messages to adjust tempo, volume, and introduce instruments.
• MIDI files are smaller and easily edited, and do not lose data through samples

Vernam Ciphers

• The Vernam Cipher is mathematically unbreakable.
• The Key must:
  • Be a truly random sequence greater or equal in length than the plaintext and only ever used once
  • Be shared with the recipient by hand, independently of the message
  • And destroyed immediately after use
• To encode you must:
  • Convert the message to 8-bit ASCII
  • Convert the key to 8-bit ASCII
  • XOR operation on the message and key
  • Encoded message is produced
• To decode:
  • Take the encrypted message in ASCII and the key
  • Perform another XOR operation
• Analogue values and TPM chips create random keys.
• The key must never be reused, is disposed of securely and transferred securely.
• Algorithmic security posits that given enough ciphertext, an algorithm can crack any key, except a one-time pad.

Secure Communications

• Methods for secure communication include:
  • End-to-end encryption
  • Asymmetric encryption (public and private keys)
  • Symmetric encryption (one key)
• Wi-Fi connections use WPA3-PSK.
• HTTPS websites start with asymmetric encryption, then shift to symmetric encryption.
• Symmetric encryption is more effective and faster for large amounts of data and keys are shared by asymmetric encryption.

Symmetric Encryption

• Symmetric encryption uses the same key to encrypt and decrypt data.
• It uses a shared key.
• Advantages:
  • Faster than asymmetric due to single key
  • Efficient for bulk data, such as databases or files
  • Commonly used in banking.
  • Easier to implement and compatible with wide range of devices.
• Disadvantages:
  • Sharing the key poses a risk if the network is insecure.
  • Compromise possible if the key is stolen
• Examples of symmetric encryption ciphers include Caesar and Vigenère ciphers.

Asymmetric Encryption

• Asymmetric encryption uses key pairs to encrypt and decrypt data. (public and private key)
• Public keys are shareable, while private keys remain with the owner.
• Senders encrypt with the recipient's public key; recipients decrypt with their private key.
• Advantages:
  • Prevents unwanted senders and is more secure due to private keys.
  • Provides easier key distribution, ensures data integrity
  • Eliminates the need to share private keys and can be used for digital signatures.
• Disadvantages:
  • Slower and less efficient than symmetric encryption.
  • More complex to manage and secure key sharing can be problematic.
  • Private keys when lost, cannot be recovered if not backed up
• Examples of asymmetric encryption include:
  • Rivest Shamir Adleman(RSA)
  • Digital Signature Standard(DSS)
  • E-commerce Transactions
• Both aim to prevent "Man in the middle" attacks and ensure intercepted is unreadable.
• The Vernam Cipher is the only mathematically secure encryption method.

Compression

• Compression reduces file sizes.
• Achieved through removing unnecessary data or slightly decreasing quality.
• Lossy compression removes data to reduce quality by removing metadata.
• Lossless compression removes significantly less data, while ensuring no data is actually lost.
• Data removed by lossy compression cannot be gotten back, but data removed by lossless is never permanent

Data Compression Reasons

• Reduced download and upload speeds
• Prevents users from getting annoyed at delayed operations by increasing speed.
• Advantages are the result in smaller file sizes, while the disadvantages are the quality is permanently reduced
• Data can be retrieved in loseless methods.
• Quality is maintained
• Faster than lossy compression

Type of Video Compression

• Lossy is used with JPEG, MPEG, MP3, and GIF
• Lossless is used with PNG, BMP, and text based files.
• Dictionary encoding assigns unique, small binary values to frequently used words in a text file.

Error Checking and Correction

• Parity bits are added to binary code for error detection.
• Odd parity sets (1), if there is an even number of 1s in the initial 7 bits, ensuring an odd number of 1s.
• Even parity sets 1, if there is an odd number of 1s, ensuring an even number of 1s.
• If any of the bits change in transmission, you will know that there is an error, but you will not know what/where the error is.
• Parity bits will only be able to detect if an odd number of errors have, occurred-you will not know that there is an issue if 2,4 etc bits are flipped

Additional Error Correction Methods

• Majority Vote transmits each bit three times.
  • Solves the problem of if one bit is corrupted.
  • Does not solve the problem if 2 bits are flipped
  • Every bit is being sent as 3 bits – 3 times the bandwidth usage

2-Dimensional Parity Check

• Arrange data into a grid of rows and calculate the parity bit for each row and column
• The intersection of your parity row and column forms your parity bit check
• This will detect an error, and also, pinpoint where it has occurred, so you can fix it and get the correct value

Check Digits

• Check digits are a digit added to a piece of data to check that it is accurate
• This allows the receiving computer to perform the same calculation and, if the calculated check digit matches the received check digit, and the data is seen to be accurate.
• However, with this algorithm, if 2 numbers swap places, the check digit is still correct, despite having a different final result
• Modulo-11 is one of the most common check digit algorithms:
  • Multiply the number and the weighting
  • Add together the weighted numbers
  • Run sum MOD 11 – This gives us the new check digit
  • This would now detect an error, as each digit has a different weighting
• Check Sums add all the bytes together and any overflow is added as a 1
• Inverse of the value is the checksum
• Add the checksum the receiving end to invert the value
• If it is 0, then your data is valid and has passed the error checking