Digital & Bandwidth Calculations.
Introduction.
This Ebook provides a detailed analysis of digital and bandwidth calculations for various types of media, including text, speech, video, and animation. We’ll explore the fundamental concepts and present formulas for calculating bandwidth requirements for each media type.
Text Bandwidth Calculations.
Text is the simplest form of digital data. Its bandwidth requirements are generally low compared to other media types.
Formula.
Bandwidth bits per second equals Characters per second time Bits per character.
Typically, ASCII characters use 8 bits 1 byte per character, while Unicode UTF 8 can use up to 32 bits for some characters.
Example.
For a typical reading speed of 200 words per minute, with an average of 5 characters per word,
Characters per second = (200 words times 5 characters) per 60 seconds = 16.67 characters per second. Bandwidth = 16.67 times 8 bits = 133.36 bits per second or 0.133 kilo bits per second.
Speech Bandwidth Calculations.
Speech bandwidth calculations depend on the encoding method used. We’ll consider uncompressed PCM (Pulse Code Modulation) audio and compressed MP3 audio.
Uncompressed PCM Audio Formula.
Bandwidth (bits per second) = Sample rate times Bit depth times Number of channels.
Example (CD-quality audio).
Sample rate = 44,100 Hertz.
Bit depth = 16 bits per Channel = 2 for stereo.
Bandwidth = 44,100 times 16 times 2 = 1,411,200 bits per second or 1.41 Mega bits per second.
Compressed MP3 Audio.
MP3 uses variable bitrate encoding, but common bitrates for speech are 64 kilo bits per second, 96 kilo bits per second, or 128 kilo bits per second.
Video Bandwidth Calculations.
Video bandwidth depends on resolution, frame rate, color depth, and compression method.
Uncompressed Video Formula.
Bandwidth in (bits per second) = Width times Height times Bit depth times Frames per second.
Example (1080p video).
Resolution = 1920 times 1080 Bit depth = 24 (8 bits each for R, G, B) at a Frame rate of 30 frames per second.
Bandwidth = 1920 times 1080 times 24 times 30 = 1,492,992,000 bits per second. Or 1 point 49 Giga bits per second.
Compressed Video.
Compressed video uses various codecs H.264, H.265, VP9 with different bitrates. For example, Netflix recommends,
5 Mega bits per second for HD for 720p.
25 Mega bits per second for 4K Ultra HD.
Animation Bandwidth Calculations.
Animation bandwidth can vary widely depending on the type (2D, 3D) and complexity. We’ll focus on web animations using GIF and HTML5 canvas.
GIF Animation.
GIF file size depends on the number of frames, image dimensions, and color palette.
Bandwidth (bits per second) = File size times 8 divided by Duration.
Example.
For a 500 Kilo bit GIF lasting 5 seconds, Bandwidth = (500 times 1024 times 8) divided by 5 = 819,200 bits per second or 0.82 Mega bits per second.
HTML5 Canvas Animation.
Canvas animations are typically more efficient than GIFs. Bandwidth depends on the complexity of the JavaScript code and the frequency of updates.
For a simple canvas animation updating at 60 frames per second, each frame might be around 1 Kilo bit.
Bandwidth = 1 Kilo Bit times 60 frames per second times 8 = 480,000 bits per second. Or 0 point 48 Mega bits per second.
Bandwidth for 15 Minutes of Animation.
To calculate bandwidth for 15 minutes of animation, we need to consider the total data transferred over this period.
Formula.
Total data (bits) = Bandwidth in bits per second times Duration in seconds.
Example. Using the HTML5 Canvas calculation from above.
Duration = 15 minutes = 900 seconds of Bandwidth = 480,000 bits per second.
Total data = 480,000 times 900 = 432,000,000 bits or 54 Megabits.
This means that over a 15-minute period, the animation would transfer approximately 54 Megabits of data.
Conclusion.
Bandwidth calculations are crucial for designing efficient digital systems and estimating network requirements. The formulas and examples provided in this ebook offer a starting point for understanding bandwidth needs across various media types. Remember that real-world scenarios often involve additional factors such as network overhead, varying compression rates, and the need for buffer capacity to ensure smooth playback.
