Question

Assume that we need to transmit a \(1,440 \times\) 900 uncompressed color image (using 16 bits per pixel) over a computer network in less than \(0.01\) second. What is the minimal necessary line speed to meet this goal?

Short answer

The minimal line speed necessary is 2,073,600,000 bits per second.

Step-by-step solution

Calculate Pixels

First, we calculate the total number of pixels in the image by multiplying the image dimensions: \(1,440 \times 900\). Thus, the total number of pixels is \(1,296,000\) pixels.

Determine Bits per Image

Each pixel uses 16 bits. Therefore, the total number of bits in the image is \(1,296,000 \times 16 = 20,736,000\) bits.

Convert Time to Suitable Units

The time available to transmit the image is \(0.01\) seconds. It is helpful to keep time in seconds for continuity when calculating bits per second.

Calculate Required Line Speed

To find the necessary line speed, divide the total number of bits by the transmission time. Thus, the required line speed is \(\frac{20,736,000}{0.01} = 2,073,600,000\) bits per second.

Key concepts

Image Transmission

Image transmission involves sending visual data over a network from one computer to another. Understanding how much data constitutes an image is crucial for efficient transmission. An image's data size is calculated by multiplying its pixel dimensions by the bits required to represent each pixel. For instance, an uncompressed color image with dimensions

• 1440 (width)
• 900 (height)
• 16 bits per pixel

means the total data size is calculated by:
\[1,440 imes 900 imes 16 = 20,736,000 \text{ bits}\]Uncompressed image transmission requires precise calculation to ensure accuracy and speed. Optimizing image transmission is often about balancing the size and quality of the image with the available network capacity.

Bandwidth Calculation

Bandwidth refers to the maximum capacity of a network to transmit data. It is crucial to understand the bandwidth required for any data transmission task to ensure timely and successful data transfer. Bandwidth is calculated as the amount of data expected to be sent divided by the time available for the transfer.
For example, transmitting an image with the size of 20,736,000 bits in less than 0.01 seconds requires the bandwidth to be:
\[\text{Bandwidth} = \frac{20,736,000 \text{ bits}}{0.01 \text{ seconds}} = 2,073,600,000 \text{ bits per second}\]To effectively calculate required bandwidth:

• Know the total data size (in bits)
• Understand the time available for transmission
• Divide the total data by time to get bits per second

This calculation ensures network readiness for data transfer and avoids transmission delays or failures.

Line Speed

Line speed, also known as data rate, is the speed at which data is transmitted over a network line. It's typically measured in bits per second (bps). Achieving the desired line speed ensures that data such as images, videos, or documents is sent both accurately and swiftly.
For large files or images, knowing the line speed is essential to determine if the network can handle the transmission without delay.

• If you need to send an image in a specific timeframe, calculate the total bits in the file and divide by the available time to find the necessary line speed.
• Always measure line speed in compatible units, such as bits, kilobits, or megabits per second.
• Consider the actual speed may be lower due to network congestion or other limitations.

Monitoring line speed helps in planning and managing resources effectively, ensuring that the network performance meets the requirements of the tasks.