Determine The Total Time To Transmit Uncompressed Data

Determine The Total Time It Takes To Transmit An Uncompressed Gray

Determine the total time it takes to transmit an uncompressed grayscale image (with 8 bits/pixel) from a screen with a resolution of 1,280 × 840 pixels using each of the following media: a. A 56 Kbps modem; b. A 1.5 Mbps DSL line; c. A 100 Mbps Ethernet link.

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

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Transmitting digital images over various media requires understanding the data size and the transmission speed to determine the total transmission time. This understanding is critical in applications such as live streaming, remote sensing, and digital broadcasting where timely delivery is essential. The calculation involves determining the total number of bits in the image and dividing by the transmission rate of the media to find the total transmission time for each case. Furthermore, for high-resolution color images, establishing the minimum bandwidth necessary to meet specific latency constraints enables efficient network planning and optimization.

Calculating Transmission Time for an Uncompressed Grayscale Image

The first task involves an uncompressed grayscale image with a resolution of 1,280 × 840 pixels, each pixel represented by 8 bits. The total number of pixels in the image is calculated by multiplying the width and height:

Total pixels = 1,280 × 840 = 1,075,200 pixels.

Since each pixel uses 8 bits (or 1 byte), the total number of bits is:

Total bits = 1,075,200 pixels × 8 bits = 8,601,600 bits.

To compute the transmission time over different media, divide the total bits by the respective transmission rate:

a. 56 Kbps modem

The bandwidth is 56 kilobits per second, which is 56,000 bits/sec.

Total transmission time: 8,601,600 bits ÷ 56,000 bits/sec ≈ 153.6 seconds.

b. 1.5 Mbps DSL line

The bandwidth is 1.5 megabits per second, which equals 1,500,000 bits/sec.

Total transmission time: 8,601,600 bits ÷ 1,500,000 bits/sec ≈ 5.74 seconds.

c. 100 Mbps Ethernet link

The bandwidth is 100 megabits per second, which equals 100,000,000 bits/sec.

Total transmission time: 8,601,600 bits ÷ 100,000,000 bits/sec ≈ 0.086 seconds.

Thus, the transmission times are approximately 154 seconds for the 56 Kbps modem, 5.74 seconds for the DSL line, and 0.086 seconds for the Ethernet link.

Determining Minimum Line Speed for a High-Resolution Color Image

Next, consider transmitting a larger, uncompressed color image of 1,440 × 900 pixels, with 16 bits per pixel. The total number of pixels is:

Total pixels = 1,440 × 900 = 1,296,000 pixels.

Each pixel requires 16 bits, so the total bits are:

Total bits = 1,296,000 pixels × 16 bits = 20,736,000 bits.

The goal is to transmit this image in less than 0.01 seconds, which requires the minimum line speed to be:

Line speed = Total bits ÷ Time constraint = 20,736,000 bits ÷ 0.01 seconds = 2,073,600,000 bits/sec.

Expressed in Mbps, this is:

2,073,600,000 ÷ 1,000,000 = 2,073.6 Mbps.

Therefore, a line speed of approximately 2.07 Gbps is required to transmit the image within 10 milliseconds. This illustrates the high bandwidth demands of high-resolution uncompressed images, which is why compression techniques are often employed in practice to reduce data size and transmission requirements.

Practical Implications and Conclusions

Understanding the relationship between image size, transmission speed, and time is crucial for designing efficient networks that handle large multimedia data. For low-bandwidth media like the 56 Kbps modem, transmitting large images is impractical within real-time constraints, highlighting the importance of image compression or downscaling in such scenarios. Conversely, high-speed networks like Ethernet can transmit high-resolution images almost instantaneously, enabling applications like remote surgery or high-definition broadcasting.

Furthermore, the calculation for the minimal line speed needed for rapid image transfer underscores the importance of bandwidth planning in network infrastructure development. As image resolutions increase with technological advances, the required network capacity grows proportionally, emphasizing the significance of scalable and high-capacity networking solutions.

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