Question

Show how a modem would encode the 5-bit binary sequence 11001 onto an analog carrier by a. Modifying its amplitude (the height of the carrier wave) b. Modifying its frequency (the number of waves per second)

Short answer

Amplitude Modulation: High-High-Low-Low-High. Frequency Modulation: High-High-Low-Low-High.

Step-by-step solution

Understanding Amplitude Modulation (AM)

Amplitude Modulation involves varying the height (amplitude) of the carrier wave to represent the binary sequence. "1" might be represented by a higher amplitude, while "0" could be represented by a lower amplitude.

Map 5-bit Sequence to Amplitude Levels

Assign amplitude levels for each bit in the sequence. For instance, use a high amplitude for '1' and a low amplitude for '0'. In the sequence 11001, the translated amplitude sequence would be High-High-Low-Low-High.

Understanding Frequency Modulation (FM)

Frequency Modulation involves changing the frequency of the carrier wave to encode data. Higher frequency might be used for '1', and a lower frequency for '0'.

Map 5-bit Sequence to Frequency Levels

Apply specific frequency values for each bit. For the binary sequence 11001, the carrier wave's frequency should be adjusted to High-High-Low-Low-High frequency.

Key concepts

Amplitude Modulation

Amplitude Modulation (AM) is a technique used to encode digital data into analog signals by varying the wave's amplitude. Imagine the carrier wave as a smooth wave-like curve that travels over time. With AM, this curve is adjusted based on the digital information it needs to represent. For illustration:

• A '1' might correspond to a high amplitude, which means the wave would appear taller or more intense.
• A '0' could be a low amplitude, making the wave seem shorter and less intense.

In the case of the 5-bit sequence 11001, each bit is mapped to a specific amplitude level: - The first '1' causes the carrier wave to have a high amplitude, - The second '1' maintains this high amplitude, - The third '0' shifts it to a low amplitude, - The fourth '0' continues with the low amplitude, - Finally, the last '1' returns the wave to a high amplitude.
This modulation technique effectively allows digital information to travel across mediums that mainly support analog signals, like radio waves.

Frequency Modulation

Frequency Modulation (FM) works by modifying the pitch of the carrier wave. Instead of amplitude, what changes this time is how frequently the wave completes a cycle. Each bit of the binary sequence influences this frequency, creating a pattern in the wave's cycles. Here's how it can be broken down:

• A '1' may increase the frequency, producing waves that are close together.
• A '0' might decrease the frequency, resulting in broader spaced waves.

Applying this to the 5-bit sequence 11001 results in: - The first '1' translating to a higher frequency, - The second '1' keeps the frequency high, - The third '0' drops it to a lower frequency, - The fourth '0' continues the lower frequency, - The last '1' lifts the frequency back to high.
FM is popularly used in broadcasting audio and music as it provides clear signal transmission with reduced noise interference compared to AM.

Binary Encoding

Binary Encoding is the backbone of digital communication and is essential for translating digital data into formats suitable for analog transmission. In essence, it involves assigning specific parameters or properties to represent the digital '1's and '0's. This encoding facilitates compatibility with various transmission techniques like modulation.

• Each bit ('1' or '0') is a fundamental piece of information and must be encoded correctly to ensure accurate data delivery.
• Binary Encoding utilizes different methods for different forms of communication, ensuring that digital information aligns well with the modulation strategy employed.

This concept is significant in both AM and FM modulation processes. For instance: - In AM, binary '1's and '0's directly adjust the wave height. - In FM, these bits tweak how frequent the wave repeats. Understanding Binary Encoding ensures clarity in how digital signals are prepared for transmission, enhancing the efficiency and accuracy of data communication systems.