Consider the periodic message signal x(t) shown below, where the period is 3 sec: x(t) 2 1 t (sec) -1 a) If the modulation is DSBSC, x(t) cos(@.t), sketch the modulated waveform. CO 3.

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**Transcription and Detailed Explanation for Educational Context:**

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### Periodic Message Signal Overview

The image showcases a periodic message signal, denoted as \( x(t) \), with a specified period of 3 seconds. The waveform is a square wave that oscillates between 1 and -1.

**Graph Details:**

- **Vertical Axis (\( x(t) \)):** Represents the amplitude of the signal, ranging from -1 to 1.
- **Horizontal Axis (\( t \)):** Represents time in seconds.

**Signal Description:**

- **Interval 0 to 1 second:** The amplitude is at 1.
- **Interval 1 to 2 seconds:** The amplitude shifts to -1.
- **Interval 2 to 3 seconds**: The amplitude returns to 1.

This pattern repeats for subsequent periods:
- **Interval 3 to 4 seconds:** Amplitude is 1.
- **Interval 4 to 5 seconds:** Amplitude is -1.
- **Interval 5 to 6 seconds:** Amplitude is 1.

### Modulation Task

**Question (a):** If the modulation is Double Sideband Suppressed Carrier (DSBSC), represented as \( x(t) \cos(\omega_c t) \), sketch the modulated waveform.

**Explanation:**

- **DSBSC Modulation:** It involves multiplying the message signal \( x(t) \) by a carrier cosine wave \( \cos(\omega_c t) \).
- **Requirement:** Sketch the resultant waveform after modulation.

The modulated waveform will have the characteristics of the original square wave, altered by the frequency and phase of the carrier cosine wave, often appearing as a varying amplitude signal shaped by \( \cos(\omega_c t) \).

---

This transcription is intended for educational purposes, providing a clear understanding of periodic signals and modulation techniques.
Transcribed Image Text:**Transcription and Detailed Explanation for Educational Context:** --- ### Periodic Message Signal Overview The image showcases a periodic message signal, denoted as \( x(t) \), with a specified period of 3 seconds. The waveform is a square wave that oscillates between 1 and -1. **Graph Details:** - **Vertical Axis (\( x(t) \)):** Represents the amplitude of the signal, ranging from -1 to 1. - **Horizontal Axis (\( t \)):** Represents time in seconds. **Signal Description:** - **Interval 0 to 1 second:** The amplitude is at 1. - **Interval 1 to 2 seconds:** The amplitude shifts to -1. - **Interval 2 to 3 seconds**: The amplitude returns to 1. This pattern repeats for subsequent periods: - **Interval 3 to 4 seconds:** Amplitude is 1. - **Interval 4 to 5 seconds:** Amplitude is -1. - **Interval 5 to 6 seconds:** Amplitude is 1. ### Modulation Task **Question (a):** If the modulation is Double Sideband Suppressed Carrier (DSBSC), represented as \( x(t) \cos(\omega_c t) \), sketch the modulated waveform. **Explanation:** - **DSBSC Modulation:** It involves multiplying the message signal \( x(t) \) by a carrier cosine wave \( \cos(\omega_c t) \). - **Requirement:** Sketch the resultant waveform after modulation. The modulated waveform will have the characteristics of the original square wave, altered by the frequency and phase of the carrier cosine wave, often appearing as a varying amplitude signal shaped by \( \cos(\omega_c t) \). --- This transcription is intended for educational purposes, providing a clear understanding of periodic signals and modulation techniques.
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