To determine the minimum sampling frequency for baseband sampling of the given amplitude modulated signal, we need to first understand the characteristics of the signal after the specified suppressions.

1. Understanding the Signal Parameters:

• Carrier Signal Frequency ($f_c$): The carrier signal has a frequency of 1 MHz, which is equivalent to 1000 kHz.
• Modulating Signal Frequency ($f_m$): The sinusoidal modulating signal has a frequency of 10 kHz.

2. Analyzing the Amplitude Modulated Signal:

In a standard Amplitude Modulated (AM) system with a sinusoidal modulating signal, the modulated signal typically contains three main frequency components:

• The carrier frequency ($f_c$).
• The Upper Sideband (USB) frequency, which is $f_c + f_m$.
• The Lower Sideband (LSB) frequency, which is $f_c - f_m$.

Let's calculate these frequencies:

• Carrier Frequency: $f_c = 1000 \text{ kHz}$
• Upper Sideband (USB) Frequency: $f_c + f_m = 1000 \text{ kHz} + 10 \text{ kHz} = 1010 \text{ kHz}$
• Lower Sideband (LSB) Frequency: $f_c - f_m = 1000 \text{ kHz} - 10 \text{ kHz} = 990 \text{ kHz}$

3. Effect of Suppression:

The question states that the "lower sideband and the carrier are suppressed". This means that only the Upper Sideband (USB) signal remains. Therefore, the signal that needs to be sampled is a Single Sideband (SSB) signal, specifically the USB signal.

The USB signal exists at the frequency $f_c + f_m$, which is $1010 \text{ kHz}$. If the modulating signal were a band of frequencies, the USB would occupy a band from $f_c$ to $f_c + f_{m\_max}$. For a single tone, it's a single frequency component. However, when we talk about a "signal" in this context, it implies the entire bandpass signal containing that information.

In this case, the highest frequency component present in the USB signal is $1010 \text{ kHz}$.

4. Applying the Nyquist-Shannon Sampling Theorem:

The Nyquist-Shannon sampling theorem states that for perfect reconstruction of a signal from its samples, the sampling frequency ($f_s$) must be at least twice the highest frequency component present in the signal ($f_{max}$).

The signal being sampled is the USB signal, and its highest frequency component is $f_{max} = 1010 \text{ kHz}$.

Therefore, the minimum sampling frequency ($f_s$) should be:

$$f_s \geq 2 \times f_{max}$$

$$f_s \geq 2 \times 1010 \text{ kHz}$$

$$f_s \geq 2020 \text{ kHz}$$

This minimum sampling frequency ensures that the sampled amplitude modulated signal (the USB signal) can be accurately reconstructed. Once reconstructed, further processing (like coherent demodulation) can then convert this high-frequency bandpass signal back to its original baseband message signal, thus achieving "baseband sampling" indirectly by processing the sampled modulated signal.

Comparing this result with the given options:

• 1000 kHz
• 990 kHz
• 1980 kHz
• 2020 kHz

The calculated minimum sampling frequency of 2020 kHz matches one of the options.