Given the continuous time digital signal as shown with an effective bit rate of 55,000 bits / sec,
Determine the **minimum sampling rate** of an ADC converter if the analog input is sampled at 8 samples per bit and the code word length is just 1 bit. Express your answer in **KHz** and in at least 3 significant figures

To determine the **minimum sampling rate** of an ADC (Analog-to-Digital Converter), we can follow the information provided:

### Given:
- **Bit rate** = 55,000 bits/sec
- **Samples per bit** = 8
- **Code word length** = 1 bit (this means that each sample is represented by a single bit)

### Steps to Determine the Minimum Sampling Rate:

1. **Bit rate** tells us how many bits are being transmitted per second. This includes the information about the rate of bits being handled.

2. **Samples per bit** means that for each bit, we are sampling the signal 8 times.

3. The **sampling rate** of the ADC should be such that it accounts for both the bit rate and the number of samples taken for each bit.

### Formula:
The **sampling rate** \( f_s \) is the product of the bit rate and the samples per bit.

\[
f_s = \text{{Bit rate}} \times \text{{Samples per bit}}
\]

### Calculation:

\[
f_s = 55,000 \, \text{bits/sec} \times 8 \, \text{samples/bit}
\]
\[
f_s = 440,000 \, \text{samples/sec}
\]

To express this in kilohertz (kHz):

\[
f_s = \frac{440,000}{1000} = 440 \, \text{kHz}
\]

### Answer:
The **minimum sampling rate** of the ADC converter is **440 kHz**, expressed to at least three significant figures.

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Do you want more details or have any questions about this calculation?

### Related Questions:
1. How does the bit rate affect the resolution of an ADC converter?
2. Why is the sampling rate directly proportional to the bit rate in this context?
3. What happens if the sampling rate of an ADC is lower than the calculated minimum?
4. Can the code word length impact the overall data rate in this system?
5. What is the significance of Nyquist theorem in determining the sampling rate for an ADC?

### Tip:
Always ensure the sampling rate is at least twice the highest frequency of the analog signal, according to the **Nyquist-Shannon sampling theorem**, to avoid aliasing.

Given the continuous time digital signal as shown with an effective bit rate of 55,000 bits / sec, Determine the **minimum sampling rate** of an ADC converter if the analog input is sampled at 8 samples per bit and the code word length is just 1 bit. Express your answer in **KHz** and in at least 3 significant figures.

Calculate the minimum sampling rate of an ADC converter for a digital signal with a 55,000 bits/sec bit rate, 8 samples per bit, and a code word length of 1 bit. Learn how to express the sampling rate in kHz and the role of the Nyquist-Shannon sampling theorem.

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