x[n] y[n] C2
Quantization and Resolution
Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.
Probability of Error
This topic is widely taught in many undergraduate and postgraduate degree courses of:
Find values of c1 and c2 that make the system stable. Why do these values make the system stable? Explain
![**Block Diagram for a Discrete Time System**
Consider the following block diagram for a discrete time system. Recall that \( z^{-1} \) is a unit delay and that triangles represent constant gains of \( c_1 \) and \( c_2 \).
**Explanation of the Diagram:**
1. **Inputs and Outputs:**
- The input signal is represented as \( x[n] \).
- The output signal from the system is represented as \( y[n] \).
2. **Delays:**
- There are two boxes labeled \( z^{-1} \) that indicate unit delays in the system. These delays are functions that shift the discrete signal by one time unit.
3. **Summation:**
- The circular symbol in the middle represents a summation junction where inputs are summed together.
4. **Gains:**
- Two triangles denote constant gains:
- \( c_1 \) and \( c_2 \) are applied to the signals before they enter the summation.
5. **Signal Flow:**
- The input \( x[n] \) first goes through a unit delay \( z^{-1} \), and then both through the gain \( c_1 \) and directly into the summation junction.
- The output of \( c_1 \) moves forward into the summation.
- Another branch from the summation goes through the gain \( c_2 \) and then into another unit delay \( z^{-1} \) before reaching the output \( y[n] \).
This block diagram represents a system involving delays and scaled signals, typically used to model digital filters or similar signal processing elements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbd9345f-cdaf-40a0-9604-7a9d3647c236%2F01ebd7ac-ba75-4423-8ca5-5e80a671a816%2F15ux4cl_processed.png&w=3840&q=75)
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