Bit Depth and Dithering
🎯 Learning Objectives:
In this topic, we will explore the concept of binary representation of states as bit, and how bit depth applies to representing audio amplitude levels. We will examine the real world affects and artifacts of low resolution audio file and hear the effects of quantization noise or error. We will look at signal to quantization noise ratio (SQNR) as a metric for measuring the dynamic range of signals.
In the previous topic we saw the need to split the amplitude axis into discrete levels. Analog values nearby are quantized or latched into these discrete levels so that we get a finite set of measurable values. The number of levels that we can use to represent different amplitude depends fundamentally on how data is represented and stored in the digital format. On fundamentally the smallest unit of data in electronics is a switch or a binary bit where data or the state value can be represented as either ON or OFF, a HIGH or LOW, a 1 or 0, two possible values. We can expand this binary system to include a cascade of switches or bits. Though a single bit can only represent two distinct values, a number of bits together can quickly escalate the number of distinct state representations possible. Two bets can represent four unique states, three bits can represent eight, four bits can represent 16 and so on. We can see a pattern here the growth is exponential. More precisely, the growth in the number of unique states possible is a power of 2 (). Here, is the number of bits used.
We can see that things grow pretty fast in an exponential setting. A 16 bits can represent 65,500 different values, 24 bits can represent 16.7 million values and 32 bits can represent a whopping 4.2 billion state values.
Let us try and draw some parallels between the binary number system or the base 2 number system and the system that we are most accustomed to, the decimal number system or the base 10 number system.
Figure 1. Sine wave of single frequency in time domain
Let us take an example of 8 bits. 8 bits can accommodate different unique states that is 256 different values from the zeroth state when all the bits are low to the 255th state when all the bits are high. The binary system is base two since each digit is capable of representing two states either zero or one and likewise the decimal system is base ten as each digit has a range between 0 and 9. Numbers in both systems are written from left to right with the most significant digit on the left side and the least significant digit on the right. The smallest group of bits is called a byte and a byte is just a group of eight bits thus a byte is the smallest addressable unit of memory in computer architectures that is one of the reasons why we find bit rates or bit depths.
🧪 Interactive Demo
Bit Depth & Dithering with Audio
📝 Key Takeaways
- Add key takeaway
🧠 Quick Quiz
1️⃣ How many unique states can be represented by a single bit?
2️⃣ If we use 4 bits, how many distinct amplitude levels can be represented?
3️⃣ Numerical: A digital audio system uses 8-bit quantization. What is the range of possible integer values it can represent?
4️⃣ What is the smallest group of bits that can be addressed as a unit in computer memory?
5️⃣ True/False: Increasing the number of bits exponentially increases the number of quantization levels.
6️⃣ Numerical: How many unique states can be represented with 12 bits?
7️⃣ How many bits are required to represent 65,536 unique amplitude levels?
8️⃣ The binary number system is base 2. What does each bit represent?
9️⃣ Numerical: A system uses 24-bit quantization. How many discrete amplitude levels does this provide?
1️⃣0️⃣ In comparing binary and decimal systems, which statement is correct?