What is Digital Signal?

Summary

This lecture distinguishes between analog, discrete time, and digital signals. It explains that digital signals discretize both time and magnitude, unlike discrete time signals which only discretize time. The lecture uses temperature and voltage examples to illustrate how digital signals can only take certain fixed levels, leading to quantization errors that can be minimized by increasing the number of levels. The need for digital signals will be discussed in the next lecture.

Takeaways

• 🕒 The lecture focuses on the concept of digital signals, which are different from analog and discrete time signals.
• 📊 Digital signals require discretization of both time and magnitude, unlike discrete time signals which only discretize time.
• ⏱️ Time discretization is achieved by dividing the time axis into equal intervals, calculated using the formula delta T = (Tn - Tn-1).
• 📉 Magnitude discretization involves dividing the magnitude axis into fixed levels, allowing the signal to take only specific values.
• 🌡️ An example is given where temperature is measured at discrete time intervals, and then the magnitude is also discretized for a digital signal.
• 📉 For digital signals, the signal value is rounded down to the nearest allowed level to minimize error, not up, highlighting the importance of selecting the lower value.
• 🔌 Another example is provided with voltage measurements, where increasing the number of allowed levels reduces the error in signal representation.
• 📊 Increasing the number of levels in a digital signal allows for more precise measurements and reduces the error compared to fewer levels.
• 💡 The lecture concludes with a teaser for the next session, which will discuss the necessity of digital signals despite the existence of analog and discrete time signals.
• 💬 The presenter encourages the audience to think about and share their thoughts on why digital signals are needed in the comments.

Q & A

What is the main difference between analog signals and digital signals?

Analog signals have continuous values over time, while digital signals are discretized both in time and magnitude, meaning they can only take specific values at specific time intervals.

How is the time axis discretized in digital signals?

In digital signals, the time axis is discretized by dividing it into equal intervals, which can be calculated using the formula delta T = (Tn - Tn-1) for any given time points Tn and Tn-1.

What is meant by discretizing the magnitude axis in digital signals?

Discretizing the magnitude axis in digital signals involves dividing the range of possible values into a fixed number of levels, and the signal can only take values that correspond to these levels.

Can you provide an example of how temperature is measured in a digital signal?

In the example given, the temperature at different times (T1, T2, T3, T4, T5) is measured in degrees Celsius. For a digital signal, the magnitude axis is discretized into levels such as 0, 15, 30, and 45 degrees Celsius, and the temperature at each time point is rounded down to the nearest allowed value.

Why is the lower value chosen when a measured value falls between two discrete levels?

The lower value is chosen to minimize the error. This approach ensures that the signal value is always closer to the actual measured value than the next higher level would be.

How does the number of levels affect the error in digital signals?

Increasing the number of levels in a digital signal reduces the error. More levels mean that the discretized values are closer to the actual continuous values, leading to a more accurate representation of the signal.

What is the significance of the statement 'the signal can take value equal to this levels only' in the context of digital signals?

This statement emphasizes that digital signals are limited to specific, predefined values or levels. They cannot represent values that lie between these levels, which is a key characteristic of digital signals.

How is the error reduced when measuring voltage in a digital signal?

The error is reduced by increasing the number of levels allowed for the voltage. In the example, when the voltage is discretized into more levels, a voltage of 2 volts can be accurately represented as 2 volts, reducing the error to zero.

What is the purpose of dividing the magnitude axis into fixed levels in digital signals?

Dividing the magnitude axis into fixed levels allows for easier digital processing and storage of the signal. It also facilitates the transmission of signals with reduced error and complexity.

What is the question posed at the end of the script regarding digital signals?

The question is: 'If we were already having analog and discrete time signals, then what is the need for digital signals?' This question prompts consideration of the advantages and applications of digital signals over analog and discrete time signals.