Advanced Digital Systems Overview

Advanced Digital Systems

• This presentation covers the fundamental concepts of advanced digital systems.

• Topics include analog-to-digital conversion, Nyquist-Shannon sampling theorem, continuous-time and discrete-time signals.

• Continuous-time signals are defined for all time within an interval on the real line.

• Discrete-time signals are sequences of values corresponding to specific moments in time.

Analog vs Digital Signals

• Analog signals have high information density and accuracy representing continuous phenomena (sound, light, temp, position, pressure).

• They are subject to noise and distortion.

• Digital signals are more secure and easily compressed due to encryption.

• Digital signals transmit over longer distances.

• Digital systems are more complex and use high power dissipation.

Analog to Digital Conversion

• The process involves sampling, quantization, and coding.

• An analog signal is transformed into a digital signal through a three-step process, using analog-to-digital converters (A/D), digital signal processors, and digital-to-analog converters (D/A).

• Sampling: Measures the continuous-time signal at discrete time instances.

• Quantization: Converts the discrete sample values to a set of quantized levels.

• Coding: Represents these quantized values using a digital code (bits).

Nyquist-Shannon Sampling Theorem

• Sampling rate must exceed the highest signal frequency by at least a factor of two.

• This ensures the original analog signal can be perfectly reconstructed. This is represented as: fs ≥ 2fmax, where fs is the sampling rate and fmax is the maximum frequency.

The Sampling Rate

• Calculated as 1/T, where T is the sampling period (time between samples).

• Example: A sampling period of 1ms results in a sampling rate of 1kHz (1000 samples per second).

Examples of Continuous & Discrete-Time Signals

• Continuous: Voice, video, sensor output

• Discrete: Average budget, crime rate, total population

Signal Representation (Continuous Time)

• A continuous-time signal can be visualized using a graph showing how the signal changes over time, e.g., a ramp, a step, a sine wave

Signal Representation (Discrete Time)

• A discrete-time signal is represented as a sequence of values at specific time points on a number line.

Discrete Time Signal - Time Shifting

• Shifting a discrete-time signal to the right or left.

Discrete Time Signal - Reflection

• Reflecting a discrete-time signal around the vertical axis.

Discrete Time Signal - Time Scaling

• Scaling or compressing the signal in the horizontal direction.

Exponential Signals

• Discrete-time signals can be exponential, increasing or decreasing.

Periodic Signals

• Continuous-time and discrete-time signals can be periodic. Periodic signifies the signal repeatedly repeats itself over time.

• Continuous-time signals repeat themselves after a period T : x(t)=x(t+T).

• Discrete-time signals repeat themselves after a period N: x[n]=x[n+N].

Even & Odd Signals

• Even signals are symmetrical around the vertical axis: x(-t) = x(t)

• Odd signals are antisymmetrical around the vertical axis: x(-t) = -x(t)

Even & Odd decomposition of discrete-time signals

• Any discrete-time signal can be split into its even and odd components.

Discrete-Time Unit Impulse

• A signal that has a value of 1 at n = 0 and zero otherwise.

Discrete-Time Unit Step

• A signal that has a value 0 for n < 0 and 1 for n ≥ 0.

Relation between Unit Impulse & Unit Step

• The unit step function can be expressed in terms of the unit impulse function: u[n] = Σ δ[m], where the summation is from ∞ to n=-∞.

Reading List

• Signals & Systems by Allan Oppenheim and Alan Wilsky, Chapter 1 (recommended textbook).

This quiz explores the fundamental concepts of advanced digital systems, including analog-to-digital conversion and signal types. Understand the differences between analog and digital signals, their characteristics, and the processes involved in conversion. Ideal for students studying digital systems.