Digital Signal Processing (LECTURE 1-4)

SIGNAL

It is a physical quantity, or quality, which conveys information

Continuous-time(CT) signals

signals that are defined at all instants of time. Usually denoted by 𝑥(𝑡)

Discrete-time (DT) signals

signals identified as sequence of numbers. Usually denoted by 𝑥[𝑛]

Continuous-valued (CV) signals

signals that takes all possible values on a finite or an infinite range

Discrete-valued (DV) signals

• signals identified as sequence of numbers. Usually denoted by 𝑥[𝑛]

• Take discrete values.
  

Multichannel Signals

signals that are generated by multiple sources or multiple sensors.

Multidimensional Signals

signals with values from multiple independent variables

Deterministic Signals

signals that can be uniquely described by an explicit mathematical expression

Random Signals

signals that cannot be exactly known or that are unpredictable

Real-valued signals

signals that contain real values.

Complex-valued signals

signals that contains two values that are typically quadrature (90-deg) separated

SYSTEM

It is an entity that manipulates one or more signals to accomplish a function, thereby yielding new signals.

SIGNAL PROCESSING

• It is the process of converting of input to output signal.

• A typical reason for signal processing is to eliminate or reduce an undesirable signal

TYPES OF SIGNAL PROCESSING

• Analog Signal Processing

• Digital Signal Processing

EXAMPLES OF DIGITAL SIGNAL PROCESSING

• Digital Filtering: Removing noise or unwanted components from signals.

• Interference Cancellation in ECG: Eliminating noise from biomedical signals.

• Signal Spectrum Analysis: Analyzing the frequency components of a signal.

• CD Recording and Playback Systems: Processing of audio signals in digital media.

Types of Signals

• Continuous-time (CT) signals: Defined at all instants of time, represented as x(t)x(t)x(t).

• Discrete-time (DT) signals: Identified as a sequence of numbers, represented as x[n]x[n]x[n].

• Continuous-valued (CV) signals: Take all possible values within a range.

• Discrete-valued (DV) signals: Take discrete values.

• Multichannel signals: Generated by multiple sources or sensors (e.g., multi-lead ECG).

• Multidimensional signals: Defined by multiple independent variables (e.g., images, TV signals).

Classification of Signals

• Deterministic signals: Can be exactly described by a mathematical expression.

• Random signals: Cannot be precisely predicted.

• Real-valued signals: Contain real values.

• Complex-valued signals: Contain two quadrature (90-degree separated) components.

Analog Signal Processing

Signals are processed in their analog form (e.g., traditional filters).

Digital Signal Processing (DSP)

Signals are converted to digital form, processed, and then converted back to analog if necessary

Typical Digital Signal Processing System

• Analog-to-Digital Conversion (A/D): Converts continuous-time continuous-value (CT-CV) analog signals into discrete-time continuous-value (DT-CV) signals.

• Digital-to-Analog Conversion (D/A): Converts processed digital signals back into analog signals.

Sampling

• The process of converting a continuous-time signal (CT) into a discrete-time signal (DT) by taking samples at regular intervals.

The number of samples taken per second (in Hz).

Nyquist-Shannon Sampling Theorem

To perfectly recover an analog signal, the sampling rate must be at least twice the highest frequency component of the signal.

Aliasing

A distortion that occurs when a signal is undersampled, causing high-frequency components to appear as lower frequencies in the sampled signal.

Analog Signals (Time and Frequency Domain)

Digital Signals (Time and Frequency Domain)

Undersampling

Occurs when the sampling rate is lower than the Nyquist rate, leading to aliasing (high-frequency signals appear as lower frequencies).

Oversampling

• Sampling above the Nyquist rate

• Oversampling creates more space in the frequency spectrum, which reduces the demands on the anti-aliasing filter.

Quantization

The process of converting a discrete-time continuous-amplitude signal into a digital signal by assigning each sample value a finite number of digits.

Two key parameters in quantization

Types of Quantization

1. Unipolar Quantizer

   • Deals with analog signals ranging from 0 volt to a positive reference voltage.

   • Maximum Error: Full step size

2. Bipolar Quantizer

   • Deals with analog signals ranging from a negative reference voltage to a positive reference voltage.

   • Maximum Error: Half step size.

Coding

The process of assigning a unique binary number to each quantization level.

Dynamic Range (DR)

The ratio between the largest and smallest value that the analog-to-digital converter (ADC) can reliably measure.

Signal-to-Quantization-Noise Ratio (SQNR)

The ratio of the signal power to the quantization noise.