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Lecture 2

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This lecture

• Concept of Signal Processing• Introduction to Signals• Classification of Signals• Basic elements of SP System• Analog to Digital Conversion

– Sampling – Quantization

• Nyquist Theorem• Applications of Signal Processing

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Signal Processing

• Representation, transformation, manipulation of signals and the information they contain.

• Classification:

Depends upon the type of signal to be processed.

• Analog Signal Processing

• Digital Signal Processing

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Signal Processing

• Analog SP

Continuous time signals are processed.

• Digital SP

Discrete - time discrete - valued signals processed by digital computers or other data processing machines.

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Signal??

• Any indication / information

• A change in which some information is residing

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Classification of Signals

• Continuous-time / Discrete-time Signals

• Continuous-valued / Discrete-valued Signals

• Deterministic / Random Signals

• One-dimensional / Multi-dimensional Signals

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Fundamental SP system

• Most signals – Analog in nature.

• Analog to Digital Converter is used as an interface between analog signal and Digital Signal Processor.

A/D Converter D/A ConverterDigital Signal

Processor

Analog

Input Signal

Analog

Output Signal

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A-D Conversion

1. Sampling• First step in going from analog to digital.• In signal processing, sampling is the

reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous-time signal) to a sequence of samples (a discrete-time signal).

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Sampling

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Nyquist Theorem

• In order the samples represent correctly the analog signal, the sampling frequency must be greater than twice the maximum frequency of the analog signal:

• fs≥2FM

• The limiting frequency 2FM is called Nyquist rate.

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Aliasing (Time Domain)

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Aliasing (Frequency Domain)

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Methods of avoiding Aliasing

• To avoid aliasing, there are two approaches: One is to raise the sampling frequency to satisfy the sampling theorem.The other is to filter off the unnecessary high-frequency components from the continuous-time signal. We limit the signal frequency by an effective low-pass filter, called anti-aliasing prefilter, so that the highest frequency left in the signal is less than half of the intended sampling rate.

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General DSP System

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Quantization

• Slide 143 CCN module 2• MIT OCW

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Applications of SP

• RADAR• SONAR• Medical• Image Processing

– Pattern recognition– Edge detection

• Audio Signal Processing– Speech generation– Speech recognition– Speaker identification

• Telecommunications– Multiplexing– Compression– Echo control