DISCRETETIME SINUSOIDAL SIGNALS Copyright 2012 Instructor Dr Glden
![To illustrate this property, let x[n]=cos (Ω 1 n) Consider frequency Ω 1 n=0,](https://slidetodoc.com/presentation_image_h2/5b4158119e9dfa33aae7c8deeadc4633/image-8.jpg "To illustrate this property, let x[n]=cos (Ω 1 n) Consider frequency Ω 1 n=0,")
- Slides: 27
DISCRETE-TIME SINUSOIDAL SIGNALS Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Properties of Discrete. Time Sinusoids: Property 1 - A discrete-time sinusoid is periodic ONLY IF ITS FREQUENCY F IS RATIONAL NUMBER I (Compare with continuous sinusoids: A continuous-time sinusoid is always periodic, for any value of its frequency, f 0) Definition: x[n] is periodic with period N (N>0 and integer) if and only if x[n]=x[n+N] for all n. The smallest value of N for which above equation is true is called the fundamental period. Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Proof of Periodicity Property: Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
To illustrate this property, let x[n]=cos (Ω 1 n) Consider frequency Ω 1 n=0, π/8, π/4, π/2, π (or equivalently, F 1=0, 1/16, 1/8, 1/4, 1/2) which result in periodic discrete-time sinusoids with periods N= ∞, 16, 8, 4, 2. Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
SAMPLING OR ANALOG SIGNALS Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
The Sampling Theorem Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING
Copyright 2012 | Instructor: Dr. Gülden Köktürk | EED 1004 -INTRODUCTION TO SIGNAL PROCESSING