ECE 2610 Introduction to Signals and Systems
Lab 02: Introduction to Complex Exponentials Multipath
Marwan Al-Juhani
17 Feb 2017
Introduction
Manipulating sinusoid functions using complex exponentials turns trigonometric
problems into simple math. In this
Chapter 3: Spectrum Representation
1
Introduction
In this chapter we will discover how useful it can be to view the frequency content of a signal graphically.
Denition 1. The spectrum of a signal is the collection of amplitude, phase, and frequency infor
ECE 2610 FALL 2012
4
H ARRISON
Periodic Waveforms
Denition 3. A signal is periodic with period T0 sec. if x(t + T0 ) = x(t) for all t.
T0 is called the period.
If T0 is the smallest repetition interval then it is called the fundamental period.
Example:
ECE 2610 FALL 2012
5
H ARRISON
Fourier Series
Any periodic signal can be synthesized with a sum of harmonically related sinusoids. However, we
may need an innite number of sinusoids to do it.
The method for doing this synthesis is called the mathematica
ECE 2610 FALL 2012
6
H ARRISON
Fourier Analysis of Periodic Signals
Since we can synthesize any periodic signal using a sum of sinusoids with harmonic frequencies, lets
pick some that should be quite challenging. In this section we will provide the Fouri
Chapter 4: Sampling and Aliasing
1
Introduction
This chapter deals with converting signals from continuous time (analog) to discrete time (digital),
and from discrete time back to continuous time.
The major result of the chapter is called the Shannon Sa
Chapter 5: FIR Filters
1
Introduction
This chapter begins our study of systems. We will often call systems lters.
The type of systems covered in this chapter are called nite impulse response (FIR) lters. For these
systems, the output is a weighted sum o
Chapter 6: Frequency Response of FIR Filters
1
Introduction
This chapter introduces the concept of the frequency response for linear time-invariant FIR lters.
The frequency response and the impulse response are uniquely related.
When the input to an LT
Chapter 7: z-Transforms
1
Introduction
z-transforms provide a robust domain for system analysis.
Just as we saw with H(ej ), well see that convolution in the time domain is analogous to multiplication in the z-domain as well.
We can represent signals a
Review Topics: ECE 2610
Not guaranteed to be an exhaustive list of important items, but Im pretty sure it is exhaustive.
1
Sinusoids
Complex numbers: Cartesian and Polar Form, conversion between forms, math with complex numbers
Trig identities
Eulers F
Chapter 2: Sinusoids
1
Introduction
This chapter introduces a general class of signals called sinusoidal signals, or sinusoids.
The general mathematical formula is
x(t) = A cos(0 t + ) = A cos(2f0 t + ),
where
0 = 2f0 .
We could also use the sin() func
ECE 2610 Lecture Notes
Chapter 1: Introduction
Reading Assignment: Chapter 1 in the text
Q: What is a signal?
A: Something that carries information
Examples: speech signals, audio signals, video or image signals, communications
signals including wireless
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Lab 08
INSTRUCTOR VERIFICATION PAGE
For each verication, be prepared to explain your answer and respond to other related questions
that the lab TAs or professors might ask. Turn this page in at the end of your lab p
ECE 2610: Introduction to Signals and Systems
Homework Assignment 7
(Due Wednesday, 5 Apr 2017)
Reading Assignment
MSY Chapters 6 and 7
Problem Assignment
Complete the following problems:1
1. A linear time-invariant system has frequency response
H.e j !O
ECE 2610: Introduction to Signals and Systems
Homework Assignment 8
(Due Wednesday, 19 Apr 2017)
Reading Assignment
MSY Chapters 7 and 8
Problem Assignment
Complete the following problems:1
1. The diagram below depicts a cascade connection of two LTI syst
ECE 2610 Introduction to Signals and Systems
Lab 1: Introduction to Matlab
Marwan Al-juhani
02/03/2017
Introduction
The purpose of this lab exercise is to familiarize the user with some basic functions
of MATLAB by generating and plotting sinusoidal signa
Determining wave frequency
from a graph
f
Frequency = #of cycles/time
Measured in Hertz (Hz)
1 cycle = 1 full wave to
repeat itself
3 cycles
1
2
3
4
5
6
Time in seconds
7
8
9
10
11
12
from 0 to 12 seconds
0
1
2
3
4
5
6
Time in seconds
7
8
9
10
11
12
f=
OpenStax-CNX module: m43413
1
Using Complex Exponentials
Chenchi Luo
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0
You should read the Pre-Lab section of the lab and do all the exercises in the Pre-L
Signal Processing First
Lab 02: Introduction to Complex Exponentials Multipath
Pre-Lab and Warm-Up: You should read at least the Pre-Lab and Warm-up sections of this lab assignment
and go over all exercises in the Pre-Lab section before going to your assi
Rice University, ELEC434
Lab 6: FIR Filtering
Fall 2004
ELEC 434
Lab 6: FIR Filtering
by Hyeokho Choi, September 2004
1
Lab Objective
In this lab, you will learn the design and implementation of FIR ltering. The discrete convolution equation
that describe
ECE 2610: Introduction to Signals and Systems
1
code needed to recreate the melody. With incorporating these
Lab 04: Synthesis of Sinusoidal Signals Music
Synthesis
AbstractThe overall lab consisted of creating and
synthesizing sinusoidal waves in order t