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
Review Topics: ECE 2610
Not guaranteed to be an exhaustive list of important items, but Im pretty sure it is exhaustive.
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Sinusoids
Complex numbers: Cartesian and Polar Form, conversion between forms, math with complex numbers
Trig identities
Eulers F
Chapter 7: z-Transforms
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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
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 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 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
ECE 2610 FALL 2012
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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
ECE 2610 FALL 2012
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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
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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:
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
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: Introduction to Signals and Systems
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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