I Previously on IET Complex Exponential Function ImAxis

  • Slides: 23
Download presentation
I. Previously on IET

I. Previously on IET

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 2

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 2

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 3

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 3

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 4

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 4

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 5

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 5

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 6

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 6

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 7

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 7

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 8

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 8

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 9

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 9

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 10

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 10

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 11

Complex Exponential Function Im-Axis ω © Tallal Elshabrawy Re-Axis 11

The Fourier Transform Representing functions in terms of complex exponentials with different frequencies ©

The Fourier Transform Representing functions in terms of complex exponentials with different frequencies © Tallal Elshabrawy 12

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal Elshabrawy 13

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal Elshabrawy 14

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal Elshabrawy 15

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal Elshabrawy 16

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal

The Fourier Transform (Cosine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal Elshabrawy 17

The Fourier Transform (Sine Function) Im-Axis ω Re-Axis - -ω Re-Axis © Tallal Elshabrawy

The Fourier Transform (Sine Function) Im-Axis ω Re-Axis - -ω Re-Axis © Tallal Elshabrawy 18

The Fourier Transform (Sine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal

The Fourier Transform (Sine Function) Im-Axis ω Re-Axis + -ω Re-Axis + © Tallal Elshabrawy 19

The Fourier Transform (Sine Function) Im-Axis Re-Axis -ω ω © Tallal Elshabrawy 20

The Fourier Transform (Sine Function) Im-Axis Re-Axis -ω ω © Tallal Elshabrawy 20

The Fourier Transform (Sine Function) -ω Im-Axis Re-Axis + Im-Axis Re-Axis ω + ©

The Fourier Transform (Sine Function) -ω Im-Axis Re-Axis + Im-Axis Re-Axis ω + © Tallal Elshabrawy 21

Fourier Transform of Sinusoids 1/2 -ω 0 1/2 j(1/2) ω -ω 0 ω -j(1/2)

Fourier Transform of Sinusoids 1/2 -ω 0 1/2 j(1/2) ω -ω 0 ω -j(1/2) Notes l l A real value for the coefficients in the frequency domain means that the starting point for rotation is on the real axis An Imaginary value for the coefficients in the frequency domain means that the starting point for rotation is on the imaginary axis © Tallal Elshabrawy 22

Fourier Transform of Real Valued Functions Im-Axis ωn ω1 Im-Axis Re-Axis ω2 Im-Axis -ω2

Fourier Transform of Real Valued Functions Im-Axis ωn ω1 Im-Axis Re-Axis ω2 Im-Axis -ω2 Re-Axis -ω1 -ωn A real-valued function in time implies that G(-f) = G*(f) © Tallal Elshabrawy 23

8 1 Exponential Growth Exponential Function Exponential function8 1 Exponential Growth Exponential Function Exponential function
Exponential Functions What is an exponential function ExponentialExponential Functions What is an exponential function Exponential
The Natural Exponential Function Natural Exponential Function AnyThe Natural Exponential Function Natural Exponential Function Any
Natural Exponential Function Natural Exponential Function The baseNatural Exponential Function Natural Exponential Function The base
Exponential Function Definition The exponential function is givenExponential Function Definition The exponential function is given
Exponential Functions An exponential function is a functionExponential Functions An exponential function is a function
EXPONENTIAL FUNCTIONS Objectives Evaluate Exponential Functions Graph ExponentialEXPONENTIAL FUNCTIONS Objectives Evaluate Exponential Functions Graph Exponential
Exponential Functions y x Exponential Growth Exponential DecayExponential Functions y x Exponential Growth Exponential Decay
Exponential Functions Warmup Exponential Funtion The exponential funtionExponential Functions Warmup Exponential Funtion The exponential funtion
Exponential EXPONENTIAL JEOPARDY Exponential GF GR GR GFExponential EXPONENTIAL JEOPARDY Exponential GF GR GR GF
I Previously on IET Introduction to Digital ModulationI Previously on IET Introduction to Digital Modulation
I Previously on IET Phase Shift Keying PSKI Previously on IET Phase Shift Keying PSK
DiscreteTime Complex Exponential Sequence 1 Real Exponential SignalDiscreteTime Complex Exponential Sequence 1 Real Exponential Signal
7 1 Exponential Functions An exponential function has7 1 Exponential Functions An exponential function has
Exponential functions The equation defines the exponential functionExponential functions The equation defines the exponential function
Exponential Functions Definition of the Exponential Function TheExponential Functions Definition of the Exponential Function The
Exponential Functions and Their Graphs The exponential functionExponential Functions and Their Graphs The exponential function
The Exponential Distribution Probability density function The ExponentialThe Exponential Distribution Probability density function The Exponential
DAY 107 EXPONENTIAL GROWTH AND DECAY EXPONENTIAL FUNCTIONDAY 107 EXPONENTIAL GROWTH AND DECAY EXPONENTIAL FUNCTION
Exponential Logarithmic Function Chapter 5 5 1 ExponentialExponential Logarithmic Function Chapter 5 5 1 Exponential
Exponential Functions Exponential Function fx ax for anyExponential Functions Exponential Function fx ax for any
Exponential Functions and Their Graphs The exponential functionExponential Functions and Their Graphs The exponential function