# Shared Flashcard Set

## Details

Fourier Series & Fourier Transform
CPE 351 - Signals & Systems (QUIZ 04)
19
Engineering
04/04/2011

Term
 List two(2) ways to compute the energy of a continuous time signal.
Definition
 1) In the time domain by integrating |x(t)|² over the entire time axis.2) In the frequency domain by integrating |X(ω)|² over the entire frequency axis.
Term
 What is the phase response of an LTI system?
Definition
 Angle of H(ω)
Term
 Continuous-Time Fourier Series means...
Definition
 Each component's importance is indicated by the Fourier coefficient, "X[k]".
Term
 For the Fourier series & the Fourier transform:Which one applies to periodic signals?
Definition
 Fourier Series...The complex exponentials form the basis for the periodic function.
Term
 For the Fourier series & the Fourier transform:Who's frequency is discrete?
Definition
 Fourier Series...The frequency band is discrete (multiples of the fundamental frequency).
Term
 What is the frequency response of an LTI system?
Definition
 The Fourier transform of the systems impulse response.
Term
Definition
 The energy of a signal & calculating it's bandwidth.Eₓ = ʃx(t)²dt <=> (1/2π)ʃ|X(ω)|²dω
Term
 What is the magnitude response of an LTI system?
Definition
 The magnitude of Fourier transform.|H(ω)|
Term
 What conditions must a LTI system satisfy for the system to be distortionless?
Definition
 The magnitude response |H(jω)| must be constant for all frequencies of interest; |H(jω)|=C
Term
 Continuous-Time Fourier Series means...
Definition
 The signal, x(t) can be decomposed into many frequency components.
Term
 Explain analysis of a signal.
Definition
 To analyze the signal x(t) by compressing it into its components.
Term
 The idea of Fourier transform:
Definition
 To decompose periodic function into many frequency components.
Term
 Explain synthesis of a signal.
Definition
 To synthesize a signal x(t) from its components, i.e. individual complex exponentials
Term
 The spectrum of x(t).
Definition
 X(ω)
Term
 The Fourier coefficient...
Definition
 X[k]
Term
 Convolution property offers a way to compute the system's response in the real frequency domain.
Definition
 x(t)*h(t) <=> X(ω)H(ω)
Term
 The dual property is...
Definition
 x₁(t)x₂(t) <=> (1/2π)X₁(ω)*X₂(ω)This is known as the frequency convolution.
Term
 The phase spectrum.
Definition
 Θₓ(ω)
Term
 The Fundamental angular frequency...
Definition
 ω = 2π/T
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