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