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Understanding Frequency Content in Discrete-Time Signals

School
University of Ottawa**We aren't endorsed by this school
Course
ELG 3125
Subject
Electrical Engineering
Date
Dec 12, 2024
Pages
15
Uploaded by DukeMuleMaster338
ELG 3125–Lab A02Yiran GUANUniversity of OttawaNov. 06, 2024Lab 6 - Frequency Content of Discrete-time SignalPlease get your MATLAB environment ready
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Quiz 2 - answersOct. 9, 2024Yiran GUAN2ELG 3125–Lab A02
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Quiz 2 - answersOct. 9, 2024Yiran GUAN3ELG 3125–Lab A02
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Quiz 2 - answersOct. 9, 2024Yiran GUAN4ELG 3125–Lab A02
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Quiz 2 - answersOct. 9, 2024Yiran GUAN5ELG 3125–Lab A02
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OutlineOct. 23, 2024Yiran GUAN6•Fourier Transform & Fourier Series•Frequency Contents of Periodic Signals•Frequency Contents of Non-Periodic SignalsELG 3125–Lab A02
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Fourier Transform & Fourier SeriesOct. 23, 2024Yiran GUAN7ELG 3125–Lab A02Time DomainFrequency DomainFourier Transform (non-periodic signals)Fourier Series (periodic signals)
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Frequency Contents of PeriodicOct. 23, 2024Yiran GUAN8•For a periodic discrete-time signal: •The Fourier transform of x[n]•Since, ELG 3125–Lab A02𝑥[𝑛] =෍?=<𝑁>𝑎?𝑒??𝑤0𝑛𝑎?=1𝑁෍𝑛=<𝑁>𝑥[𝑛]𝑒−??𝑤0𝑛𝑋𝑒?𝜔=෍𝑛=−∞+∞𝑥𝑛 𝑒−?𝜔𝑛𝑎?=1𝑁𝑋𝑒??𝑤0
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Frequency Contents of PeriodicOct. 23, 2024Yiran GUAN9•In MATLAB, to calculate the Fourier transform of x[n]•For a periodic signal, the frequency components:ELG 3125–Lab A02X_ejw = fft (x[n])𝑎?=1𝑁fft(x[n])
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•A periodic square wave 𝑥[n] with period N= 50•Oct. 23, 2024Yiran GUAN10ELG 3125–Lab A02Example𝑥[𝑛] = ቊ1, 0, 10 < 𝑛 < 500 < 𝑛 < 10
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•Frequency content of x[n]: •ak =1/N* fft(x[n])Oct. 23, 2024Yiran GUAN11ELG 3125–Lab A02Example
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•Frequency content of x[n]: •ak_s = fftshift(ak) •shift zero frequency to the centerOct. 23, 2024Yiran GUAN12ELG 3125–Lab A02Example
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Frequency Contents of Non-PeriodicOct. 23, 2024Yiran GUAN13•In MATLAB, to calculate the Fourier transform of x[n]•For a non-periodic signal, the spectrum in frequency domain is continuous.ELG 3125–Lab A02X_ejw = fft (x[n])
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•A non-periodic square wave 𝑥[n], duration N= 50•Oct. 23, 2024Yiran GUAN14ELG 3125–Lab A02Example𝑥[𝑛] = ቊ1, 0, 10 < 𝑛 < 500 < 𝑛 < 10
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•Frequency content of x[n]: •X_ejω= fft(x[n])•ω= k*2π/NOct. 23, 2024Yiran GUAN15ELG 3125–Lab A02Example
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