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freq-intro.slides.printing.6

# freq-intro.slides.printing.6 - Introduction to Frequency...

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Introduction to Frequency Analysis Introduction to Frequency Analysis CS 450: Introduction to Digital Signal and Image Processing Bryan Morse BYU Computer Science Introduction to Frequency Analysis Frequency Analysis Idea: Decompose signals into sinusoids of different frequencies Why? Musical analysis Speech recognition Filtering: attenuating or boosting specific frequencies Linear systems analysis Introduction to Frequency Analysis Linear Systems and Sinusoids Sinusoids have an interesting property when passing through a linear, shift-invariant system: sin ( 2 π ut ) A ( u ) sin ( 2 π ut + T ( u )) cos ( 2 π ut ) A ( u ) cos ( 2 π ut + T ( u )) Sinusoids entering a linear, shift-invariant system produce a sinusoid of exactly the same frequency : May be amplified/attenuated: A ( u ) May be delayed slightly: T ( u ) The amplification and delay are a function of the frequency (different frequencies may have different amplifications/delays) Introduction to Frequency Analysis Linear Systems and Sinusoids

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freq-intro.slides.printing.6 - Introduction to Frequency...

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