2025-L08 - ECE-2025 Spring-2008 Lecture 8 Sampling&...

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Unformatted text preview: ECE-2025 Spring-2008 Lecture 8 Sampling & Aliasing 19-Sept-08 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 2 Lab & HW Info ¡ Lab #4 ¡ Basic Music Synthesis ¡ Lab #5 ¡ Sound illusion ¡ Honor Code !!! ¡ Don’t exchange anything written or any electronic files 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 3 ¡ Use Short-Duration Sinusoids: ¡ Amp, Phase, Frequency & Duration ¡ Freq will change every FRAME ¡ Then ADD several sinusoids together Sinusoidal Synthesis const. 1 = = − + F k k T t t 1 for ) 2 cos( ) ( + ≤ ≤ + = k k k k k t t t t f A t x ϕ π t k ≤ t ≤ t k + 1 Fixed frame: 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 4 ANALYSIS --> SYNTHESIS BREAK INTO FRAMES Amp Phase Freq Per Frame Amp Phase Freq Per Frame PUT FRAMES BACK TOGETHER SMOOTHLY x(t) y(t) ADD UP the SINUSOIDS add_cos( ) FFT: DO FOURIER ANALYSIS ∑ + = k k k k t f A t x ) 2 cos( ) ( ϕ π 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 5 FRAME = WINDOW of DATA frame th i frame ) 1 ( th i + frame ) 2 ( th i + Non- overlapped frames Data also can be extracted from overlapped frames – overlapped characteristics means smoother transitions F T 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 6 PUT FRAMES BACK Non-overlapped frames Overlap-add: synthesized data for overlapped frames are accumulated by adding the corresponding sample values in the buffer (usually weighted) to form the final output “Output buffer” F T 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 7 Sine Synthesis: SPEECH ¡ FRAME Length = 10 millisec ¡ Examples: ¡ Original ¡ 9 sinusoids per frame ¡ 4 sinusoids ¡ 2 sinusoids ¡ Need to SMOOTH Boundaries Common practice in sinusoidal modeling, transform coding or sub-band coding ∑ − = + = N N k k k k t f A t x ) 2 cos( ) ( ϕ π 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 8 Time-Varying FREQUENCIES “Diagram” F r e q u e n c y i s t h e v e r t i c a l a x i s Time is the horizontal axis 09/16/2008 EE-2025 Fall-2008 jMc-BHJ 9 4-SINES Spectrogram F r e q u e n c y i s t h e v e r t i c a l a x i s 09/16/2008...
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2025-L08 - ECE-2025 Spring-2008 Lecture 8 Sampling&...

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