SPFirst-L05

SPFirst-L05 - © 2003 JH McClellan& RW Schafer 1 Signal...

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Unformatted text preview: 1/28/2005 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 5 Periodic Signals, Harmonics & Time-Varying Sinusoids 1/28/2005 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS ¡ This Lecture: ¡ Chapter 3, Sections 3-2 and 3-3 ¡ Chapter 3, Sections 3-7 and 3-8 ¡ Next Lecture: ¡ Fourier Series ANALYSIS Fourier Series ANALYSIS ¡ Sections 3-4, 3-5 and 3-6 1/28/2005 © 2003, JH McClellan & RW Schafer 4 Problem Solving Skills ¡ Math Formula ¡ Sum of Cosines ¡ Amp, Freq, Phase ¡ Recorded Signals ¡ Speech ¡ Music ¡ No simple formula ¡ Plot & Sketches ¡ S(t) versus t ¡ Spectrum ¡ MATLAB ¡ Numerical ¡ Computation ¡ Plotting list of numbers 1/28/2005 © 2003, JH McClellan & RW Schafer 5 LECTURE OBJECTIVES ¡ Signals with HARMONIC HARMONIC Frequencies ¡ Add Sinusoids with f k = kf FREQUENCY can change vs. TIME Chirps: Introduce Spectrogram Visualization (specgram.m) (plotspec.m) x ( t ) = cos( α t 2 ) ∑ = + + = N k k k t kf A A t x 1 ) 2 cos( ) ( ϕ π 1/28/2005 © 2003, JH McClellan & RW Schafer 6 SPECTRUM DIAGRAM ¡ Recall Complex Amplitude vs. Freq k k a X = 2 1 100 250 –100 –250 f (in Hz) 3 / 7 π j e 3 / 7 π j e − 2 / 4 π j e − 2 / 4 π j e 10 ) 2 / ) 250 ( 2 cos( 8 ) 3 / ) 100 ( 2 cos( 14 10 ) ( π π π π + + − + = t t t x k j k k e A X ϕ = ∗ k X 2 1 1/28/2005 © 2003, JH McClellan & RW Schafer 7 SPECTRUM for PERIODIC ? ¡ Nearly Periodic in the Vowel Region ¡ Period is (Approximately) T = 0.0065 sec 1/28/2005 © 2003, JH McClellan & RW Schafer 8 PERIODIC SIGNALS ¡ Repeat every T secs ¡ Definition ¡ Example: ¡ Speech can be “quasi-periodic”...
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SPFirst-L05 - © 2003 JH McClellan& RW Schafer 1 Signal...

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