SPFirst-L05

SPFirst-L05 - 1/28/2005 2003, JH McClellan & RW...

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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( t 2 ) = + + = N k k k t kf A A t x 1 ) 2 cos( ) ( 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 j e 3 / 7 j e 2 / 4 j e 2 / 4 j e 10 ) 2 / ) 250 ( 2 cos( 8 ) 3 / ) 100 ( 2 cos( 14 10 ) ( + + + = t t t x k j k k e A X = 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 - 1/28/2005 2003, JH McClellan & RW...

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