Lecture 1

Lecture 1 - Lecture 1 Review ECSE304 Signals and Systems II...

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1 Lecture 1 – Review ECSE304 Signals and Systems II Welcome to ECSE304 – List of Topics • Discrete-Time Fourier Series and DT Fourier Transform • The Z – Transform • Time and Frequency Analysis of DT Signals and Systems • Sampling Systems • Application to Communications Systems • State Models of Continuous Time LTI Systems • Linear Feedback Systems 2 Lecture 1 – Review ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 1: Review of C-T Systems - Elementary Signals and Systems - Reading: O and W, Chaps 1 and 2 - Continuous-Time Fourier Series - Reading: O and W, Secs. 3.2 – 3.5 - Continuous-Time Fourier Transform - Reading: O and W, Chap 4 Richard Rose McGill University Dept. of Electrical and Computer Engineering
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3 Lecture 1 – Review ECSE304 Signals and Systems II • Motivation: Transform Domain Representations – Our First 3 Modules relate to Discrete Time (D-T) Transforms: • D-T Fourier Series and D-T Fourier Transforms • Z-Transforms • Time and Frequency Analysis of D-T Signals and Systems • Review of C-T Systems – Complex Exponentials Eigenfunctions of C-T LTI Systems – Linear Time Invariant System Properties – C-T Fourier Series for Periodic Signals • Definition and Properties – C-T Fourier Transform for Aperiodic Signals • Definition and Properties Outline () st st eH s e 4 Lecture 1 – Review ECSE304 Signals and Systems II • There are many applications where these representations reveal the underlying structure if a system: Introduction Spectrograms: The distribution of energy in time and frequency: Speech Spectrogram Music (Piano) Spectrogram
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5 Lecture 1 – Review ECSE304 Signals and Systems II Spectrum Representations: Music Spectrogram • Representations of Piano: • We can see note values and durations as well as the tonal harmonics of the fundamental in the spectrogram Time Waveform Representation Spectrogram Representation 6 Lecture 1 – Review ECSE304 Signals and Systems II Spectrum Representations of Speech Signals 0 T A simple speech production model x(t): output from glottis h(t): vocal tract impulse response y(t) = x(t)*h(t): radiated pressure wave : Fourier Transform of y(t) x(t) h(t) y(t) • The Fourier Transform of the Sound Pressure Wave associated with vowel utterances contains information about the speech production system () ()() Y j X j H j ω ωω = Spectral Resonances Fourier Transform of Radiated Pressure Wave 00 1/ : Fundamental Frequency FT =
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Lecture 1 - Lecture 1 Review ECSE304 Signals and Systems II...

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