Lecture 2

Lecture 2 - Lecture 2 Discrete-Time Fourier Series ECSE304...

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1 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 2: Discrete-Time Fourier Series Reading: O and W, Secs. 3.6 and 3.7 Richard Rose McGill University Dept. of Electrical and Computer Engineering 2 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II Impact of Digital Signal Processing on Advances in Speech Synthesis • It became common place for research on speech, audio, and images to be performed with discrete time algorithms on digital computers in the 1960s • Before that time, implementing these systems was done in hardware using analog components • Constructing systems could take years and was dominated by the effort required to build the hardware • It was researchers in the areas of speech, audio, imaging, and communications that led the effort to use computers to process signals [Millman, 1984]
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3 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II The First Electronic Speech Synthesizer • Homer Dudley’s “Voder” Speech Synthesizer from Bell Laboratories Voder Operator at the Voder Console Schematic Diagram of Operator’s Console [Millman, 1984] [Millman, 1984] 4 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II Analog Filters and Oscillators under Digital Control • Gunar Fant’s Orator Verbis Electris OVE-II cascade formant Speech Synthesizer from KTH in Sweden A 1962 photograph of the racks of analog filters and oscillators
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5 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II • George Rosens DAVO articulatory speech synthesizer at MIT (1958) A circuit schematic using passive analog filter components Analog Filters and Oscillators under Digital Control 6 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Discrete-Time Fourier Series Reading: O and W, Secs. 3.6 and 3.7 Boulet, Chapter 12
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7 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II • Complex exponentials as eigenfunctions of discrete linear time-invariant (DLTI) systems • Linear Combinations of Harmonically Related Complex Exponentials • Determination of Discrete-Time Fourier Series (DTFS) Representation of a Periodic Signal • Examples of DTFS for Common Signals • Properties of DTFS Outline 8 Lecture 2 – Discrete-Time Fourier Series ECSE304 Signals and Systems II • Response of LTI Systems to Complex Exponential, , is the same complex exp. with only a change in amplitude: • For LTI system with impulse response, , and input,
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This note was uploaded on 08/17/2011 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

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Lecture 2 - Lecture 2 Discrete-Time Fourier Series ECSE304...

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