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Unformatted text preview: 1 LAB 1 (04/01) Signals in the Time and Frequency Domains 1. Introduction 2. Periodic Signals 3. Fourier Series Expansion of Periodic Signals 4. Spectral Representation of Periodic Signals 5. Duty Cycle of a Rectangular Wave 6. RMS Voltage and Power Spectrum of Aperiodic Signals 7. Discrete Fourier Transform (DFT) 8. Signal Strength 9. Signal Bandwidth 10. Conclusion 2 Introduction • The tasks of communication is to encode information as a signal level, transmit this signal , then decode the signal at the receiver. • An analog signal varies continuously with time, and has an infinite number of possible signal levels. • A discrete signal changes only once during a certain time interval. The signal value during this time interval (sampling period) is one sample. Each sample has a infinite number of possible signal levels. • A digital signal is discrete, but each sample has a finite number of possible signal levels. The limited number of levels means that each sample transmits a single information. It also means that each sample can be represented as digital data , a string of ones and zeroes. • A digital signal is preferred in computer communications because computers already store and process information digitally. 3 S(t) t S(t) t Sampling Period S(t) t Sampling Period 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 • In an analog signal , noise are added to the signal during transmission. The received signal will never be identical to the original signal. • A digital signal will still be subject to noise, but the difference between signal levels (an “0101” and an “0110”) will be sufficiently large so that the receiver can always determine the original signal level in each sampling period. The regenerated , so that the received digital data is an exact replica of the original digital data. • Analog to digital conversion reduces the amount of information of the signal by approximating the analog signal with a digital signal. The sampling period and number of levels of the digital signal should be selected in order to capture as much information of the original signal as possible 4 S(t) t Sampling Interval • A periodic signal satisfies the condition: • “ Period ” of the signal. • “ Aperiodic .” signals • An even function S (t) = S (t) • “ Symmetric ” . • The phase of the signal. ∞ + < < ∞ = + t t S T t S ); ( ) ( Signal Properties 5 S(t) θ A T t A · cos( 2 π · f · t ) A · cos( 2 π · f · t  θ ) f A 1/T A f A 1/T θ =0 1/T f A θ = π / 4 6 Digital signals in the time and the frequency domain. • The time domain is the signal level expressed as a function of time. • The frequency domain is comprised of amplitude and a phase for an infinite number of sinusoidal functions. These correspond to the superposition of an infinite number of sinusoidal waveforms in the time domain....
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 Spring '09
 DZHANIDZE
 Fourier Series, Signal Processing

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