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University of Hertfordshire STUDENT'S GUIDE FROM ANALOG TO DIGITAL OBJECTIVES LECTURE 2 FROM ANALOG TO DIGITAL This lecture should achieve the follow ing: Introduce sampling , the Nyquist Limit (Shannon's Sampling Theorem) and representation of signals in the frequency domain Introduce basic concepts of Analog-to-Digital Conversion and quantization noise Consider practical ADC and DAC devices Consider the functional blocks of the DSP Starter Kit board LECTURE 2 45 2-1 ~ TEXAS IN SIRUMENTS

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University of Hertfordshire STUDENT'S GUIDE FROM ANALOG TO DIGITAL SI GNA LS IN TIM E AND FR EQU EN CY DOM A IN S TIME DO MAIN T ,=1 /f, A MPLITUDE : _: ~ C\ ~ d c V ~ V T I M~ FR EQ U ENC Y DOMA IN AM PLITUDE --L- r, FREQU ENCY T, =1/f , AMP LITUD E :-..: r 1\ 1\ 6 ~ I\ { vvv v vv , TIME AM PLI TUDE --lL f, F REQUENCY T = period f = fre q u e n c y All electronic signals can be visualized (signal representation) using two basic methods - the time domain and the frequency domain. If we have an electronic signal running along a copper wire, we need some method of displaying what that signal is. Time Domain The time domain is the form of visualization that most people are familiar with. This method shows variations of a signal with time. The most common time domain instrument is the oscilloscope, which has graduations of volts on the Y axis and graduations of time on the X axis. A pure sine wave is shown on the left side of the above diagram. The signal has afreque ncy (the number of times that the signal repeats itself in a second) and a period (the time duration of one complete signal cycle). Frequency and period are not different quantities, but different methods of describing the time measurement of a signal. The diagram shows two waveforms. The lower one has a higher frequency (more cycles per a second) and a shorter period (less time to complete one signal). Both signals have the same amplitude. Freq uency Domain The frequency domain is not as well-known as the time domain, but is very important in the field of DSPs. Instead of showing the variation of a signal with respect to time, we show the variation of the signal with respect to frequency. Most people are familiar with the graphical displays in music systems that show how much bass or treble is in music; this is a frequency domain display. The most common instrument for displaying the frequency domain is the spectrum analyzer. The right side of the diagram shows a frequency domain display. In the top graph, we see a single line representing a single pure frequency (f.). In the lower graph, we see a higher-frequency signal (f 2 ) . This line is further to the right on the frequency axis. LECTURE 2 46 2-2
University of Hertfordshire STUDENT'S GUIDE REA L S IGNALS FROM ANALOG TO DIGITAL A MPL ITUD E ~~ 7 'Z..<7 ' » TIME A MPLITUDE IAI • REAL LIF E SIGNALS ARE A COMB INA TION OF MANY FR EQUENCI ES THE Y HAVE BA ND WI DTH 2'.

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