Ae104a_2010_handout_6

# Ae104a_2010_handout_6 - 7 Signal and its Conditioning...

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7. Signal and its Conditioning Suggested reference: Holman 7.1 Digital techniques Figure 1: Digital coding system: sample and quantise. converts it. A-D converter: converts each input sample to a digital value. D-A converter: converts back to an analog voltage. 7.2 Types of signal Once we have a digital signal, how do we transmit or record it? Work with a basic unit pulse. This can be transmitted either in serial or parallel modes. Serial: four consecutive pulses is recorded as the number 4. 20

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Parallel: need to understand binary data, or counting in base 2. For example, a “four- bit” sequence of pulses can be used to represent numbers up to 15. A “1” in the ﬁrst, most signiﬁcant bit (MSB) corresponds to a contribution of 2 4 - 1 = 8 to the output, a “1” in the i -th bit corresponds to 2 4 - i , a “1” in the 4-th bit corresponds to 2 4 - 4 = 1, etc. Thus a binary code of 1010 5, etc. 7.3 Analog to digital converters (A/D) 7.3.1 Basic concepts An A-D converter converts a continuous analog signal to a series of discrete digital numbers and can be modeled by a sampling function (impulse train) with sampling period T = 2 π/ω s (where ω s is the sampling frequency): p ( t ) = Σ + n = -∞ δ ( t - nT ) . Then the sampled signal, x p ( t ) is given by x p ( t ) = x ( t ) p ( t ) = Σ + n = -∞ x ( nT ) δ ( t - nT ) . From convolution theorem, X p ( ω ) = 1 2 π [ X ( ω ) * P ( ω )] and P ( ω ) = 2 π Σ + k = -∞ δ ( ω - s ) , so X p ( ω ) = 1 T Σ + k = -∞ X ( ω - s ) . X p ( ω ) is a periodic function of frequency consisting of a sum of shifted replicas of X ( ω ) scaled by 1 /T . For ω s > 2 ω max , where ω max is the highest frequency contained in the signal, x ( t ) can be recovered exactly (Nyquist criterion). It is likely that we also use a window function on the temporal signal.
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Ae104a_2010_handout_6 - 7 Signal and its Conditioning...

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