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The plots on this slide and the next demonstrate the relationship between P and D with respect to the map. As mentioned previously, D directly impacts spur magnitude while P establishes the total number of spurs. This group of plots are for a map with D equals 3. That is, the map output constitutes 3 bits allowing for eight possible output values. The upper plots are time domain waveforms and the lower plots are their corresponding spectra. The pair of plots on the left are for a map with P equals 4. That is, the map input constitutes 4 bits allowing for sixteen possible input values. The pair of plots on the right are for P equals 8 allowing for two hundred and fifty six possible input values. In the upper plots, the horizontal axis corresponds to the x input values to map ranging from 0 to 2 to the P. The vertical axis is amplitude. Each upper plot has 3 traces. The blue trace consists of sample points (dots) that represent exact sinusoidal values. The black trace is the map output. The red trace is the difference between the black and blue traces. Hence, the red trace is the quantization error of the map. The lower plots show the output spectrum as a bar plot. The horizontal axis represents frequency with an index range of zero to 2 raised to the P minus 1 power corresponding to a frequency range of DC to Nyquist. Each vertical bar is a spur with the top of the bar representing the spur magnitude. The magnitudes are normalized to the spur in frequency position 1, which corresponds to the fundamental frequency of the map output. The spectral plots clearly show that P establishes the number of spurs, but has little impact on spur magnitude. Note that both spectral plots have a maximum spur level of approximately -25dB relative to the fundamental.
