FREQUENCY DOMAIN EFFECTS OF ALIASING ASED BANDWIDTH CASE t ' a',. REPEATS 2 CASE 3 a CASE 4 Figure 5.4 From Figure 5. 4, we make the extremely important observation that regardless of where the analog signal being sampled happens to lie in the frequency spectrum(as long as it does not lie on multiples of fs/2), the effects of sampling will cause either the actual signal or an aliased component to fall within the Nyquist bandwidth between dc and fs/2. Therefore, any signals which fall outside the bandwidth of interest, whether they be spurious tones or random noise, must be adequately filtered before sampling. If unfiltered, the sampling process will alias them back within the Nyquist bandwidth where they can corrupt the wanted signals Methods exist which use aliasing to our advantage in signal processing applications Figure 5.5 shows four cases where a signal having a 1MHz bandwidth is located in different portions of the frequency spectrum. The sampling frequency must be chosen such that there is no overlapping of the aliased components. In general, the sampling frequency must be at least twice the signal bandwidth, and the sampled signal must not cross an integer multiple of f/2.5 FREQUENCY DOMAIN EFFECTS OF ALIASING Figure 5.4 From Figure 5.4, we make the extremely important observation that regardless of where the analog signal being sampled happens to lie in the frequency spectrum (as long as it does not lie on multiples of fs/2), the effects of sampling will cause either the actual signal or an aliased component to fall within the Nyquist bandwidth between dc and fs/2. Therefore, any signals which fall outside the bandwidth of interest, whether they be spurious tones or random noise, must be adequately filtered before sampling. If unfiltered, the sampling process will alias them back within the Nyquist bandwidth where they can corrupt the wanted signals. Methods exist which use aliasing to our advantage in signal processing applications. Figure 5.5 shows four cases where a signal having a 1MHz bandwidth is located in different portions of the frequency spectrum. The sampling frequency must be chosen such that there is no overlapping of the aliased components. In general, the sampling frequency must be at least twice the signal bandwidth, and the sampled signal must not cross an integer multiple of fs /2