Question:Which of the following signals can be downsampled by a factor of 2using the system in Figure 4.19 without any loss of information?Answer :Refer Figure 4.19 in the textbook for the compressor or digital-timesampler.The DTFT of down sampled signal is,Here, the signal is down sampled by a factor 2. So, substitute 2 forin the equation.
(a)Consider the following signal:Calculate DTFT of the signal.The DTFT of down sampled signal is,Draw the waveforms ofandforequals to 1.
Figure 1Since the spectraandoverlap each other, there is a loss ofinformation while down sampling the signal.(b)Consider the following signal:Calculate DTFT of the signal.
The DTFT of down sampled signal is,Since there is no overlap of delta functions in spectrum, there is no loss of