Say whether each of the following statements is True or False and give a brief j
ID: 1716666 • Letter: S
Question
Say whether each of the following statements is True or False and give a brief justification. No partial credit will be given for answers without explanation. A sufficient condition for a linear system to be distortionless is to be all-pass. The Fourier series of an energy signal (time limited) is periodic over the domain where the signal is defined. According to Nyquist, every practical signal can be reconstructed from its samples provided it is sampled at sufficiently high frequency. To avoid aliasing, we can use an antialiasing filter after sampling the signal. It is recommended to sample at a frequency a bit higher than the Nyquist rate to avoid aliasing. Non-uniform quantization is recommended to reduce the signal bandwidth. Using Differential Pulse Code Modulation (DPCM) instead of PCM can lead to reductions in bandwidth requirements. ON-OFF coding uses more bandwidth than polar coding but is more power efficient. Based on Nyquist criterion for zero Intersymbol Interference (IS1), we should use time-limited pulses to avoid interference between neighboring pulses. Raised-cosine pulses are favored over sine pulses because they have better bandwidth.Explanation / Answer
1.
A system is said to be distortionless if the system provides uniform gain with in the frequency band and the system must delay each frequency component by the same discrete-time value. but in the case of all pass filter the first condition is satisfied. it provides uniform gain over the frequency range but phase shift due to the all pass filter varies as a function of frequency. So the given statement is false.
3. Nyquist criteria states that for the signal to be successfully reconstructed the minimum sampling rate is double that of maximum frequency present in the signal. if the signal is sampled at sufficiently high freqeuncy then it can be done to reconstuct from its samples. so the given statement is true
4.
The given statement is false. this is because the antialiasing filter is used before the sampler in order to restrict the maximum frequency component of the signal that means to satisfy the sampling theorem. otherwise nyquist criteria may not be satisfied.
5.
theoretically we can reconstruct the signals from its samples with the sampling rate of 2fm. but in practical this is not possible. this is because we do not have ideal filters. so that is why it is recommended to sample at a frequency a bit higher than nyquist rate to avoid aliasing.