Consider a continuous 2d signal of. 5 points each please provide brief explanations for your answers in order to receive full credit.
Select a suitable sampling rate.
Suppose you wish to design a sampling reconstruction system. Sampling and reconstruction 10 point sampling. 2 the system has no prior knowledge of the band locations. Spectrum xf w analyzed by dtft frequency variable w wt.
Clearly if the sampling signal s frequency is low enough one or. So for example if the sampling signal is 7khz the lowest frequency components of the sampled message become 2khz 5khz and 9khz. View homework help ps6 w14 from ec engr 114 at university of california los angeles.
Discrete time x n x n t at n t n integer. Continuous time x t speciﬁed for all t. There is a lot of symmetry between the two processes.
We want to design a dt system with ideal sampling and reconstruction to replace the ct system. The sampling frequency or sample rate is fs 1 t in units of samples second or sometimes hertz or ws 2p t in units. Assignment according to the sampling reconstruction system shown below the previous example had t 1 x since w.
1 the sampling rate should be as low as possible. 16 36 communication systems engineering quiz 1 march 5 2009 part 1. Bandwidth w rad sec sampler.
Spectrum xf w analyzed by ctft frequency variable w. A signal x t with bandwidth w is sampled at a sampling rate 2w. In a traditional centralized sampling and reconstruction system the ℓ 2 stability of the sensing matrix could be verified by its central processor but the above procedure is infeasible in a distributed sampling and reconstruction system as it is decentralized.
Sampling captures a continuous signal up to a maximum frequency and the reconstruction process does the reverse turning discrete samples back into a continuous waveform. 11 1 sampling a sampler for complex valued signals is a system samplert reals complex integers complex. The system is depicted in ﬁgure 11 1.
Of electrical engineering ee 114 winter 2014 problem set 6 1. We wish to design a sampling system for signals from the model mthat satisﬁes the following properties. Stability criterion for distributed sampling and reconstruction systems.
11 1 where t is the sampling interval it has units of seconds sample. Both rely on low pass filters to function correctly which presents some challenges. Time shifting a signal changes its frequency composition.
Bandwidth w rad sec 0 2x t for each homework problem below draw your version of the diagram above as shown below specifying what r t is equal to and the values of w1 ws and w. You d still get the message but the frequency of the aliases would go down as well. An actual sampling system mixes continuous and discrete time.
1 5 w 3 and w 1 5. Suppose that a continuous time signal x t is bandlimited by 1hz and it is processed by a ct system with transfer function for noise clean up. 3 the system can be implemented with existing analog 1.
Now suppose the frequency of the sampling signal is lowered. Quick questions 50 points.