Sampling theorem state that the bandpass signal x(t) whose maximum bandwidth is 2w can be completely represented into and recovered from its samples, if it is sampled at the minimum rate of twice the bandwidth.
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Comparison of PCM, DM, and ADM: Which one is the best for digital communication?
When the analog signal is sampled, it can be quantized and encoded by any one of the following techniques-
i) Pulse code modulation (PCM)
ii) Delta Modulation (DM)
iii) Differential pulse code modulation (DPCM)
These techniques convert an analog pulse to its digital equivalent. The digital information is then transmitted over the channel. The major difference among the techniques are given below:
PCM is a digital pulse modulation technique where an analog signal is sampled and quantized to a discrete signal. The analog signal is first sampled at regular intervals and then quantized to the nearest level. PCM has the advantage of having a simple implementation and being able to achieve high signal-to-noise ratios. However, it requires high bandwidth and is sensitive to quantization errors.
Delta modulation (DM) is a digital pulse modulation technique that approximates the waveform of the analog signal by a series of pulses. DM samples the analog signal and then compares the present sample with the previous sample to determine the next pulse. DM has a simple structure and requires low bandwidth. However, it has poor performance in low signal-to-noise ratio conditions and produces high quantization noise.
Adaptive Delta Modulation (ADM) is an improved version of DM that adjusts the step size of the quantization to track the changes in the input signal. ADM overcomes the limitations of DM and produces better performance in low signal-to-noise ratio conditions. However, ADM requires more complex implementation and is more sensitive to changes in the input signal.
In summary, PCM is suitable for high signal-to-noise ratio conditions, DM is appropriate for low bandwidth and low-complexity applications, and ADM is ideal for low signal-to-noise ratio conditions. The choice of which technique to use depends on the specific requirements of the application.
Nodal Analysis of an Electric Circuit: Finding Node Voltages and Branch Currents
Find the node voltages and branch currents of the following electric circuit using nodal analysis:
According to the method of Nodal analysis, first of all we need to determine all the nodes of the circuit. Then select the reference node which must be located to ground. After all denote all the unknown node voltages and all the branch currents. Now the modified circuit looks like below:
Here we have four nodes in the circuit. The reference node is represented by yellow node. The pink color node voltage is known. So remaining two unknown nodes are represented by green color.
The tricks is that the number of equations need to solve the problem equal to the number of unknown nodes.
According to KCL, we get-
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