how to plot sine wave signal with synchronous and non synchronous sampling?

how to plot sine wave signal with synchronous and non synchronous sampling in time domain with formula

s(t) = A*sin(2*pi*f*t + phi )

the graph must s(t) versus number of cycle?

where should i coded the number of cycles?

Answer 1

[recent works]

Please check the python code:

Import the necessary libraries:

import numpy as np

import matplotlib.pyplot as plt

Define the parameters of your sine wave signal, including amplitude (A), frequency (f), phase (phi), and the sampling rate (Fs).

A = 1.0 # Amplitude of the sine wave

f = 5.0 # Frequency of the sine wave (in Hz)

phi = 0.0 # Phase of the sine wave (in radians)

Fs_sync = 50.0 # Synchronous sampling rate (samples per second)

Fs_non_sync = 10.0 # Non-synchronous sampling rate (samples per second)

Define the time vector for both synchronous and non-synchronous sampling. The number of cycles should be specified here.

# Number of cycles for the signal

num_cycles = 5

# Time vector for synchronous sampling

t_sync = np.arange(0, num_cycles * 1 / f, 1 / Fs_sync)

# Time vector for non-synchronous sampling

t_non_sync = np.arange(0, num_cycles * 1 / f, 1 / Fs_non_sync)

Calculate the sine wave signal for both sampling rates:

# Calculate the synchronous sine wave

s_sync = A * np.sin(2 * np.pi * f * t_sync + phi)

# Calculate the non-synchronous sine wave

s_non_sync = A * np.sin(2 * np.pi * f * t_non_sync + phi)

Plot the results using Matplotlib:

# Plot the synchronous sampled signal

plt.figure(figsize=(12, 6))

plt.subplot(2, 1, 1)

plt.plot(t_sync, s_sync)

plt.title('Synchronous Sampling')

plt.xlabel('Time (s)')

plt.ylabel('Amplitude')

plt.grid()

# Plot the non-synchronous sampled signal

plt.subplot(2, 1, 2)

plt.plot(t_non_sync, s_non_sync)

plt.title('Non-Synchronous Sampling')

plt.xlabel('Time (s)')

plt.ylabel('Amplitude')

plt.grid()

plt.tight_layout()

plt.show()

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[Walter Roberson]

Using a lower sampling frequency is not non-synchronous sampling !

https://ieeexplore.ieee.org/document/513417

In fully digital receivers, carrier and timing information is derived from samples of the (anti-aliasing-filtered) received continuous-time signal. In case of synchronized sampling, this information is used to align the sampling clock of the receiver with the remote transmit clock. In nonsynchronized sampling systems, the sampling at the receiver is performed by means of a fixed free-running clock, and additional post-processing is necessary to perform timing correction in the digital domain.

In other words, for non-synchronous sampling, you need to do clock recovery from the waveform, somehow .

Imagine for example that you are generating a sine wave on the International Space Station and sending it to a ground station on Earth. For simplification, suppose we have a pretty decent Phased Locked Loop (PLL) clock on the ISS, that is accurate to (say) 1 part in 1 billion -- that is, for the purpose of this particular example, assume that the source timer is very reqular. So this accurate sine signal is generated and beamed to Earth, and the ground station samples it with a high accuracy receiver... and as far as the ground receiver can tell, the signal generator on the ISS must be malfunctioning.

Why? Because the ISS is moving faster than the ground station, and so is subject to relativistic time dilation. "One second" as experienced in the ISS is a different duration than "one second" as experienced by the ground station.

Therefore if you were sending a communications signal from ISS to a ground station, then even if you have excellent clock sources on both sites, you need to do "clock recovery" on the received signal: the received signal is non-synchronous.

This is, by the way, a real issue. GPS satellites are traveling faster than people on the ground, so they had to include time dilation correction into the design of GPS systems.

But more generally, you might be running a source system that does not have the most accurate of clocks. Two CPUs the same computer will run at slightly different rates. Clock cycles can be lost if a host is servicing interrupts. "Clock drift" happens all of the time . Synchronizing the time between different systems is hard (you can sort of do it for adjacent systems, but as soon as you move one of them you lose synchronization due to time dilation effects.)