Hướng dẫn plotting signals in python
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To get the signal plot, we can take the following steps − Show
Exampleimport matplotlib.pyplot as plt
import numpy as np
plt.rcParams["figure.figsize"] = [7.50, 3.50]
plt.rcParams["figure.autolayout"] = True
np.random.seed(0)
dt = 0.01 # sampling interval
Fs = 1 / dt # sampling frequency
t = np.arange(0, 10, dt)
# generate noise:
nse = np.random.randn(len(t))
r = np.exp(-t / 0.05)
cnse = np.convolve(nse, r) * dt
cnse = cnse[:len(t)]
s = 0.1 * np.sin(4 * np.pi * t) + cnse
fig, axs = plt.subplots()
axs.set_title("Signal")
axs.plot(t, s, color='C0')
axs.set_xlabel("Time")
axs.set_ylabel("Amplitude")
plt.show()Output
Updated on 16-Jun-2021 12:09:32
AWe distinguish real and complex signals. A real valued signal x is a mapping from time to a scalar value x(t). We call x a signal and also denote the signal as x(t).Nội dung chính
A complex valued signal $x$ is a mapping from . We can characterize signals by looking at the time domain. Traditionally time is represented as a real value running from to . Such signals are called continuous time signals.When using computers we start to represent signal with a discrete and countable stream of numbers: we call these numbers signal samples. At every time instance the signal value is stored in memory. All signal valuess between the sample times are simply ignored. These signals are called discrete time signals.Plotting real values signals¶Consider a CT signal . A real valued CT signal is plotted using the standard ways to plot a function . Consider the sinusoidal signalt = np.linspace(-0.02, 0.05, 1000) plt.plot(t, 325 * np.sin(2*np.pi*50*t)); plt.xlabel('t'); plt.ylabel('x(t)'); plt.title(r'Plot of CT signal \$x(t)=325 \sin(2\pi 50 t)\$'); plt.xlim([-0.02, 0.05]); #@savefig sineplot.png plt.show() (Source code, png, hires.png, pdf) Evidently the above plot is a lie. You cannot plot a CT signal on a digital device. In Computer Graphics class you have or will learn that a function (signal) is plotted as a chain of straight lines (and even the straight lines are discretized as a set of dots). But it sure looks like a CT signal doesn’t it? Things are different when we consider a DT signal. Given the values of for say to we could use the same strategy and plot it as we did for the CT signal: just connect the dots $(n, x[n])$. That is done in practice often. However in these notes when dealing with the differences between CT and DT signals we want to stress that a DT signal essentially is just a sequence of numbers. There is no need to think about in the discrete domain and certainly no need to visualize it.Therefore a DT signal is plotted as a sequence of vertical bars. A stem plot: n = np.arange(50); dt = 0.07/50 x = np.sin(2 * np.pi * 50 * n * dt) plt.xlabel('n'); plt.ylabel('x[n]'); plt.title(r'Plot of DT signal \$x[n] = 325 \sin(2\pi 50 n \Delta t)\$'); #@savefig dtsineplot.png plt.stem(n, x); (Source code, png, hires.png, pdf) Plotting Complex Valued Signals¶Now consider the complex valued CT signal: Plotting such a signal as if it were a real valued signal results in a Python warning that complex numbers are casted to real by discarding the imaginary parts. To see everything we have to plot both the real and imaginary part of the signal. t = np.linspace(-0.02, 0.05, 1000) plt.subplot(2,1,1); plt.plot(t, np.exp(2j*np.pi*50*t).real ); plt.xlabel('t'); plt.ylabel('Re x(t)'); plt.title(r'Real part of \$x(t)=e^{j 100 \pi t}\$'); plt.xlim([-0.02, 0.05]); plt.subplot(2,1,2); plt.plot(t, np.exp(2j*np.pi*50*t).imag); plt.xlabel('t'); plt.ylabel('Im x(t)'); plt.title(r'Imaginary part of \$x(t)=e^{j 100\pi t}\$'); plt.xlim([-0.02, 0.05]); #@savefig csineplot.png plt.show() (Source code, png, hires.png, pdf) Instead of plotting the real and imaginary part of a complex signal, we can also plot the magnitude and angle of the complex values. t = np.linspace(-0.02, 0.05, 1000) plt.subplot(2,1,1); plt.plot(t, np.abs(np.exp(2j*np.pi*50*t)) ); plt.xlabel(r'\$t\$'); plt.ylabel(r'\$|x(t)|\$'); plt.title(r'Absolute value of \$x(t)=e^{j 100 \pi t}\$'); plt.xlim([-0.02, 0.05]); plt.subplot(2,1,2); plt.plot(t, np.angle(np.exp(2j*np.pi*50*t))*360/(2*np.pi)); plt.xlabel('\$t\$'); plt.ylabel(r'\$\angle x(t)\$'); plt.title(r'Phase of \$x(t)=e^{j 100 \pi t}\$'); plt.xlim([-0.02, 0.05]); #@savefig cabsanglesineplot.png plt.show() (Source code, png, hires.png, pdf) Note that both plots of the complex signal are equivalent. They both do represent the same signal. Also note the seemingly strange behaviour of the phase (angle) plot. It looks quite discontinuous. But it is really not because the phase jumps from +180 degrees to -180 degrees and that is of course the same angle! This phenomenon will be seen quite a lot when plotting the phase of complex signals and functions. It is called phase wrapping. If we would allow angles outside the range from -180 to +180 we could obtain a perfectly straight line (doing just that is called phase unwrapping). A few special functions¶In DSP we use some special functions: 1. Constant signal Constant Function¶
**2. Step function ** A step function is like a light switch which is turned on at t = 0. Step Function¶
3. Pulse function The pulse function, also called the impulse function, in DT is easy: everywhere zero except at $n=0$ where the values is . The DT pulse is written as .In CT it is more difficult. The pulse in CT is written as . It is mathematically defined with the sifting
A usefull way to think about a pulse signal is to consider a signal in which you want to concentrate a finite amount of energy in a short a time interval as possible. Energy in a signal is measured by integrating a signal over a period of time. onsider for instance the signal $x_a(t)$ defined as: The total energy in this signal is $1$ (the integral of $x(t)$ over the entire domain). This is true irrespective of the value of $a$. In the limit when $arightarrow0$ the value but still the total area under the function remains 1. In a sloppy way we may define:The strange thing thus is that the function value is infinite (well more accurate said it is not well defined) at $t=0$ whereas the integral over the entire domain is finite and equal to 1. We will see many uses of the pulse function. The translated CT pulse function is plotted as:n = np.arange(10); x = np.zeros_like(n); x[2]=3; plt.vlines(n,0,x,'b'); plt.ylim(-1,4); plt.plot(n,0*n, 'b'); #@savefig pulseplot.png plt.show(); (Source code, png, hires.png, pdf) The straight line indicates it is a pulse and the length of the line indicates the total energy. Pulse Function¶
Exercises¶Write Python functions to plot signals/functions like the examples above. Plot the following functions:
a graph and plot the sine as well. Change the number of samples to a lower number. What can you deduce from the result? How do you plot a discreteA discrete time signal just means sampling your continuous signal at discrete time intervals. The simplest way this can be done is by increasing your step in n. n = [-5:0.25:5]; y = 5*cos(pi*(n/2)-(pi/2)); How do you plot a digital signal in Python?MatPlotLib with Python. Set the figure size and adjust the padding between and around the subplots.. Get random seed value.. Initialize dt for sampling interval and find the sampling frequency.. Create random data points for t.. To generate noise, get nse, r, cnse and s using numpy.. Which command is used for plotting graphs of discreteIt is common to graph a discrete-time signal as dots in a Cartesian coordinate system. This can be done in the Matlab environment by using the stem command. What does plot () do in Python?The plot() function is used to draw points (markers) in a diagram. By default, the plot() function draws a line from point to point. The function takes parameters for specifying points in the diagram. |
