File:Root-raised-cosine-impulse.svg
Summary
| Description |
English: impulse response of root-raised-cosine filter
Deutsch: Impulsantwort des Root-Raised-Cosine Filters |
| Date | |
| Source |
Own work based on: Raised-cosine-impulse.svg:  by Krishnavedala |
| Author | Chris828 |
![{\displaystyle h(t)={\begin{cases}{\dfrac {1}{\sqrt {T_{s}}}}\left(1-\beta +4{\dfrac {\beta }{\pi }}\right),&t=0\\{\dfrac {\beta }{\sqrt {2T_{s}}}}\left[\left(1+{\dfrac {2}{\pi }}\right)\sin \left({\dfrac {\pi }{4\beta }}\right)+\left(1-{\dfrac {2}{\pi }}\right)\cos \left({\dfrac {\pi }{4\beta }}\right)\right],&t=\pm {\dfrac {T_{s}}{4\beta }}\\{\dfrac {1}{\sqrt {T_{s}}}}{\dfrac {\sin \left[\pi {\dfrac {t}{T_{s}}}\left(1-\beta \right)\right]+4\beta {\dfrac {t}{T_{s}}}\cos \left[\pi {\dfrac {t}{T_{s}}}\left(1+\beta \right)\right]}{\pi {\dfrac {t}{T_{s}}}\left[1-\left(4\beta {\dfrac {t}{T_{s}}}\right)^{2}\right]}},&{\mbox{otherwise}}\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1336f8b15e830501ee52c3d2ecd6b444d902fd39)
Source code
This media was created with Matplotlib (comprehensive library for creating static, animated, and interactive visualizations in Python)Category:Images with Matplotlib source code
Here is a listing of the source used to create this file.
Here is a listing of the source used to create this file.
from numpy import *
from matplotlib.pyplot import *
from mpl_toolkits.axes_grid.axislines import SubplotZero
def makeT(lim=1): # Make the X-axis
result = linspace(-lim,lim,1000)
return result
def RootRaisedCos(x,B=0,T=1): # define root raised cosine function
return (1/sqrt(T))*(sin(pi*x/T*(1-B))+4*B*x/T*cos(pi*x/T*(1+B)))/(pi*x/T*(1-(4*B*x/T)**2))
fig = figure(figsize=(8,4))
ax = SubplotZero(fig,111)
fig.add_subplot(ax)
ax.grid(True)
ax.set_xticks([-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10])
#ax.set_xticklabels(["-10T","-9T","-8T","-7T","-6T","-5T","-4T","-3T","-2T","-T","0","T","2T","3T","4T","5T","6T","7T","8T","9T","10T"])
ax.set_ylim((-.4,1.4))
ax.set_yticklabels([])
for direction in ["xzero","yzero"]:
ax.axis[direction].set_axisline_style("->")
ax.axis[direction].set_visible(True)
for direction in ["left","right","bottom","top"]:
ax.axis[direction].set_visible(False)
t = makeT(10)
ax.plot(t,RootRaisedCos(t,1.),'b',label=r"$\beta=1$")
ax.plot(t,RootRaisedCos(t,0.5),'r',label=r"$\beta=0.5$")
ax.plot(t,RootRaisedCos(t),'g',label=r"$\beta=0$")
ax.text(9.,-.25,r"$t/T_s$")
ax.text(.5,1.3,r"$h(t)$")
ax.legend()
#fig.show()
fig.savefig("Root-raised-cosine-impulse.svg",bbox_inches="tight",\
pad_inches=.15)
Licensing
Chris828, the copyright holder of this work, hereby publishes it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution:
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- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
