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Summary
| Description |
English: impulse response of root-raised-cosine filter
Deutsch: Impulsantwort des Root-Raised-Cosine Filters |
| Date | |
| Source |
modified python script from user Krishnavedala for creating plot  |
| 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)
Created using python and matplotlib library.
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
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- 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.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:00, 28 March 2015 | | 600 × 314 (52 KB) | Chris828 | {{Information |Description ={{en|1=impulse response of root-raised-cosine filter}} {{de|1=Impulsantwort des Root-Raised-Cosine Filters}} |Source =modified python script from user Krishnavedala |Author =[[User:C... |
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