File:Raised-cosine-impulse.svg
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Original file (SVG file, nominally 585 × 314 pixels, file size: 44 KB)
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Summary
| Description |
English: Impulse response of raised-cosine filter given by
for different values of . 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,100)
return result
def sinc(x): # define normlized sinc function
return sin(pi*x)/(pi*x)
def raisedCos(x,B=0,T=1): # define raised cosine function
return sinc(x/T) * cos(pi*B*x/T) / (1 - (4*B*B*x*x/(T*T)) )
fig = figure(figsize=(8,4))
ax = SubplotZero(fig,111)
fig.add_subplot(ax)
ax.grid(True)
ax.set_xticks([-3,-2,-1,0,1,2,3])
ax.set_xticklabels(["-3T","-2T","-T","0","T","2T","3T"])
ax.set_ylim((-.3,1.2))
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(3.5)
ax.plot(t,raisedCos(t),label=r"$\beta=0$")
ax.plot(t,raisedCos(t,0.25),label=r"$\beta=0.25$")
ax.plot(t,raisedCos(t,0.5),label=r"$\beta=0.5$")
ax.plot(t,raisedCos(t,1.),label=r"$\beta=1$")
ax.text(3.5,0.,"t")
ax.text(0.1,1.1,"h(t)")
ax.legend()
#fig.show()
fig.savefig("Raised-cosine-impulse.svg",bbox_inches="tight",\
pad_inches=.15)
|
| Date | |
| Source | Own work |
| Author | Krishnavedala |
| Other versions | File:Raised-cosine-impulse.png |
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
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- 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.
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:58, 28 August 2011 | | 585 × 314 (44 KB) | Krishnavedala | Corrected the X-axis labels |
| 17:44, 3 June 2011 |  | 585 × 314 (44 KB) | Krishnavedala | {{Information |Description ={{en|1=Impulse response of raised-cosine filter given by <math>h(t)=\mathrm{sinc} \left( \frac{t}{T} \right) \cos\left(\frac{\pi\beta t}{T}\right) \left(\frac{1}{1 - \frac{4\beta^2 t^2}{T^2} }\ |
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