57. phase shift examples

Here is what the sine and cosine waves look like for different phase shifts. Note that positive phase shifts move the peaks to the left. For radar, that means that a positive phase change is associated with motion twoards the radar.

import numpy as np
from numpy import pi
import matplotlib.pyplot as plt

thetime=np.arange(0.,2*pi,0.05)
thewave=thetime/(2.*pi)
thirty=30.*pi/180.
sixty=2.*thirty
ninety=3.*thirty
onetwenty=2.*sixty
oneeighty=3.*sixty

fig1,axis1=plt.subplots(1,1)
axis1.plot(thewave,np.cos(thetime),'b-',label='0')
axis1.plot(thewave,np.cos(thetime + thirty),'c-',label='30')
axis1.plot(thewave,np.cos(thetime + sixty),'g-',label='60')
axis1.plot(thewave,np.cos(thetime + ninety),'k-',label='90')
axis1.plot(thewave,np.cos(thetime + onetwenty),'m-',label='120')
axis1.plot(thewave,np.cos(thetime + oneeighty),'r-',label='180')
axis1.set_xlabel('horizontal position (in wavelengths)')
axis1.set_ylabel('amplitude')
axis1.set_title('cosine waves for 5 phase shifts')
axis1.legend(loc='best')
axis1.grid(True)

fig2,axis2=plt.subplots(1,1)
axis2.plot(thewave,np.sin(thetime),'b-',label='0')
axis2.plot(thewave,np.sin(thetime + thirty),'c-',label='30')
axis2.plot(thewave,np.sin(thetime + sixty),'g-',label='60')
axis2.plot(thewave,np.sin(thetime + ninety),'k-',label='90')
axis2.plot(thewave,np.sin(thetime + onetwenty),'m-',label='120')
axis2.plot(thewave,np.sin(thetime + oneeighty),'r-',label='180')
axis2.set_xlabel('horizontal position (in wavelengths)')
axis2.set_ylabel('amplitude')
axis2.set_title('sine waves for 5 phase shifts')
axis2.legend(loc='best')
axis2.grid(True)

fig3,axis3=plt.subplots(1,1)
line1=axis3.plot(thewave,np.cos(thetime),'b-')
newX=thetime
#zero out the inital wave so it looks like a reflection
newX[newX > 0.75*2.*pi]=np.nan
#
#  add a pi phase shift
#
newX = newX + pi
line2=axis3.plot(thewave,np.cos(newX),'r-')
axis3.set_xlabel('horizontal position (in wavelengths)')
axis3.set_ylabel('amplitude at receiver')
axis3.set_title('phase shift for a reflection occuring at 0.75 wavelengths')
axis3.legend((line1[0],line2[0]),('first pulse reflected at 1 wavelength',
                                  'second pulse reflected at 3/4 wavelength'));

plt.show()