---
jupytext:
  formats: ipynb,md:myst
  notebook_metadata_filter: all,-language_info,-toc,-latex_envs
  text_representation:
    extension: .md
    format_name: myst
    format_version: 0.13
    jupytext_version: 1.16.6
kernelspec:
  display_name: Python 3 (ipykernel)
  language: python
  name: python3
---

(phase_shiftb)=
# 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.

```{code-cell} ipython3
import numpy as np
from numpy import pi
import matplotlib.pyplot as plt
```

```{code-cell} ipython3
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
```

```{code-cell} ipython3
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)
```

```{code-cell} ipython3
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)
```

```{code-cell} ipython3
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'));
```

```{code-cell} ipython3
plt.show()
```