In [1]:

    

%matplotlib inline
from lcapy import *
from lcapy.discretetime import *


    

    




Warning, this is experimental and probably riddled with bugs!

In [11]:

    

h = 2 * ui(n) - ui(n-2)
h


    

    
Out[11]:





$$2 \delta\left[n\right] - \delta\left[n - 2\right]$$

In [3]:

    

h.plot();


    

In [4]:

    

H = h(z)
H


    

    
Out[4]:





$$2 - \frac{1}{z^{2}}$$

In [5]:

    

ax = H.plot();


    

In [6]:

    

H.DTFT()


    

    
Out[6]:





$$2 - e^{- 4 \mathrm{j} \pi \Delta_{t} f}$$

In [7]:

    

H.DTFT().subs(dt, 1).plot();


    

In [8]:

    

h.difference_equation()


    

    
Out[8]:





$$y(n) = 2 x(n) - x(n - 2)$$

In [9]:

    

h.difference_equation()(z)


    

    
Out[9]:





$$Y(z) = 2 X(z) - \frac{X(z)}{z^{2}}$$