Generating Basic Discrete Time Signals

Last Updated : 02 Sep, 2020

Generating basic discrete-time signals for Discrete-Time Signal ProcessingUnit Step, Unit Impulse, Unit Ramp, exponential signals are very commonly used signals in signal processing to perform various operations.

Unit step signal is given by
Unit impulse signal is given by
Unit ramp signal is given by
Exponential signal is given by

Examples:

Input :
Unit Step Signal u[n-2]
 
Output :


Input :
Unit Impulse Signal d(4)

Output :


Input :
Unit Ramp Signal

Output:


Input:
Exponential signal for a=2

Output:

Code: Python code implementation to generate the basic discrete time signals

# importing libraries
import numpy as np
import matplotlib.pyplot as plt
  
# function to generate unit step u[n-a]
# LL and UL are lower and upper limits of discrete time line
def unit_step(a, n):
    unit =[]
    for sample in n:
        if sample<a:
            unit.append(0)
        else:
            unit.append(1)
    return(unit)
  
# plot unit step function u[n-a]
a = 2 # Enter delay or advance
UL = 10
LL = -10
n = np.arange(LL, UL, 1)
unit = unit_step(a, n)
plt.stem(n, unit)
plt.xlabel('n')
plt.xticks(np.arange(LL, UL, 1))
plt.yticks([0, 1])
plt.ylabel('u[n]')
plt.title('Unit step u[n-a]')
plt.savefig('UnitStep.png')
  
# Function to plot Impulse signal d(a)
def unit_impulse(a, n):
    delta =[]
    for sample in n:
        if sample == a:
            delta.append(1)
        else:
            delta.append(0)
              
    return delta
  
a = 4 # Enter delay or advance
UL = 10
LL = -10
n = np.arange(LL, UL, 1)
d = unit_impulse(a, n)
plt.stem(n, d)
plt.xlabel('n')
plt.xticks(np.arange(LL, UL, 1))
plt.yticks([0, 1])
plt.ylabel('d[n]')
plt.title('Unit Impulse d[4]')
plt.savefig("UnitImpulse.png")
  
  
# Function to generate unit ramp signal r(n)
# r(n)= n for n>= 0, r(n)= 0 otherwise
def unit_ramp(n):
    ramp =[]
    for sample in n:
        if sample<0:
            ramp.append(0)
        else:
            ramp.append(sample)
    return ramp
  
UL = 10
LL = -10
n = np.arange(LL, UL, 1)
r = unit_ramp(n)
plt.stem(n, r)
plt.xlabel('n')
plt.xticks(np.arange(LL, UL, 1))
plt.yticks([0, UL, 1])
plt.ylabel('r[n]')
plt.title('Unit Ramp r[n]')
plt.savefig("UnitRamp.png")
  
# Function to generate exponential signals e**(at)
def exponential(a, n):
    expo =[]
    for sample in n:
        expo.append(np.exp(a * sample))
    return (expo)
         
a = 2
UL = 1
LL = -1
n = np.arange(LL, UL, 0.1)
x = exponential(a, n)
plt.stem(n, x)
plt.xlabel('n')
plt.xticks(np.arange(LL, UL, 0.2))
# plt.yticks([0, UL, 1])
plt.ylabel('x[n]')
plt.title('Exponential Signal e**(an)')
plt.savefig("Exponential.png")

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