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
Python3
# importing librariesimport numpy as npimport matplotlib.pyplot as plt# function to generate unit step u[n-a]# LL and UL are lower and upper limits of discrete time linedef 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 advanceUL = 10LL = -10n = 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 deltaa = 4 # Enter delay or advanceUL = 10LL = -10n = 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 otherwisedef unit_ramp(n): ramp =[] for sample in n: if sample<0: ramp.append(0) else: ramp.append(sample) return rampUL = 10LL = -10n = 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 = 2UL = 1LL = -1n = 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") |
Time Complexity: O(n)
Auxiliary Space: O(n)
