DSP - types of sequences

In the last post, I demonstrated plotting of analog and digital signals. It may be noted that the plotted sine wave is basically a combination of a lot of discrete values, as can be seen from the code.

In this post, I shall be focusing on different sequences, namely, impulse, unit step, exponential, sinusoidal, random and periodic sequences. Most of the DSP operations are carried out on these sequences. So, we move forward one by one.

• Unit Impulse signal, also known as a unit sample sequence. The value of such a signal is unity at n = 0, that is the home position (in context of robotics). Consider a clap. A clap is like an impulse signal, momentary, maximum value at one point in time. The following figure shows the impulse signal. Here's the code.
  
  
  
  
• Unit step signal - Simply, consider switching on a fan. It starts working. The analogy can be extended to understanding unit step signal. Therefore, until a certain point in time, the value of a signal is zero, and after that time, the signal's value is 1. The following figure shows a unit step signal. Here's the code.

• Exponential signal - Consider population explosion, humans were hardly near 500 million people near 1600 AD and we rose to nearly 2 billion in 300 years (1900 A.D.) which plummeted to 6 billion in just 100 more years. Such an increase is exponential in nature. The plot below shows a real valued exponential signal. Code. Complex exponential signals' code can be seen here. As you'll see on implementing, it is sinusoidal in nature (Euler's formula).

• Sinusoidal signal - Consider the transmitting of signals in AC systems. The signals show a sinusoidal variance with respect to time. The following figure shows a sinusoidal variation. Here's the code.

• Random sequences - Most of the stuff happening around us is random in nature. The following figure shows a random curve. Here's the code.

• Periodic sequences - These are the sequences which repeat after a certain amount of time. A sinusoidal signal is periodic sequence. Each periodic signal has a period, which is the time after which the signal repeats. For the sinusoid given above, the period is (2*pi/5 = 1.257) approximately 1.26 seconds.