A static system is a system in which output at any instant of time depends on the input sample at the same time. In other words, the system in which output depends only on the present input at any instant of time then this system is known as the static system. A static system is … Read more
Energy signal is a signal whose energy is finite and power is zero whereas Power signal is a signal whose power is finite and energy is infinite. For the energy signal, we have 0 < E < ∞ and P = 0 where E is the energy of the signal and P is the … Read more
Bounded Signal is a signal which is having a finite value at all instants of time. Consider a continuous-time signal x(t) such that x(t) has finite-amplitude (value) at all time (t) as shown in figure 1 is an example of the bounded signal. Examples of bounded signals are sin(t), cos(t), u(t). All these three signals … Read more
A system is said to be causal system if its output at all the instants depends on the past value and/or present value of the input. A system is said to be a non-causal system if its output at any instant depends on the future value of the input. Consider the following system. x(t) is … Read more
A system is an interconnection/arrangement of different physical components which maps a set of inputs to a set of outputs to achieve certain objectives. How to express the system? There are a number of ways to express/describe systems. Systems can be described by 1. Input-output relationship example, y(t) = t x(t) 2. Differential equation example, … Read more
In this article, we will see Parseval’s theorem proof. Before we go any further, first learn What is Parseval’s theorem? It states that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform. Parseval’s theorem is also known as Rayleigh’s energy theorem or Rayleigh’s Identity … Read more
In signal processing, signal undergoes several manipulations of independent variable i.e. time. Based upon that we can classify operation as Operations corresponding to transformation of independent variable (Time) Time Shifting Time Scaling Time Reversal Let us see each operation one by one. Time Shifting A signal x(t) may be shifted in time by replacing the … Read more
Invertible System The system is invertible if by observing the output, we can determine its input i.e. we can construct an inverse system that when cascaded with the given system, as shown in figure1, yields an output equal to the original input of the given system. The inverse system ‘undoes’ what the given system does … Read more
Time-Invariant System The system is time invariant if the behaviour and characteristic of the system are fixed over time. In other words, a system is said to be time invariant if a time shift in the input signal causes an identical time shift in the output signal. It means that for continuous time if x(t) → y(t), then x(t-to) → y(t-to) … Read more
Linear System A system is said to be linear if superposition principle is applicable to the system. Superposition Principle The response resulting from several input signals can be computed as the sum of the responses resulting from each input signal acting alone. Let x1(t) and x2(t) be the two inputs. The corresponding responses/output are y1(t) … Read more