- Digital Signal Processing Tutorial
- DSP - Home
- DSP - Signals-Definition
- DSP - Basic CT Signals
- DSP - Basic DT Signals
- DSP - Classification of CT Signals
- DSP - Classification of DT Signals
- DSP - Miscellaneous Signals

- Operations on Signals
- Operations Signals - Shifting
- Operations Signals - Scaling
- Operations Signals - Reversal
- Operations Signals - Differentiation
- Operations Signals - Integration
- Operations Signals - Convolution

- Basic System Properties
- DSP - Static Systems
- DSP - Dynamic Systems
- DSP - Causal Systems
- DSP - Non-Causal Systems
- DSP - Anti-Causal Systems
- DSP - Linear Systems
- DSP - Non-Linear Systems
- DSP - Time-Invariant Systems
- DSP - Time-Variant Systems
- DSP - Stable Systems
- DSP - Unstable Systems
- DSP - Solved Examples

- Z-Transform
- Z-Transform - Introduction
- Z-Transform - Properties
- Z-Transform - Existence
- Z-Transform - Inverse
- Z-Transform - Solved Examples

- Discrete Fourier Transform
- DFT - Introduction
- DFT - Time Frequency Transform
- DTF - Circular Convolution
- DFT - Linear Filtering
- DFT - Sectional Convolution
- DFT - Discrete Cosine Transform
- DFT - Solved Examples

- Fast Fourier Transform
- DSP - Fast Fourier Transform
- DSP - In-Place Computation
- DSP - Computer Aided Design

- Digital Signal Processing Resources
- DSP - Quick Guide
- DSP - Useful Resources
- DSP - Discussion

Previously, we saw that the system needs to be independent from the future and past values to become static. In this case, the condition is almost same with little modification. Here, for the system to be causal, it should be independent from the future values only. That means past dependency will cause no problem for the system from becoming causal.

Causal systems are practically or physically realizable system. Let us consider some examples to understand this much better.

Let us consider the following signals.

**a) $y(t) = x(t)$**

Here, the signal is only dependent on the present values of x. For example if we substitute t = 3, the result will show for that instant of time only. Therefore, as it has no dependence on future value, we can call it a Causal system.

**b) $y(t) = x(t-1)$**

Here, the system depends on past values. For instance if we substitute t = 3, the expression will reduce to x(2), which is a past value against our input. At no instance, it depends upon future values. Therefore, this system is also a causal system.

**c) $y(t) = x(t)+x(t+1)$**

In this case, the system has two parts. The part x(t), as we have discussed earlier, depends only upon the present values. So, there is no issue with it. However, if we take the case of x(t+1), it clearly depends on the future values because if we put t = 1, the expression will reduce to x(2) which is future value. Therefore, it is not causal.

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