Integration of Signals

What are Basic Signal Operations?

Basic Signal Operations refer as the fundamental operations that can be performed on signals. These operations are fundamental in analyzing and manipulating signals for various operations such as telecommunications, audio processing, image processing, and control systems. These operations can be modified with respect to time and amplitude characteristics. Next, we will classify the Basic Operation of Signals...

Classification of Basic Operation on Signals

The operation of the Signal can be performed on two variable parameter...

Basic Signal Operations Performed on Amplitude

Basic operations on dependent variable amplitude also known as amplitude transformations. In which we manipulate or modify the amplitude of the signal by applying mathematical operations to its amplitude while the time axis of the signal is constant....

Amplitude Scaling of Signals

Amplitude scaling is the amplification or attenuation of the signal. By using amplitude scaling, we can increase or decrease the strength or gain of the signal, which depends on the scaling factor....

Amplitude Reversal of Signals

The amplitude reversal is the folding of the signal about the horizontal axis, or it is simply a mirror image about the horizontal axis. Amplitude reversal gives a 180-degree phase shift with respect to the horizontal axis....

Addition of Signals

The addition operation of two or more signals consists of adding amplitude of all the signal at every instant of time or space, resulting in new signals that have the characteristics of all signals combined together....

Multiplication of Signals

Signal multiplication is also a basic signal operation. The multiplication of two or more signals involves multiplying their amplitudes, which creates a new signal. This basic operation is very useful in the process of modulation, filtering etc....

Differentiation of Signals

The operation of differentiation of signal is only applicable to continuous–time signals as differentiation is not defined for discontinuous signals. It represents instantaneous slope or the rate of change of the continuous signal with respect to time....

Integration of Signals

In the same manner as differentiation, integration of signals can only be applied to continuous-time signals. It is the definite integration of the signal over the interval from negative infinity to present time t. This operation is used to find the area under the curve of the signal....

Integration of square wave signal

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Basic Signal Operations Performed on Time

Basic operations on independent variable time are also known as Time transformations. In which we manipulate or modify the time axis of a signal by applying mathematical operations to its independent variable denoted as ‘ t ‘ while the amplitude of the signal is constant....

Time-Shifting of Signals

Time shifting is the shifting of the entire signal along the time axis. By applying this operation, shape of the signal remains the same, only the position of the signal changes. It is nothing but the shifting of the origin of the signal....

Time-Scaling Operation of Signals

Time scaling is the compression or expansion of the signal on its time axis. It increases or decreases the duration of the existence of the signal. when we manipulate the time axis of a signal by multiplying a constant by its independent variable denoted as ‘ t ‘ . the compression or expansion of the signal depends on a constant or scaling factor....

Time-Reversal of Signals

The time reversal of a signal is the folding of the signal about the vertical axis, or the line t = 0. It is simply taking a mirror image of the signal about the vertical axis. Time reversal and time shifting are both very useful in finding the convolution of signals....

Conclusion

In conclusion, Basic signal operations are very important tools for audio, video and image processing, communication systems, control systems etc. We learned basic signal operations performed on dependent amplitude and independent variable time. In which we discussed various types of time transformation like time-shifting of signals, time-scaling of signals, reflection of signals and various amplitude transformations such as amplitude scaling of signals, amplitude reversal, addition of signals, multiplication of signals, differentiation of signals and integration of signals. Throughout our discussion, we used examples to illustrate how these operation are applied in practice....

Basic Signal Operations – FAQs

What do you understand by a time-invariant system?...