Why we use Fourier analysis for communication system?

In the theory of communication a signal is generally a voltage, and Fourier transform is essential mathematical tool which provides us an inside view of signal and its different domain, how it behaves when it passes through various communication channels, filters, and amplifiers and it also help in analyzing various …

Why do we take Fourier and Laplace transform of signal?

3. Fourier transform helps us to study anything in the frequency domain whereas laplace transform is usually done for complex analysis (when anything is not easier to analyse in time domain, we convert it into s domain and then take the inverse laplace transform to complete the analysis).

Why do we use Laplace in control system?

The Laplace transform plays a important role in control theory. It appears in the description of linear time invariant systems, where it changes convolution operators into multiplication operators and allows to define the transfer function of a system.

Why do we use Fourier?

The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The Fourier Transform is used in a wide range of applications, such as image analysis, image filtering, image reconstruction and image compression.

How Fourier transform is used in wireless network communication?

The Fourier Transform is an algorithm used in many functions, including signal processing or statistical applications across a broad range of applications. Every wireless device–netbook, notebook, tablet, and phone have been built in high-speed cellular data connection, just like Fourier Transform.

What is Fourier series in signals and systems?

The Fourier series represents periodic, continuous-time signals as a weighted sum of continuous-time sinusoids. It is widely used to analyze and synthesize periodic signals. The trigonometric form expresses real-valued signals as weighted sums of harmonically related sines and cosines.

What is the main difference between Fourier transform and Laplace transform?

Fourier transform is defined only for functions defined for all the real numbers, whereas Laplace transform does not require the function to be defined on set the negative real numbers. Every function that has a Fourier transform will have a Laplace transform but not vice-versa.

How is Laplace transform useful in the analysis of LTI system?

The Laplace transform is a powerful tool to solve linear time-invariant (LTI) differential equations. We have used the Fourier transform for the same purpose, but the Laplace transform, whether bilateral or unilateral, is applicable in more cases, for example, to unstable systems or unbounded signals.

What is control system and why it is required?

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines.

How Fourier series is important in explaining the general motion of continuous system?