The Fourier transform, named after Joseph Fourier, is a mathematical transformation employed to transform signals between time (or spatial) domain andfrequency domain, which has many applications in physics and engineering. It is reversible, being able to transform from either domain to the other. The term itself refers to both the transform operation and to the function it produces.
This is the basic mathematical tool used for the calculation of difficult mathematical problems, specially, when the problem is related to any domain. like time domain, frequency domain, space domain and others.
This is the basic mathematical tool used for the calculation of difficult mathematical problems, specially, when the problem is related to any domain. like time domain, frequency domain, space domain and others.
Fourier transform converts every domain to s domain which has real and negative part. The poles and zeros are on either real part or on imaginary part. If they are on real axis and at negative side then the system is stable, If the are on positive side then system is unstable. If they are on imaginary axis then system is marginal stable.
Fourier transform gives the relation between time domain to frequency domain, so we can easily convert a signal in other domains. In frequency domain it is very easier to solve and complex problem. but in time domain it very easier to design the system. So for system designing and its performance characterization we need Fourier Transform.
Fourier transform is the natural mechanism used by the nature to solve the optical problem as the lens give the Fourier transform of any signal at its focus, when signal is originated from its other focus. It can be so simple in the solving a differentiation or integral problem. Since it is in the form of exponential and differentiation and integration of the exponential is exponential.
Fourier transform gives the relation between time domain to frequency domain, so we can easily convert a signal in other domains. In frequency domain it is very easier to solve and complex problem. but in time domain it very easier to design the system. So for system designing and its performance characterization we need Fourier Transform.
Fourier transform is the natural mechanism used by the nature to solve the optical problem as the lens give the Fourier transform of any signal at its focus, when signal is originated from its other focus. It can be so simple in the solving a differentiation or integral problem. Since it is in the form of exponential and differentiation and integration of the exponential is exponential.
The Fourier Transform is extensively used in the field of Signal Processing. In fact, the Fourier Transform is probably the most important tool for analyzing signals in that entire field.
So what exactly is signal processing? I'll try to give a one paragraph high level overview.
A signal is any waveform (function of time). This could be anything in the real world - an electromagnetic wave, the voltage across a resistor versus time, the air pressure variance due to your speech (i.e. a sound wave), or the value of Apple Stock versus time. Signal Processing then, is the act of processing a signal to obtain more useful information, or to make the signal more useful.
How can a signal be made better? Suppose that you are listening to a recording, and there is a low-pitched hum in the background. By applying a low-frequency filter, we can eliminate the hum. Or suppose you have a digital photograph, and it is very noisy (that is, there are random specs of light everywhere). We can use signal processing and fourier transforms to filter out this undesirable "noise".
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