# What Are the Applications of Fourier Transform?

Fourier transform is an important mathematical formula that can be used to transform a signal from the time domain to the frequency domain or vice versa. It has many applications in engineering, physics, and other sciences. The most common application of the Fourier transform is in spectroscopy.

#### Spectroscopy and the Fourier Transform

Spectroscopy is an important area of research that involves the measurement of the wavelength distribution of radiation in order to identify and understand its properties. Spectroscopy is used in many fields including biological and chemical analysis, environmental science, astronomy, military and aerospace, and medical diagnosis. The use of the Fourier transform in spectroscopy is especially useful for the accurate and sensitive measurement of line-shaped feature patterns.

In a Fourier Transform, a function is decomposed into its component frequencies (also known as harmonics) and then rebuilt from these components. This process can be applied to any signal, no matter how complex or complex-looking.

The Fourier transform can also be used to decompose signals that have been corrupted with random noise. This technique is often applied in scientific applications, where signals are frequently corrupted by the presence of random noise that hides their frequency components.

For example, a signal can be distorted by random noise that makes it look like a square wave or other non-periodic function. The Fourier transform can reveal the frequencies of these spikes and allow us to reconstruct the original signal.

Stroboscopes are another application of the Fourier transform. The Fourier transform can be applied to a stroboscope and the resulting artificial signal can be used to determine where in the cycle a target is oscillating.

#### FT-IR Spectroscopy

FT-IR spectroscopy is an important type of spectroscopic technology. Using the Fourier transform, a spectrum can be resolved to a much higher resolution than is possible with conventional spectroscopic techniques. This technique is widely used in the field of infrared absorption spectroscopy, but is also applicable to the visible and the ultraviolet.

Interferometers are another application of the Fourier transform. These spectrometers are used to collect interferograms from an electromagnetic radiation source in the time-domain or space-domain, and then convert them to frequency-domain. These spectrometers are often used for infrared absorption spectroscopy, as well as for surface infrared reflectometry and pulsed laser ablation (Back, 1991; Johnston, 1991).

#### Digital image processing

Image reconstruction is an application of the Fourier transform that can be performed on digital images. The transform is useful for reducing the amount of data needed to store an image, while still maintaining a high quality. The transform is commonly used in the JPEG compression algorithm, which uses a variant of the Fourier transform to compress small square pieces of an image into a very compact representation.

The Fourier transform has a vast spectrum of scientific applications, in physics, number theory, combinatorics, signal processing, probability, statistics, cryptography, acoustics, optics, and other areas. The transform has also been used in a variety of mathematical techniques, including convolution, and is sometimes called the “discrete cosine transform.” It can be quickly calculated by digital computers.