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Radiowaves diffract around mountains

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Tuning fork and guitar

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A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument.
The spectrum analyzer, also referred to as a dynamic signal analyzer, use digital signal processing to sample the input signal and convert it to the frequency domain. This conversion is done using the Fast Fourier Transform (FFT).

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The layout of the keys of a piano (bottom) are like the Fourier transform of the sound the piano makes (top). If you could see sound, it would look like air molecules bouncing back and forth very quickly.  But oddly enough, when you hear sound you’re not perceiving the air moving back and forth, instead you experience sound in terms of its frequencies.  For example, when somebody plays middle C on a piano, you don’t feel your ear being buffeted 261 times a second (the frequency of middle C), you just hear a single tone.  The buffeting movement of the air is the signal, and the tone is the Fourier transform of that signal.

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Application of Fourier series in audio demo of piano

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Tuning fork

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Earthquake : Identification of Earthquake Induced Damage Areas

Fourier series can be used to identify different spatial frequencies in images obtained before and after the earthquake which indeed lead information about the earthquake-induced damages.

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Adriana Shamisa Binti Shazarm A20EB0088 

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Adriana Shamisa Binti Shazarm A20EB0088 

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Advanced noice cancellation and cellphone networks technology uses fourier series where digital filtering used to minimize noise and bandwith demand respectively.

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Spectrum Analyzer:
This instrument reads a signal (usually a voltage) and provides the operator with the Fourier coefficients which correspond to each of the sine and cosine terms of the Fourier expansion of the signal.

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Mohammad Firdaus Bin Mohd Salleh (A20EB0035)

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Mohammad Firdaus Bin Mohd Salleh (A20EB0035)

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WIFI modulation uses orthogonal combinations of amplitude and phase to encode every bit in a stream, and even makes room for redundant data to counter the loss due to fading, reflections, multi-path, etc. All this is synthesized in a DSP engine using FFT and IFFT.

Source: https://www.quora.com/Why-are-Fourier-series-important-Are-there-any-real-life-applications-of-Fourier-series

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CONTEMPORARY DIGITAL HEARING AIDS
Fourier analysis is used in contemporary digital hearing aids for noise cancellation, equalization, feed back elimination, etc. by isolating individual components of a continuous complex waveform, and concentrate them for easier detection and/or removal.

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Nur Farisha Hanna Binti Hamizun A20EB0052

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Nur Farisha Hanna Binti Hamizun A20EB0052

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Military:
To perform reliable and safe communication. by decode the message in a special way. It can send a message under the noise level.

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Heat Distribution Mapping
is an aggregated visualization of user mouse movement, scrolling, clicks, and taps. Heat maps used by designers, UX specialists, and marketers to discover website usage patterns and make data-informed optimizations to increase conversion rate and revenue.

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A familiar clinical example of a Fourier space is the frequency and amplitude spectrum obtained  during MR spectroscopy . The multiple peaks (amplitudes) in the MR spectroscopy spectrum represent the relative contributions of particular biologic metabolites in a given region of interest (ROI), each differing slightly in resonance frequency as a result of its unique chemical structure .

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It’s a bit obvious for to write that there would be digital telecom without Nyquist-Shannon theorem and Fourier Transform. Both are extremely important. Fourier transform has greatly improved the way we are sending/collecting data. Note that mp3 file format uses transform. Transforms are used in file compression: for instance cosinus transform is also used in jpeg file compression. There are numerous applications in telecoms, and therefore I decided not to dwell on them and go further.

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Noise cancellation and cell phone network technology uses Fourier series where digital filtering is used to minimize noise ans bandwidth demands respectively

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Monsoon rainfall
- Monsoon rainfall brings trouble since it always brings to flood.
- Predicting the rainfall with rainfall model has been conducted but it is too complex since it involves different set of parameters which are spatial and temporal variation .
- Thus, a technique often incorporated into the rainfall model is the harmonic analysis of Fourier series.
-  This technique focuses on two main category which are representing seasonal variation of rainfall process throughout the year and investigating the pattern of spatial variation of rainfall process within a large region.

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Fourier series is used in telecommunication to improved data sending and collecting process.

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Nuraisyah Amira Binti Mohd Daman Huri A20EB0056

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Nuraisyah Amira Binti Mohd Daman Huri A20EB0056

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Spectrum Analyzer measures the input signal versus frequency within the full frequency range of the instrument.

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1)Sound processing by brain through the vibration in inner ear.
2)Planetary motions (eg. orbits of moon surrounds the earth)

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Application of Fourier series in blood pressure.

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Violin

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Computerized axial tomography uses X-ray waveform to make images of bone, soft tissue, and organs of the human body without harming the matter.

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Hiss and pop in sound recordings can be cleaned up using Fourier analysis. What is static but a super-high frequency sound--higher than most sounds that normally appear in music and speech, etc. When a time-domain signal is represented in the frequency domain, i.e., as a sum of sine waves, you can cure the static by simply erasing all the highest frequencies and then reconstituting the sound.

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Radio waves

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Hearing aids
Fourier analysis is a technique that is used to determine which sine waves constitute a given signal, i.e., to deconstruct the signal into its individual sine waves.

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Image Processing
It used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalently.

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Medicine – imaging and MRI/CT

MRI is using fourier transform to obtain an image from the device measurments. Note that there are two possible ways of storing image: the first one – colour based, that we are used to and the second one – using spectrum. You can switch between them using Fourier transform.

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Guitar

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Military
The main point of Fourier Transform in military applications is: perform reliable and safe communication. Using fourier transform you can decode your message in a special way.

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Use of Fourier Transforms in MP3 Audio Compression

With MP3, the sound samples are transformed using methods that involve Fourier Series Transformations. You take a sound, expand its Fourier Series. It'll most likely be an infinite series BUT it converges so fast that taking the first few terms is enough to reproduce the original sound. The rest of the terms can be ignored because they add so little that a human ear can likely tell no difference. So I just save the first few terms and then use them to reproduce the sound whenever I want to listen to it and it takes much less memory.

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approximation theory-We use Fourier series to write a function as a trigonometric polynomial.

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Signal Processing.
It may be the best application of Fourier analysis.

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MUHAMMAD ALIF ZAWAWI BIN AHMAD SAFUAN B20EM0053

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MUHAMMAD ALIF ZAWAWI BIN AHMAD SAFUAN B20EM0053

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Voice recognition systems

The system verify the user by analyzing its voice using Fourier Transform.

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Fourier Series used in communication (cell phones) :
Fourier series shows the waveform of frequencies that are allowed in transmission on cell phones. Fourier series is used to determine the signal of voice that enters or leaves a phone's microphone. For example, white noise is a superposition of all frequencies with equal amplitudes. We can determine which frequencies make it through even if we send many frequencies at once.

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The fourier series found in vibration of guitar strings

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Fourier also used in military for realiable and safe communication. Using fourier transform you can decode your message in a special way.. It will send a message under the noise level.

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Military Applications for Fourier Transform Infrared (FTIR) Spectroscopy

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UV WAVES

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one of the best way of the application of fourier series would be its usage on signal. Signal itself works on a lot of technologies these days, such as smartphone, vehicles, aircraft until as advanced as satellite.

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X-rays

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Application of Fourier Series in FFT Spectrum Analysis.
Hollingsworth, M. (2019). Applications of the Fourier Series.

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Fourier series can use in image compression

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In the field of astronomy, sometimes you need to use radio waves or radar instead of light. These radar signals are treated just like any other ordinary time varying voltage signal and can be processed digitally. Magellan is a satellite that was sent to Venus had radar and advanced Digital Signal Processing (signal processing techniques consist of Fourier-transforming a signal, manipulating the Fourier-transformed data in a simple way, and reversing the transformation) that was designed to see through this cloud layer.

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sound wave

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Use in landslide analysis.
- the landslide process is reconstructed and compared with the DEM simulation, after analyzing the short-time Fourier transform (STFT) and fast Fourier transform (FFT) characteristics of the signal.

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Motor Tester
Fast Fourier Transform allows us to view voltage and current waveforms from another direction; from the perspective of frequency. This view enable us to see distortions in the waveforms in a different presentation, allowing us to pinpoint how these distortions occur in relation to one another.

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Fetal Ultrasound Image

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X0000_GE_Volusion E10 ultrasound fetal 3D 4D image_1

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Heat flow

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If you think about how a speaker can play music:
-It is a single cone that moves up and down to form a wave.
-If you want to play a chord lets say, you must be able to play more than one note at the same time. Meaning that you must add together waves of different wavelengths/frequencies to form a more complex wave.

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Heat Distribution Map for Football Data Statistics Analysis

Spectogram or known as heat map utilizes Fourier Series Transform to obtain optical spectometer to find magnitude of the frequency of each object.

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Using Fourier series to draw the scalable vector graphic

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Image processing

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Heat Distribution Mapping

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Fourier transforms are useful tools for the analysis of sounds and images. In this case, the calibration of tuning fork use by otolaryngologist.
The sound wave of the middle A on a tuning fork, is a perfect example of a sine wave, written mathematically as sin(x).
The expression of a sound wave, or any signal varying over time, as the sum of its constituent sine waves, is known as the Fourier transform of that signal.

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can be used for image processing tool which used to decompose image into sine and cosine components.

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spectrum of a violin

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cab help to tuning the guitar

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Fourier series can be used to accurately isolate the ECG data from that which is recorded and may contain noise.

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WIFI

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Nurul Aina Haziqah binti Riduan A20EB0059

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Nurul Aina Haziqah binti Riduan A20EB0059

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The Fourier transform has an analytical form applicable to continuous functions and also has a discrete form applicable to discrete functions That one is called Discrete Fourier Transform (DFT). From the DFT, we can obtain estimates for the PSD of experimental real-time series. The statistics that gives an estimation of the relative energy among the different frequencies present in a signal is called the periodogram.

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Any waveform is actually just the sum of a series of simple sinusoids of different frequencies, amplitudes, and phases.  A Fourier series is that series of sine waves; and we use Fourier analysis or spectrum analysis to deconstruct a signal into its individual sine wave components.  The result is acceleration/vibration amplitude as a function of frequency, which lets us perform analysis in the frequency domain (or spectrum) to gain a deeper understanding of our vibration profile. Most vibration analysis will typically be done in the frequency domain.

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Biological Sequence Analysis

Biological Sequence analysis based on Ramanujan-Fourier transform (RFT), in which complete information of DNA sequences is retained. We represent DNA sequences as four binary indicator sequences and apply RFT on the indicator sequences to convert them into frequency domain. The Euclidean distance of the complete RFT coefficients of DNA sequences are used as similarity measure. To address the different lengths in Euclidean space of RFT coefficients, we pad zeros to short DNA binary sequences so that the binary sequences equal the longest length in the comparison sequence data. Thus, the DNA sequences are compared in the same dimensional frequency space without information loss.

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

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advanced noise cancellation and cell phone network technology uses Fourier series where digital filtering is used to minimize noise ans bandwidth demands respectively

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digital communication that use discrete Fourier transforms to extract signals that are so deeply buried in noise that the human ear would not notice it. This allows communication with very low power which is at reduced speed.

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X-ray crystallography is a method for determining the arrangement of atoms within a crystal structure.

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Sound waves are one type of waves that can be analyzed using Fourier series, allowing for different aspects of music to be analyzed using this method. Musical instruments produce sound as a result of the vibration of a physical object such as a string on a violin, guitar, or piano, or a column of air in a brass or woodwind instrument. This vibration causes a periodic variation in air pressure that is heard as sound.

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image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent.

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Telecommunications System
For modulation and demodulation of voice signals, also the input,output and calculation of pulse and their sine or cosine graph.

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1- Voice recognition systems
2- Hearing devices
3- Telecommunication

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instrument sound wave

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Fourier at the heart of computer music: From harmonic sounds to texture Fourier at the heart of computer music: from harmonic sounds texture

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In communication, the Fourier Series is used (cell phones)
The waveform of frequencies that are allowed in cell phone transmission is represented by the Fourier series.The Fourier series is used to calculate the signal of voice entering or leaving a phone's microphone. White noise, for instance, is a superposition of all frequencies of equal amplitude. Even if we don't see which frequencies make it through,we can figure out which ones do.

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Nurin Zafirah binti Mohd Nasran A20EB0057

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Nurin Zafirah binti Mohd Nasran A20EB0057

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Speech recognition

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The wave equation is an important second-order linear partial differential equation. The applications occur in classical physics such as light wave.

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In the use of MRI in medical field

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Fourier analysis is used to decompose sound or any other periodic function into its constituent sine waves or cosine waves. We can characterize the sound wave according to the amplitude of the sine wave that composes it.

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Aiman Nurizzah Binti Syahrul Anuar A20EE0243

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Aiman Nurizzah Binti Syahrul Anuar A20EE0243

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ventilator wave form

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Foirier series in musical instrument

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Image Processing

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Natural frequency of bridge and building

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telecommunication-sending and collecting data

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MUHAMMAD AMMAR YASEER BIN AZIZAN (A20EE0136)

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MUHAMMAD AMMAR YASEER BIN AZIZAN (A20EE0136)

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Heat Distribution Mapping

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Used in advanced noise cancellation technology (digital filtering)

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uses in military applications;
-perform reliable and safe communication
-fourier transform can decode messages in a special way
-to sent a message under the noise

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Cell phone network technology

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Use to understand the wave properties of light

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piano sound wave

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Compressing audio file into .mp3 format.
A lossless audio file (.FLAC) has a very big filesize. With fourier transform it is possible to make an software that reproduce the original sound quality without the excess file size.

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sum of sound wave in musical instruments

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Use for radiation measurements.
- A Fourier-transform radiometer is used to measure blackbody temperatures in the 500–1000-K range.

-The measurements involve collecting mid-infrared spectra.

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Cellphone also is one of item that use Fourier Series that is transmitting or receiving signal waves.

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FTIR can be an important analytical instrument in a forensic investigation. A FTIR can be useful in detecting both organic chemicals (i.e., those that contain carbon) and inorganic chemicals. ... The basis of FTIR is the absorption of the infrared light by various molecules in a sample.