When electromagnetic radiation passes through a material, atoms or molecules transition from a lower to a higher energy state by absorbing radiation corresponding to the energy difference between the two states. The absorption of infrared (IR) radiation causes transitions between vibrational energy levels in a molecule. Therefore, IR spectroscopy is a useful analytical tool for determining the molecular structure of molecules.
Different compounds display unique properties due to their...

IR spectra are divided into two main regions: the diagnostic region and the fingerprint region. The diagnostic region of the spectrum lies above 1500 cm−1. The absorptions resulting from single-bond vibrations of the N–H, C–H, and O–H stretch at higher wavenumbers and appear on the left side of the spectrum. The stretching absorptions of the C≡C and C≡N occur between 2100–2300 cm−1. In contrast, those arising from stretching absorptions of the C=O, C=N, and C=C occur between 1600–1850 cm−1.
The...

There are two main infrared (IR) spectrophotometers: dispersive IR spectrometers and Fourier transform infrared (FTIR) spectrometers. In a dispersive IR spectrometer, a beam of infrared radiation produced by a hot wire is divided into two parallel equal-intensity beams using mirrors. One beam passes through the sample, while another is a reference beam. The beams then move through the monochromator, which separates the radiations into a continuous spectrum of different frequencies. The...

In IR spectroscopy, signals produced by the X−H bonds (such as C−H, O−H, or N−H) can be observed in the frequency range of  2700–4000 cm–1. The C−H stretching vibration forms sharp bands in the region 2850–3000 cm–1. The presence of the O−H stretching vibration leads to the forming of an absorption band in the frequency range 3650–3200 cm−1. At the same time, N−H stretching can be confirmed by absorption bands in the 3500–3100 cm−1 range. Even though both O−H and N−H bonds vibrate at a similar...

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...