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...

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...

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...

Bacterial signaling can occur within bacteria (intracellular) or between bacteria (intercellular). At times, a group of bacteria behaves like a community. To achieve this, they engage in quorum sensing, the perception of higher cell density that causes changes in gene expression. Quorum sensing involves both extracellular and intracellular signaling. The signaling cascade starts with a molecule called an autoinducer (AI). Individual bacteria produce AIs that move out of the bacterial cell...

In analyzing the behavior of diodes in circuits, the relationship between the current through a diode and the voltage across it is of particular interest, especially when considering the effect of a direct current (DC) bias voltage. When applied, this DC bias influences the diode's operating point, known as the Q point, around which the current-voltage (I-V) characteristic of the diode exhibits exponential behavior. Introducing a small, time-varying signal on top of this bias aids in examining...

Yeasts are single-celled organisms, but unlike bacteria, they are eukaryotes (cells with a nucleus). Cell signaling in yeast is similar to signaling in other eukaryotic cells. A ligand, such as a protein or a small molecule released from a yeast cell, attaches to a receptor on the cell surface. The binding stimulates second-messenger kinases to activate or inactivate transcription factors that further regulate gene expression. Many of the yeast intracellular signaling cascades have similar...