A sine wave with infinite duration refers to a waveform that continues indefinitely without any end or limit. In other words, it extends infinitely in both the positive and negative time directions.
In mathematics, a sine wave is a smooth, periodic oscillation that represents a fundamental waveform. It is characterized by its amplitude (peak value), frequency (number of cycles per unit of time), and phase (the starting point of the waveform).
When we say a sine wave has an infinite duration, it means that the waveform repeats itself endlessly without any interruption. Each cycle of the sine wave is identical to the previous and subsequent cycles. This concept of infinite duration is primarily used in theoretical discussions, mathematical models, and idealized representations.
In practice, real-world signals are typically of finite duration since they are often generated or captured over a specific time interval. However, using an infinite-duration sine wave in mathematical models allows for more accurate analysis and simplifies calculations in certain cases.