Fourier Series

A Fourier series is a mathematical technique that breaks down periodic functions into an infinite series of sinusoidal harmonics. The trigonometric …

In audio signal processing, the exponential Fourier series is essential for synthesizing sounds. For instance, a complex musical note can be decomposed …

The exploration of the properties of the Fourier series begins with linearity. When considering two periodic signals and forming a third by their linear …

When a signal undergoes time scaling, the Fourier series coefficients remain the same, but the representation of the Fourier series changes due to an …

Parseval's theorem states that if a function is periodic, then the average power of the signal over one period equals the sum of the squared …

The Fourier series of a signal is an infinite sum of complex exponentials. The infinite sum is often truncated to a finite partial sum to make it …

The Discrete-Time Fourier Series is a counterpart to the Fourier-series expansion of continuous-time periodic signals. Calculating the expansion …