Chapter 16
Fourier Series
Trigonometric Fourier series
A Fourier series is a mathematical technique that breaks down periodic functions into an infinite series of sinusoidal harmonics.
The trigonometric ...
Exponential Fourier series
In audio signal processing, the exponential Fourier series is essential for synthesizing sounds. For instance, a complex musical note can be decomposed ...
Properties of Fourier series I
The exploration of the properties of the Fourier series begins with linearity.
When considering two periodic signals and forming a third by their linear ...
Properties of Fourier series II
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
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 ...
Convergence of Fourier Series
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 ...
Discrete-Time Fourier Series
The Discrete-Time Fourier Series is a counterpart to the Fourier-series expansion of continuous-time periodic signals.
Calculating the expansion ...
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