Chapter 16
Fourier Series
Trygonometryczny szereg Fouriera
A Fourier series is a mathematical technique that breaks down periodic functions into an infinite series of sinusoidal harmonics.
The trigonometric ...
Wykładniczy szereg Fouriera
In audio signal processing, the exponential Fourier series is essential for synthesizing sounds. For instance, a complex musical note can be decomposed ...
Własności szeregu Fouriera 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 ...
Własności szeregu Fouriera 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 ...
Twierdzenie Parsevala
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 ...
Zbieżność szeregów Fouriera
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 ...
Dyskretny szereg Fouriera w czasie
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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