Section II Digital Signal Processing ES & BM.

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Presentation transcript:

Section II Digital Signal Processing ES & BM

Topics to be covered Fourier Series Fourier Transform Inverse Fourier Transform Discrete Fourier Transform Fast Fourier Transform Laplace Transform Z Transform Inverse Z Digital Signal Processing ES & BM

Fourier Series Fourier series decomposes a periodic function or periodic signal into a sum of simple oscillating functions, namely sines and cosines. Fourier series has many applications in electrical engineering, vibration analysis, acoustics, optics, signal processing, image processing, quantum mechanics, etc. Digital Signal Processing ES & BM

Fourier's formula for 2π-periodic functions using sines and cosines For a 2π-periodic function ƒ(x) that is integrable on [−π, π] Digital Signal Processing ES & BM

Digital Signal Processing ES & BM

Digital Signal Processing ES & BM

Fourier Transform Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Digital Signal Processing ES & BM

DFT The Discrete Fourier Transform (DFT) allows the computation of spectra from discrete-time data. Digital Signal Processing ES & BM

FFT The Fast Fourier Transform (FFT) is another method for calculating the DFT. While it produces the same result as the other approaches, it is incredibly more efficient, often reducing the computation time by hundreds. This is the same improvement as flying in a jet aircraft versus walking! Digital Signal Processing ES & BM