1. Section II
Digital Signal Processing
ES & BM

2. 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
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3. 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

4. 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
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5. Digital Signal Processing
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6. Digital Signal Processing
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7. 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
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8. DFT
The Discrete Fourier Transform (DFT) allows the computation of spectra from discrete-time data.
Digital Signal Processing
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9. 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