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Understanding Frequency Domain Analysis in Signal Processing

Frequency domain analysis involves interpreting signals in frequency space using techniques like Fourier Series, Fourier Transforms, and Discrete Cosine Transform. Fourier Series represents periodic functions as a sum of sines and cosines. Examples include energy maps and frequency maps. Learn about 1D and 2D signal spectrum interpretation and filtering using FT Matlab demos.

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Understanding Frequency Domain Analysis in Signal Processing

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  1. Image Fourier Transform Faisal Farooq Q: How many signal processing engineers does it take to change a light bulb? A: Three. One to Fourier transform the light bulb, one to apply a complex exponential rotational shifting operator, and one to inverse transform the removed light bulb

  2. What is frequency domain analysis ? • Analyzes the signals in the frequency space. • Primarily involves interpreting the spectrum.

  3. What are the techniques? • Fourier Series • Fourier Transforms • Discrete Cosine Transform

  4. Fourier Series A Fourier Series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Every periodic function can be represented as a sum of sine and cosine components. Why? Trust me!!!

  5. Examples

  6. Fourier Transform

  7. Representation • Energy Map • Frequency Map • Log(Abs(FT)), Why? • Demo Don’t just trust me!

  8. Document Images and FT

  9. Matlab Demos • 1D Signal Spectrum interpretation • 1D Signal Filtering • 2D Signal Spectrum interpretation • 2D Signal Filtering

  10. Discrete Cosine Transform • Similar to Fast Fourier Transform(FFT) • Note: FT = N2 , FFT = NlgN • Read Up! Next: Hough Transform and Moments Thank You!

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