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Digital Signal Processing

Digital Signal Processing. Discrete Fourier Transform. Discrete Fourier Transform. Inverse Discrete Fourier Transform. Properties of DFT. DFT has the same number of datapoints as the signal The signal is assumed to be periodic with a period of N

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Digital Signal Processing

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  1. Digital Signal Processing

  2. Discrete Fourier Transform Discrete Fourier Transform Inverse Discrete Fourier Transform

  3. Properties of DFT • DFT has the same number of datapoints as the signal • The signal is assumed to be periodic with a period of N • X[k] corresponds to the amplitude of the signal at frequency f=k/(NT) • The frequency resolution of the DFT is Df=1/(NT), i.e. the # of samples determines the frequency resolution

  4. Steps for Calculating DFT • Determine the resolution required for the DFT, establish a lower limit on the # of samples required, N. • Determine the sampling frequency to avoid aliasing • Accumulate N samples • Calculate DFT

  5. Matlab Example of FFT

  6. Digital Filtering a1*y(n) = b1*x(n) +b2*x(n-1) + ... + bnb+1x(n-nb) - a2*y(n-1) - ... – ana+1*y(n-na) A=[a1,a2,..., ana+1] Filter parameters B=[b1,b2,..., bnb+1] X=[x(n-nb),..., x(n-1), x(n)]: input signal Y=[y(n-na),..., y(n-1), y(n)]: filtered signal

  7. Ideal Filters • Low pass filter • High pass filter • Bandpass filter • Bandstop filter

  8. Butterworth filter: Common Filters • Chebyshev filter:

  9. Comparison of Common Filters

  10. MATLAB example of Filtering

  11. MATLAB Example of Undersampling

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