Digital Signal Processing

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
• Xk corresponds to the amplitude of the signal
  at frequency fk/(NT)
• The frequency resolution of the DFT is Df1/(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
a1y(n) b1x(n) b2x(n-1) ...
bnb1x(n-nb) - a2y(n-1) - ...
ana1y(n-na)
Aa1, a2, ..., ana1
Filter parameters
Bb1, b2, ..., bnb1
Xx(n-nb), ..., x(n-1), x(n) input signal
Yy(n-na), ..., y(n-1), y(n) filtered signal
7
Ideal Filters

• Low pass filter
• High pass filter
• Bandpass filter
• Bandstop filter

8
Common Filters

• Chebyshev filter

9
Comparison of Common Filters
10
MATLAB example of Filtering
11
MATLAB Example of Undersampling