• • Define how to characterize a signal
  • Examine the Fourier analysis of signals
  • Outline wavelet analysis
  • Explain the sampling theorum
  • Discuss how to ensure cyclic continuity
  • Review various data smoothing techniques

Signal Noise and Data Smoothing

What are the sources of error that may lead to a noisy signal?

Sinusoidal time-varying signal

• Frequency (f)
• Amplitude (a)
• Offset (a₀)
• Phase angle (θ)

h(t) = a₀ + a sin(2πft + θ)

2πft = ω

h(t) = a₀ + a sin(ω + θ)

Fourier Transform

Padding data

• Multiply the power at each frequency by (N+L)/N, where N is the number of nonzero values and L is the number of padded zeros

Padding discontinuities

• Windowing or subtract a trendline

Sampling Theorum

• The process signal must be sampled at a frequency greater than twice as high as the highest frequency present in the signal itself
• Minimum sampling frequency is called: Nyquist sampling frequency
  • Highest voluntary human motion: 10-20 Hz
• Shannon's reconstruction formula

Smoothing Data

• Polynomial Smoothing
  • 
  • Ninth order or less works well for human motion
  • Interpolation (Good and bad)
  • Spreadsheet
• Splines
  • Cubic and quintic splines are most common in biomechanics
• Fourier Smoothing
  • Inverse transformation
• Moving Average
  • Three and five-point
  • Spreadsheet
• Digital Filtering
  • Low Pass
  • High Pass
  • Band Pass
  • Notch
  • Spreadsheet
• End Point Problems

How do we determine the appropriate filter settings (Filtered Data, Power Sprectrum)?

Mini-Project #4