Sign or Signum Signal

1
Sign or Signum Signal

• The sign or signum function is defined as

The signum function can be expressed as the limit
of xn(t) defined by
Fourier transform
when n?8.
2
Hilbert Transform

• Hilbert transform is defined as

• Hilbert transform is equivalent to a -p/2 phase
  shift for positive frequencies and a p/2 phase
  shift for negative frequencies.

• The energy contents of a signal is equal to the
  energy contents of its hilbert transform.

3
Example Hilbert Transform

• Determine the hilbert transform of

Taking the inverse transform, we have
4
Energy and Power
Energy of the signal
Power of the signal
Trignometric relation
5
Energy Type signals
Autocorrelation
Energy spectral density
Input output relationship
6
Power Type signals
Autocorrelation
Power spectral density
Input output relationship
7
Periodic signals
Autocorrelation
Power spectral density
Input output relationship