
48 Practical Biomedical Signal Analysis Using MATLAB
R
2. Create a vector h:
h(i)=
⎧
⎨
⎩
1fori = 1, (n/2)+1
2fori = 2, 3,...,(n/2)
0fori =(n/2)+2, ...,n
(2.65)
3. Calculate the element-wise product of X and h: Y = X ·h
4. Calculate the inverse FFT of Y.
This algorithm is implemented in MATLAB Signal Processing Toolbox as
hilbert
. The analytic signal can be presented in the form:
x
a
(t)=A(t)cos(φ(t)) (2.66)
where A(t)=|x
a
(t)| is called the instantaneous amplitude, φ(t)=arg(x
a
(t)) and
f (t)=
1
2π
d arg(x
a
(t))
dt
is called the instantaneous frequency
1
.
The concepts of instantaneous amplitude and frequency are useful in case of sim-
ple signals without overlapping frequency ...