Real-time digital signal processing: implementations, ... changes in the input signal is limited by its internal clock rate, so that it may be slow to
Document source : notes.ump.edu.my
The maximum value of the array xn can be found using the MATLAB function
Mx max(xn);
The energy of the signal xn is defined as
E
x
n
jxnj
2
:
3:2:4
The energy of a real-valued xn can be calculated by the MATLAB statement:
Ex sum(abs(xn).^ 2);
Periodic signals and random processes have infinite energy. For such signals, an
appropriate definition of strength is power. The power of signal xn is defined as
P
x
lim
L3I
1
L
LÀ1
n0
jxnj
2
:
3:2:5
If xn is a periodic signal, we have
xn xn kL,
3:2:6
where k is an integer and L is the period in samples. Any one period of L samples
completely defines a periodic signal. From Figure 3.7, the power of xn can be
computed by
P
x
1
L
n
lnÀL1
jxlj
2
1
L
LÀ1
l0
jxn À lj
2
:
3:2:7
For example, a real-valued sinewave of amplitude A defined in (3.1.6) has the power
P
x
0:5A
2
.
In most real-time applications, the power estimate of real-valued signals at time n can
be expressed as
^
P
x
n
1
L
LÀ1
l0
x
2
n À l:
3:2:8
Note that this power estimate uses L samples from the most recent sample at time n
back to the oldest sample at time n À L 1, as shown in Figure 3.7. Following the
derivation of (3.2.2), we have the recursive power estimator
^
P
x
n ^
P
x
n À 1
1
L
x
2
n À x
2
n À L:
3:2:9
86
DSP FUNDAMENTALS AND IMPLEMENTATION CONSIDERATIONS
Summary :
In most real-time applications, the power estimate of real-valued signals at time n can be expressed as ^ P x n 1 L LÀ1 l0 x 2 n À l: 3:2:8 Note that this power estimate uses L samples from the most recent sample at time n back to the oldest sample at time n À L 1, as shown in Figure 3.7.
Tags :
power,signal,energy,signals,realalued,time,defined,periodic,hae,là1,samples,figure,matlab