Fourier Transform and Signal Spectrum - Digital Signal Processing: A Practitioner's Approach - page 80

Figure 4.1 An engineer's view of (4.1)

Figure 4.2 Digital spectrum analyser

The frequency f k is a staircase function totally defined by the step duration N and
the step height n, where n is the number of samples of the spectrum.

A typical block diagram of this method is shown in Figure 4.2 along with the
staircase function. It has three components: a BPF, a square function and a
synchronised block averager. This block averager is discussed in Chapter 3 and
is shown as a recursive filter. We can depict Figure 4.2 in the form of digital filters:

f ¼ 0 : 5 =

u k ¼ s k x k ; ð 4 : 3 Þ

ð u k u k 2 Þ;

1 r 2
2

z k ¼ rpz k 1 r 2 z k 2 þ

ð 4 : 4 Þ

E k ¼ z k ; ð 4 : 5 Þ

!
y k 1 þ

E k ;

1
1 þ

1
N þ 1

y k ¼ ð 4 : 6 Þ

1
N

where the value of p lies between 2 and þ 2. Equation (4.6) is for obtaining the
mean recursively, as described in (3.3). The initial conditions need to be reset at
each step change.

4.1.1.1 Output

A spectrum analyser is implemented using r ¼ 0 98 and p ¼ 0 for the BPF. The

staircase function is used with N ¼ 150 and n ¼ 200.

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