Fourier Transform and Signal Spectrum - Digital Signal Processing: A Practitioner's Approach - page 96

Figure 4.17 Frequency sweeping input for an unknown device

fi fi

N k þ

Let the input u i k ¼ cos ð 2

N k Þ and the output measured be y i k ¼ A i cos ð 2

i

Þ
under steady-state conditions. The term f N ¼ f n is the normalised frequency. For
each frequency f , measurements are made to obtain A i and

i at steady state. For

fi
N , y k , y k 1 , y k 2 , u k ,

each measurement of A i and

i at a specific frequency value of

u k 1 , and u k 2 are computed as follows:

fi
N k þ

y i k ¼ A i cos 2

i

; ð 4 : 36 Þ

fi
N ð k 1 Þþ

y i k 1 ¼ A i cos 2

i

; ð 4 : 37 Þ

fi
N ð k 2 Þþ

y i k 2 ¼ A i cos 2

i

; ð 4 : 38 Þ

fi
N k

u i k ¼ cos 2 ; ð 4 : 39 Þ

fi
N ð k 1 Þ

u i k 1 ¼ cos 2 ; ð 4 : 40 Þ

fi
N ð k 2 Þ

u i k 2 ¼ cos 2

: ð 4 :

41 Þ

Now we can rewrite (4.35) using the above data as

i t

y i k ¼ g

p; ð 4 : 42 Þ