User`s guide

Chirp
5-66
examine the following table and the diagram in “Shaping the Frequency
Sweep by Setting Frequency Sweep and Sweep Mode” on page 5-62.
Table 5-2 contains the following variables:
•f
i
(t) — the user-specified frequency sweep
•f
i(actual)
(t) — the actual output frequency sweep, usually equal to f
i
(t)
•y
chirp
(t) — the Chirp block output
• — the phase of the chirp signal, where
, and is the
derivative of the phase
• — the
Initial phase parameter value, where
.
Output Computation Method for Linear, Quadratic, and Logarithmic Frequency Sweeps.
The derivative of the phase of a chirp function gives the instantaneous
frequency of the chirp function. The Chirp block uses this principle to calculate
ψ t() ψ0() 0= 2πf
i
t()
f
i
t()
1
2π
------
dψ t()
dt
---------------
⋅=
φ
0
y
chirp
0() φ
0
()cos=
Table 5-2: Equations Used by the Chirp Block for Unidirectional Positive Sweeps
Frequency
Sweep
Block Output Chirp Signal User-Specified
Frequency
Sweep,
f
i
( t )
Actual Frequency
Sweep,
f
i(actual)
( t )
Linear
Quadratic
Same as Linear
Logarithmic
Same as Linear
Note f
i
(0) = f
0
+1
Where
f
i
(t
g
)>f
0
Swept cosine
Same as Linear Same as Linear
β
y
chirp
t()
ψ t() φ
0
+()cos= f
i
t() f
0
βt+=
β
f
i
t
g
()f
0
–
t
g
--------------------------=
f
i actual()
t() f
i
t()=
f
i
t() f
0
βt
2
+=
β
f
i
t
g
()f
0
–
t
g
2
--------------------------=
f
i actual()
t() f
i
t()=
f
i
t() f
0
10
βt
+=
β
f
i
t
g
()f
0
–[]log
t
g
----------------------------------------=
f
i actual()
t() f
i
t()=
y
chirp
t() 2πf
i
t()t φ
0
+()cos=
f
i actual()
t() f
i
t() βt+=