5th order Polynomial not accurate enough?

136 Views Asked by At

I have a data plot XY that goes from (X 0-127, Y -70.0 - 6.0 db)

Im using the 5th order polynomial function from plotting this data on this site [http://www.zizhujy.com/en-us/Plotter][1]

However, its not accurate at all at the top end (comes out at 8.5 db when it should be 6 db)

Is there any way of getting a more accurate curve (especially at the top end)? I cant use any more than 5th order polynomial (im using it in a development environment and can only input a set amount of characters)

[1]: http://www.zizhujy.com/en-us/Plotter db

0   -100
1   -78
2   -66
3   -59
4   -54
5   -50
6   -47
7   -44
8   -42
9   -40
10  -38
11  -36
12  -35
13  -33
14  -32
15  -31
16  -30
17  -29
18  -28
19  -27
20  -26
21  -25
22  -24
23  -24
24  -23
25  -22
26  -21
27  -21
28  -20
29  -20
30  -19
31  -18
32  -18
33  -17
34  -17
35  -16
36  -16
37  -15
38  -15
39  -14
40  -14
41  -13
42  -13
43  -13
44  -12
45  -12
46  -11
47  -11
48  -11
49  -10
50  -10
51  -9.7
52  -9.4
53  -9
54  -8.7
55  -8.4
56  -8.1
57  -7.8
58  -7.5
59  -7.2
60  -6.9
61  -6.6
62  -6.3
63  -6.1
64  -6.1
65  -6.1
66  -6.1
67  -6.1
68  -6.1
69  -6.1
70  -5.2
71  -4
72  -3.7
73  -3.5
74  -3.3
75  -3
76  -2.8
77  -2.6
78  -2.4
79  -2.1
80  -1.9
81  -1.7
82  -1.5
83  -1.3
84  -1.1
85  -0.9
86  -0.7
87  -0.5
88  -0.3
89  -0.1
90  0.1
91  0.3
92  0.5
93  0.7
94  0.8
95  1
96  1.2
97  1.4
98  1.6
99  1.7
100 1.9
101 2.1
102 2.2
103 2.4
104 2.6
105 2.7
106 2.9
107 3.1
108 3.2
109 3.4
110 3.5
111 3.7
112 3.9
113 4
114 4.2
115 4.3
116 4.5
117 4.6
118 4.8
119 4.9
120 5
121 5.2
122 5.3
123 5.5
124 5.6
125 5.7
126 5.9
127 6
2

There are 2 best solutions below

1
On BEST ANSWER

You can do it with the zizhujy.com/en-us/Plotter : checkbox "Logarithm fit" (see the result below, very closed to my own result) But this program cannot compute the parameter $c$ . So, I added $c=0.3$ to the input $x$ data. (without a more sophisticated software, anyway you can approximate $c$ by groping).

enter image description here

3
On

A very good fit is obtained with a function of the form $y=a+b\ln(x+c)$

enter image description here