How to get rid of sign() in diff() results?

I have a symbolic function. diff() produces the result with sign(). The next derivative has dirac() in it. Is there a way to get rid of sign() in the diff() result?

Answer 1

[Paul]

If the goal is to get an expression for the amplitude of the frequency response of H(s) and then differentiate ...

syms R1 R2 C1 C2 w real
assume(R1>=0); assume(R2>=0); assume(C1>=0); assume(C2>=0);
syms s
H(s)=1/(C1*C2*R1*R2*s^2 + (C2*R1 + C2*R2)*s + 1);
A = abs(H(1j*w))

A = 

A = rewrite(A,'sqrt')

A = 

A_R1 = diff(A,R1)

A_R1 = 

A_R1_R1 = diff(A,R1,2)

A_R1_R1 = 

[Valeri Aronov]

This method does not work for my other case:

syms s

syms C1 C2 C3 R1 R2 R3 w real

syms T3(s, C1, C2, C3, R1, R2, R3)

T3(s, C1, C2, C3, R1, R2, R3) = 1/(C1*C2*C3*R1*R2*R3*s^3 + (C1*C3*R1*R2 + C1*C3*R1*R3 + C2*C3*R1*R3 + C2*C3*R2*R3)*s^2 + (C1*R1 + C3*R1 + C3*R2 + C3*R3)*s + 1);

A = abs(T3(1j*w, C1, C2, C3, R1, R2, R3));

A = rewrite(A, 'sqrt')

[Paul]

Running the code here in 2021b yields the following results where it it looks like the rewrite command doesn't accmomplish anything.

syms s
syms C1 C2 C3 R1 R2 R3 w real

ans = 

syms T3(s, C1, C2, C3, R1, R2, R3)
T3(s, C1, C2, C3, R1, R2, R3) = 1/(C1*C2*C3*R1*R2*R3*s^3 + (C1*C3*R1*R2 + C1*C3*R1*R3 + C2*C3*R1*R3 + C2*C3*R2*R3)*s^2 + (C1*R1 + C3*R1 + C3*R2 + C3*R3)*s + 1);
A = abs(T3(1j*w, C1, C2, C3, R1, R2, R3))

A = 

A = rewrite(A, 'sqrt')

A = 

But running the exact code in 2019a yields

which I guess is the result you're looking for.

I'm not sure if the issue is with rewrite, or the fact that the declaration of T3 removes the assumptions on the C* and R* variables, and then rewrite() can't deal with complex variables.

clear all
syms s
syms C1 C2 C3 R1 R2 R3 w real
assumptions

ans = 

syms T3(s, C1, C2, C3, R1, R2, R3)
assumptions

ans = 

In 2019a, the declaration of T3 does not clear the assumptions on C* and R*. I don't know which is the expected behavior.

But I think the code can run the way you want with a simple modification:

clear all
syms s
syms C1 C2 C3 R1 R2 R3 w real
% syms T3(s, C1, C2, C3, R1, R2, R3)  this line not needed
T3(s, C1, C2, C3, R1, R2, R3) = 1/(C1*C2*C3*R1*R2*R3*s^3 + (C1*C3*R1*R2 + C1*C3*R1*R3 + C2*C3*R1*R3 + C2*C3*R2*R3)*s^2 + (C1*R1 + C3*R1 + C3*R2 + C3*R3)*s + 1);
A = abs(T3(1j*w, C1, C2, C3, R1, R2, R3));
A = rewrite(A, 'sqrt')

A = 

[Valeri Aronov]

Wow, Paul. May I apologize for unaccepting your original answer - it did answer the original question, after all. I thought that this way I will signal the new turn to you and preserve the context.

2021b result looks logical now.

Answer 2

[Image Analyst]

Not sure what you mean because you did not give any examples, but if you want the differences to always be positive, you can pass the results of diff() into abs():

d = abs(diff(v));

[Paul]

The code as written is differentiating the magnitude of the transfer function wrt to R1? If you don't mind me asking, what is the purpose of this operation?

Or is it really intended to differentiate the amplitude of the frequency response of the transfer function wrt to R1?

[Valeri Aronov]

May I kindly refer you to my description in recent "Using Hessian for least-squares problem" in this forum. Thanks.

[Paul]

I read the post. Sill not clear to me that the intent is to get the derivative of H(s) wrt R1 or if the goal is to get the derivative of abs(H(jw)) wrt R1.

[Valeri Aronov]

The purpose is to get the latter - abs(H(jw)) wrt R1.