I see you've already imported numpy because you're using np.linspace in the code. You are probably confusing numpy's abs, which will happily work on lists and arrays, with __builtin__.abs, which only works for scalars.

Change this:

abs(wf[0:100])

To this:

np.abs(wf[0:100])

Looking at the docs docs, it seems that you mistook inputs for outputs. residue takes a and b and returns r, p and k.

Third parameter (tol) should be a number but you are passing a list.

You might be using wrong method. Take a look at scipy.signal.invres, that should be what you are looking for.

That's because numpy.ndarray implements the __abs__(self) method. Just provide it for your own class, and abs() will magically work. For non-builtin types you can also provide this facility after-the-fact. E.g.

class A:
    "A class without __abs__ defined"
    def __init__(self, v):
        self.v = v

def A_abs(a):
    "An 'extension' method that will be added to `A`"
    return abs(a.v)

# Make abs() work with an instance of A
A.__abs__ = A_abs

However, this will not work for built-in types, such as list or dict.

So I'm assuming here that fp(x) or f(x) are functions that don't return anything.

Take a look at this,

def fp(x):
    print(x)

print(fp(10))

You might think that the output of this would be 10 but you get this,

10
None

Take a look at this function,

def fp():
    pass
print(fp())

Output:

None

Functions by default return a None type. So in your case when you are doing abs(fp(x)) the problem seems to be that you are doing abs() on None that's why you get the error.

Look at this,

def fp():
        pass
abs(fp())

Output:

TypeError: bad operand type for abs(): 'NoneType' python error

So add a return statement to the function and you can see the error will be gone

def fp(x):
    return x
some_value = abs(fp(-10.5))
print(some_value)

Output:

10.5

Now the error is gone.

The quoted documentation is obsolete.

The new documentation (for Python 3.8.3) states:

abs(x)
Return the absolute value of a number. The argument may be an integer or a floating point number. If the argument is a complex number, its magnitude is returned. If x defines __abs__(), abs(x) returns x.__abs__().

The last sentence is new, and it explains the question:

NumPy ndarray class and pandas Series class both define the magic __abs__() method.