A memristor is, _by definition_, an element whose constitutive relation is of the type \[1\]

$$g(\varphi,q)=0,$$

where $\varphi = \int_{-\infty}^t v(s)\,\mathrm{d}s$ is the flux linkage and $q= \int_{-\infty}^t i(s)\,\mathrm{d}s$ is the charge.

If the relationship $g(\varphi,q)=0$ is linear, the memristor degenerates into a linear resistor and, thus, its impedance coincides with the resistance.

When the relationship $g(\varphi,q)=0$ is nonlinear, the memristor becomes a nonlinear element for which the concept of impedance is valid only in the so-called _small signal_ approximation, that is, when the applied signal around a certain operating point is sufficiently small that the nonlinearity can be neglected. This kind of linearization is well known in circuit theory, and, for instance, it is commonly applied when analyzing diode circuits and transistor amplifiers. Let's see how this can be done in the case of the memristor.

If the relationship $g(\varphi,q)=0$ can be solved for $\varphi$, that is, we can write $\varphi = f_\mathrm{M}(q)$ (at least in a certain interval) the memristor is called _charge-controlled_ and its $iv$ characteristic is given by \[1\]

$$v = R(q)i,\qquad\qquad(1)$$

where

$$R(q) = \frac{\mathrm{d}f_\mathrm{M}(q)}{\mathrm{d} q}$$

is a charge-dependent resistance. Since $q= \int_{-\infty}^t i(s)\,\mathrm{d}s$, the charge $q$ at any given instant depends on the past history of the current. But once you have reached a certain operating point $q$, the one of interest, you can think of applying a sine wave with infinitely small amplitude, so that the charge remains virtually constant. Around this operating point, you can see from (1) that the voltage across the memristor is proportional to the current, that is, for small signals the memristor behaves like a resistor with _differential_ resistance $R(q)$. Hence, the small signal impedance will be $R(q)$, _independent of frequency_.

A similar conclusion can be obtained for the case in which the relationship $g(\varphi,q)=0$ can be solved for $q$.

To sum up, the _small-signal_ (I cannot stress this enough) impedance of a memristor is resistive, independent of frequency, and, because of memristor nonlinearity, dependent on the operating point. 

A more detailed analysis of the circuit behaviour of the memristor can be found in Chua's papers \[1-3\]. In [3], in particular, it is discussed the impedance. For more general information on small-signal analysis you can have a look at \[4\] (Chua again!).

\[1\] L. O. Chua, "Memristor - The missing circuit element," _IEEE Trans. Circuit Theory_, CT-18, 507–519, 1971.

\[2\] L. O. Chua, "The fourth element", _Proc. IEEE_, 100, 1920-1927, 2012.

\[3\] L. O. Chua, "Nonlinear circuit foundations for nano devices, Part I: The Four-Element torus," _Proc. IEEE_, 91, 1830–1859, 2003.

\[4\] L. Chua, C. A. Desoer, and E. S. Kuh, _Linear and nonlinear circuits_, McGraw-Hill, 1987.