A traditionally Freudian view of Charlotte Perkins Gilman "The Yellow Wallpaper," would locate the narrator's anxieties and neuroses in her own childhood experiences, as well as in the repression of her Id, or her inner self, where her desires are located.
Thus, such a view could possibly interpret the narrator's post-partum depression as a result of unresolved anxieties about her relationship with her mother, or her resentment of her husband coupled with the fact that she is conflating him with her father, as part of a resurfaced Electra complex.
However, traditional Freudian analysis has often been criticized for ignoring the external, patriarchal forces that influence women's psyches. A more useful Freudian approach is one informed by Feminist criticism. Thus, through a revised version of Freudian analysis, we can say that the woman's anxieties are the result of a repression of both her deepest desires (Id) as well as her actual repression and confinement by her husband. Further, Freud said dreams often revealed symbols of the repressed Id: in this case the narrator's visions in the wallpaper could be said to substitute dreams. Thus, the wallpaper becomes a lexicon for the symbols of her unconscious desires, and her repression. One of these desires, would obviously be for freedom.
Finally, her Electra complex, or romantic feelings for her father as a child, which she now projects/transfers on her husband, calling him "Daddy," can also be viewed as her realization that power has passed from her husband to her father, leaving her with none. Certainly her husband infantilizes her, often referring to her as "girl" and carrying her ups the stairs. For the narrator, the father and the husband now become similar oppressive forces in her life. Cracking under the conflict of her social role as a wife and mother, and the call of her Id, the narrator finally gives in to "madness."
However, this madness itself is questionable. Is it really madness, or a symbol of her freedom? Gilman leaves things open-ended.