The aromatic infrared bands (AIBs) observed in the mid infrared spectrum are attributed to Polycyclic Aromatic Hydrocarbons (PAHs). We observe the NGC 7023-North West (NW) PDR in the mid-infrared (10 - 19.5 micron) using the Infrared Spectrometer (IRS), on board Spitzer. Clear variations are observed in the spectra, most notably the ratio of the 11.0 to 11.2 micron bands, the peak position of the 11.2 and 12.0 micron bands, and the degree of asymmetry of the 11.2 micron band. The observed variations appear to change as a function of position within the PDR. We aim to explain these variations by a change in the abundances of the emitting components of the PDR. A Blind Signal Separation (BSS) method, i.e. a Non-Negative Matrix Factorization algorithm is applied to separate the observed spectrum into components. Using the NASA Ames PAH IR Spectroscopic Database, these extracted signals are fit. The observed signals alone were also fit using the database and these components are compared to the BSS components. Three component signals were extracted from the observation using BSS. We attribute the three signals to ionized PAHs, neutral PAHs, and Very Small Grains (VSGs). The fit of the BSS extracted spectra with the PAH database further confirms the attribution to ionized and neutral PAHs and provides confidence in both methods for producing reliable results. The 11.0 micron feature is attributed to PAH cations while the 11.2 micron band is attributed to neutral PAHs. The VSG signal shows a characteristically asymmetric broad feature at 11.3 micron with an extended red wing. By combining the NASA Ames PAH IR Spectroscopic Database fit with the BSS method, the independent results of each method can be confirmed and some limitations of each method are overcome.