Derivative spectroscopy is the easiest way to see how many bands are existing in the broad spectral envelop. Then you can do curve fitting using a software like Origin or specialized software (PeakFit for instance). When use Origin take care about the band shape function especially if your spectrum is linear in the wavelength scale. You can find details in the attached paper.
Through Grams AI 8 software (https://www.thermofisher.com/order/catalog/product/INF-15000#/legacy=thermoscientific.de). It is applicable for IR, Raman, UV, chromatograms and more. Moreover, it has a large set of algorithms for nD data processing including chemometrics under a large scale approaches yielding to a high degree of reliability match over the experimental patterns.
You can pay attention to ref. 1, figure 4 where deconvolution is applied to IRLD spectra.
As you could expect for such powerful software it is not free of charge; it is with personal license and hardware protection. But...it is among best available in the marken currently between spectroscopic softwares.
[Ref. 1]. Amino Acids, 2009, 37:693,l-Leucinamide hydrogensquarate: spectroscopic and structural elucidation, T. Kolev, S. Zareva, H. Mayer-Figge, M. Spiteller, W. Sheldrick, B. Koleva