Typha latifolia L. is native to Alberta. Typha angustifolia L. is not. The two species form a sterile, but very invasive, hybrid T. latifolia x T. angustifolia which has also been classified as, T. glauca Godr. These three kinds of cattail are not easy to distinguish, and all 3 occur in many parts of North America, including all Canadian provinces that adjoin the lower 48 states of the USA, with the exception of Alberta, according to the USDA Plants Database.
The origin of Typha angustifolia is uncertain. Some authors believe that it was an early European introduction (see eFlora FNA: ). USDA Plants shows it to be native in the lower 48 states, but introduced in Canada. In any event it has spread over the last 100 years or so. The hybrid is particularly successful as clonal stands in disturbed habitats and may also invade native aquatic habitats.
Because identification is difficult, and because the range of T. angustifolia has been expanding, it is possible that the non-native as well as the native cattails occur here without having been reported and confirmed. Identification generally requires microscopic examination of the flowers. For a key, see eFlora FNA: 
Steven E. Travis et al, Hybridization dynamics of invasive cattail (Typhaceae) stands in the Western Great Lakes Region of North America: a molecular analysis, Journal of Ecology, Vol 98, No. 1, ppg 7-16, 2010. Abstract: