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We present an analytic expression for this joint PDF and calculate the presampling and digital NPS of CdTe SPCDs and SXDs. We calibrate our charge sharing model using the energy response of a cadmium zinc telluride (CZT) spectroscopic x\u2010ray detector and compare theoretical results with Monte Carlo simulations.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>Our analysis shows that charge sharing increases pixel signal\u2010to\u2010noise ratio (SNR), but degrades the zero\u2010frequency signal\u2010to\u2010noise performance of SPCDs and SXDs. In all cases considered, this degradation was greater than 10%. Comparing the presampling NPS with the sampled NPS showed that degradation in zero\u2010frequency performance is due to zero\u2010frequency noise aliasing induced by charge sharing.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>Noise performance, including spatial and energy correlations between elements and energy bins, are described by the joint PDF of deposited energies which provides a method of determining the photon\u2010counting NPS, including noise\u2010aliasing effects and spatio\u2010energetic effects in spectral imaging. Our approach enables separating noise due to x\u2010ray interactions from that associated with sampling, consistent with cascaded systems analysis of energy\u2010integrating systems. Our methods can be incorporated into task\u2010based assessment of image quality for the design and optimization of spectroscopic x\u2010ray detectors.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.14160","type":"journal-article","created":{"date-parts":[[2020,4,2]],"date-time":"2020-04-02T07:55:05Z","timestamp":1585814105000},"page":"2881-2901","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Frequency\u2010dependent signal and noise in spectroscopic x\u2010ray imaging"],"prefix":"10.1002","volume":"47","author":[{"given":"Jesse","family":"Tanguay","sequence":"first","affiliation":[{"name":"Department of Physics Ryerson University Toronto Ontario M5B 2K3 Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinwoo","family":"Kim","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering Pusan National University Busan 609\u2010735 Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ho Kyung","family":"Kim","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering Pusan National University Busan 609\u2010735 Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kris","family":"Iniewski","sequence":"additional","affiliation":[{"name":"Redlen Technologies Saanichton British Columbia Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ian A.","family":"Cunningham","sequence":"additional","affiliation":[{"name":"Imaging Research Laboratories, Robarts Research Institute Western University London Ontario Canada"},{"name":"Department of Medical Biophysics, Schulich School of Medicine &amp; Dentistry Western University London Ontario Canada"},{"name":"Biomedical Engineering Western University London Ontario Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2020,4,22]]},"reference":[{"key":"e_1_2_14_2_1","doi-asserted-by":"crossref","unstructured":"VennartW.ICRU report 54: medical imaging \u2010 the assessment of image quality. 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