A procedure for calculating the best exponents for signal representation

The approximation of a given signal over (0,^ ) by a linear combination of a given number n of exponentials in such a sense that the integrated squared error is minimized over both the coefficients of the linear combination and the exponents used is discussed. The necessary conditions for the minimizations lead to nonlinear equations. Analog and digital computer implementations have been developed that are capable of adjusting the exponents of the basis functions and the coefficients of the linear combinations to minimize the integrated squared error between a signal and its representation. The influence of each parameter of the orthonormal filters on the performance criterion is determined using an iterative convergent process. These parameter changes are introduced into the analog and digital systems to form a closed loop system

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was <1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified