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Calculating
Published in Victor A. Bloomfield, Using R for Numerical Analysis in Science and Engineering, 2018
R can be used, without any programming, as a powerful calculator. It has all the standard arithmetic operators and functions, which operate on numeric or complex vectors (including scalars, which are vectors of length 1). Arithmetic operators: The binary arithmetic operators are +, -, *, /, ^ (exponentiation), %% (mod), and %/% (integer division).Logarithms and exponentials: log (natural log), log10, (base 10 log), log2 (base 2 log), log (x,b) (log of x to base b). log1p(x) computes log(1+x) accurately for |x| << 1.exp computes the exponential function, and expm1 computes exp(x)-1 accurately for |x| << 1.Trigonometric functions : cos(x), sin(x), tan(x), acos(x), asin(x), atan(x), atan2(y,x) where angles are in radians and x and y are numeric or complex scalars or vectors. atan2(y,x) = atan(y/x) for positive arguments. The pracma package, to which we will refer later, adds more trigonometric functions: cot(x), csc(x), sec(x), acot(x), acsc(x), asec(x).Hyperbolic functions : cosh(x), sinh(x), tanh(x), acosh(x), asinh(x), atanh(x). pracma adds coth(x), csch(x), sech(x), acoth(x), acsch(x), asech(x).Miscellaneous mathematical functions: abs(x), sqrt(x).
Optimization of Discrete Anamorphic Stretch Transform and Phase Recovery for ECG Signal Compression
Published in IETE Journal of Research, 2021
R. Thilagavathy, B. Venkataramani
The Local Frequency (LF) of the DAST kernel is obtained by differentiating the DAST Kernel phase function Φ[n]. LF functions corresponding to Sublinear, Linear and Superlinear kernels are given by [34] where a and b are real-valued numbers. tan and atan are the tangent and inverse tangent (tan−1) functions respectively. The variable “n” denotes the lag/lead of a sample w.r.t. the sample whose DAST is computed. The normalized lag/lead of a sample (n) is obtained by dividing “n” by M ((kernel size −1)/2). The plots of the LF function as a function of n are given in Figure 1. Normalized lag/lead is used for the plot in order to make the limits of the X-axis to be independent of M. From the equations (3a) and (3c), it may be noted that the maximum value of (b.n), i.e. (b.M) should be less than π/2 to ensure that LF of DAST kernel is bounded.