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VTU NOTES
Subject code
BMATEC301
Semester
3rd

## Module - 1

Periodic functions, Dirichlet’s condition. Fourier series expansion of functions with period 2𝜋 and with arbitrary period: periodic rectangular wave, Half-wave rectifier, rectangular pulse, Saw tooth wave. Half-range Fourier series. Triangle and half range expansions, Practical harmonic analysis, variation of periodic current.

## Module - 2

Infinite Fourier transforms, Fourier cosine and sine transforms, Inverse Fourier transforms, Inverse Fourier cosine and sine transforms, discrete Fourier transform (DFT), Fast Fourier transform (FFT).

## Module - 3

Definition, Z-transforms of basic sequences and standard functions. Properties: Linearity, scaling, first and second shifting, multiplication by n. Initial and final value theorem. Inverse Z- transforms. Application to difference equations.

## Module - 4

Higher-order linear ODEs with constant coefficients – Inverse differential operator, problems.Linear differential equations with variable Coefficients-Cauchy’s and Legendre’s differential equations–Problems. Application of linear differential equations to L-C circuit and L-C-R circuit.

## Module - 5

Principles of least squares, Curve fitting by the method of least squares in the form 𝑦 = 𝑎 + 𝑏𝑥 , 𝑦 = 𝑎 + 𝑏𝑥 + 𝑐𝑥2 , and 𝑦 = 𝑎𝑥 𝑏 . Correlation, Coefficient of correlation, Lines of regression, Angle between regression lines, standard error of estimate, rank correlation.