QUESTION 3 (a) There are 4 different types of transform (i to iv), can be used to represent a continuous and discrete time signal. The chosen types of transform are selected based on the finite or infinite duration and also the generated signal either periodic or aperiodic. In the table, fill in the blanks with i, ii, iii or iv depending on which transform(s) can be used to represent the signal described. i- Contimuous-time Fourier Series (CTFS) ii- Discrete-time Fourier Series (DTFS) 111- Contimuous-time Fourier Transform (CTFT) iv- Discrete-time Fourier transform (DTFT) Signal description Transform Continuous time Infinite duration Periodic Discrete time Infinite duration Aperiodic
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
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