Let us remember the basic setup of the probability theory: “…….A random experiment is an action for which all possible outcomes can be listed, but…
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Time and frequency considerations It is impossible to read a continuous signal into a computer. Hence, reading a continuous signal always involves some sort of…
Comments closedCompression property of fourier transformation and bandwidth of a signal. When we record a speech signal $x(t)$ for 10 minutes, the intensity of the speech…
Comments closedLinearity If $FT[x_1(t)] = X_1 (\omega)$ and $FT[x_2(t)] = X_2 (\omega)$, and if $a_1, a_2 \in \mathbb{R}$, then $FT[a_1x_1(t) + a_2x_2(t)] = a_1X_1 (\omega) +…
Comments closedDiscrete functions (or, discrete signals in engineer talk) also form a vector space. Consider a discrete signal \(X[i]\), ie \begin{eqnarray} \ldots \, X[-3] , X[-2]…
Comments closedVector Spaces Merriam-webster dictionary defines a vector as “….a quantity that has magnitude and direction and that is commonly represented by a directed line segment…
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Before going on with deicrete signals, let us remember what continuous signals are: Continuous signals are defined on real numbers \(\mathbb{R}\). Notationally they are denoted…
Comments closedWe assume that the student has the basics of the complex numbers. The purpose of this chapter is to remind this basics and introduce some…
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