Signals and Systems Quiz

4s/(s² + w²)

The Fourier cosine transform of a function f(x) is defined as Fc(ω) = ∫[0 to ∞] f(x)cos(ωx)dx. Example: The Fourier cosine transform is used in image processing to filter out high-frequency noise.

U(z) = 7z / (z - 1), |z| > 1

<p>A harmonic function is a function that satisfies Laplace's equation. Example: The electric potential around a charged sphere is a harmonic function.</p> Signup and view all the answers

<p>A singularity is a point where a complex function is not defined or is infinite. Example: The function f(z) = 1/z has a singularity at z = 0.</p> Signup and view all the answers

<p>An inner product space is a vector space with an inner product that satisfies certain properties. Example: The set of all complex-valued functions on the unit interval [0, 1] with the inner product 〈f, g〉 = ∫[0 to 1] f(x)g(x)dx is an inner product space.</p> Signup and view all the answers