What is convolution and how is it used in signal processing?

Convolution is a mathematical operation that combines two signals to produce a third: y(t) = x(t) * h(t) = integral of x(tau)*h(t-tau)d(tau). For LTI systems, output equals input convolved with impulse response. Properties: commutative, associative, and distributive. Convolution in time equals multiplication in frequency domain (and vice versa). Applications: Filter implementation (signal convolved with filter impulse response), Image processing (2D convolution with kernels), and System analysis (cascade systems multiply frequency responses).