Digital Signal Processing Introduction

Introduction to Signals and Systems

• Signals are classified into continuous and discrete time signals.
• Continuous time signals are represented by x(t) and discrete time signals are represented by x[n].

Signal Operations

• Time shifting is the shifting of a signal in time by adding or subtracting a quantity to the time parameter.
  • Subtracting a fixed positive quantity from the time variable will shift the signal to the right (delay) by the subtracted quantity.
  • Adding a fixed positive amount to the time variable will shift the signal to the left (advance) by the added quantity.
• Time scaling compresses or dilates a signal by multiplying the time variable by some quantity.
  • If the quantity is greater than one, the signal becomes narrower and the operation is called compression.
  • If the quantity is less than one, the signal becomes wider and is called dilation.
• Time reversal of a continuous-time signal x(t) is given by y(t) = x(-t).
• Time reversal of a discrete-time sequence x(n) is given by y(n) = x(-n).
• Amplitude shifting means shifting of signal in the amplitude domain around the X-axis.
  • When K is greater than zero, the shifting of signal takes place towards up in the X-axis (upward shifting).
  • When K is less than zero, the shifting of signal takes place towards down in the X-axis (downward shifting).
• Amplitude scaling of a signal rescales the amplitude of the signal, either amplifying or attenuating it.
  • The shape of the resulting signal remains the same as that of the original signal, but the amplitude is altered.

Systems

• A system is a mathematical model that represents the transformation of some input signal x(t) into an output signal y(t).
• In the digital domain, a system may be a digital filter.
• Digital filters use a digital processor to perform numerical calculations on sampled values of the signal.

Introduction to digital signal processing, including signals and systems, classification and representation, and types of systems. Covers continuous and discrete time signals, signal operations, and more.