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.