Digital Signal Processing
Digital signal processing (DSP) represents signals as sequences of numbers and manipulates, analyzes, and synthesizes them using mathematical algorithms executed on digital hardware. Many of these signals originate in the physical world as continuous analog waveforms, captured through sampling and quantization; others are digital from the outset, such as data read from storage or received over a network. This fundamental technology underlies virtually every modern electronic system, from the audio processing in smartphones to the radar systems guiding aircraft, from medical imaging equipment revealing the body's interior to the communications networks connecting billions of devices worldwide.
The power of digital signal processing lies in its precision, repeatability, and flexibility. Unlike analog circuits whose behavior drifts with temperature and age, digital algorithms produce identical results every time they execute. Complex operations impractical with analog electronics, such as steep linear-phase filtering, adaptive noise cancellation, and large-scale spectral analysis, become routine with digital implementation. Software updates can improve performance or add capabilities without hardware changes. These advantages have driven the progressive migration of signal processing from analog to digital domains across every industry.
A typical processing chain begins with conversion: an analog-to-digital converter samples the input at a fixed rate and quantizes each sample to a finite number of bits. The Nyquist-Shannon sampling theorem governs this step, requiring a sampling rate of at least twice the highest frequency present in the signal to avoid aliasing. Once in numerical form, the signal passes through algorithms built from a small set of recurring operations: addition, multiplication, delay, and the multiply-accumulate that dominates filtering and transforms. Operations divide broadly into time-domain methods, such as finite impulse response (FIR) and infinite impulse response (IIR) filtering, and frequency-domain methods, such as the fast Fourier transform (FFT) that efficiently computes the discrete Fourier transform. A digital-to-analog converter then reconstructs a continuous waveform where an analog output is required.
The topics below develop these foundations in turn, moving from data conversion and core algorithms through transforms and filter realization to the specialized processor architectures and phase-locked loops that make real-time signal processing practical.