<P> Frequency domain analysis is also called spectrum - or spectral analysis . </P> <P> Digital filters come in both IIR and FIR types . FIR filters have many advantages, but are computationally more demanding . Whereas FIR filters are always stable, IIR filters have feedback loops that may resonate when stimulated with certain input signals . The Z - transform provides a tool for analyzing potential stability issues of digital IIR filters . It is analogous to the Laplace transform, which is used to design analog IIR filters . </P> <P> In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled . As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information. The accuracy of the joint time - frequency resolution is limited by the uncertainty principle of time - frequency . </P> <P> The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, digital synthesizers, radar, sonar, financial signal processing, seismology and biomedicine . Specific examples are speech compression and transmission in digital mobile phones, room correction of sound in hi - fi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, medical imaging such as CAT scans and MRI, MP3 compression, computer graphics, image manipulation, hi - fi loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers . </P>

Representation of analog signals in the digital domain