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Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, seismology, among others.
DSP can involve linear or nonlinear operations. Nonlinear signal processing is closely related to nonlinear system identification and can be implemented in the time, frequency, and spatio-temporal domains. The application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.
Sampling is usually carried out in two stages, discretization and quantization. Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude. Quantization means each amplitude measurement is approximated by a value from a finite set.
Rounding real numbers to integers is an example. Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal. In practice, the sampling frequency is often significantly higher than twice the Nyquist frequency. Numerical methods require a quantized signal, such as those produced by an ADC.
The processed result might be a frequency spectrum or a set of statistics. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is, the frequency spectrum. The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering.
Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. Linear filters satisfy the superposition condition, i. A non-causal filter can usually be changed into a causal filter by adding a delay to it. A “stable” filter produces an output that converges to a constant value with time, or remains bounded within a finite interval.
An “unstable” filter can produce an output that grows without bounds, with bounded or even zero input. FIR filters are always stable, while IIR filters may be unstable. A filter can be represented by a block diagram, which can then be used to derive a sample processing algorithm to implement the filter with hardware instructions.
A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response. The output of a linear digital filter to any given input may be calculated by convolving the input signal with the impulse response. Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency.
Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared. The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing. In addition to frequency information, phase information is often needed.
This can be obtained from the Fourier transform. With some applications, how the phase varies with frequency can be a significant consideration.