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Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. DSP and analog signal processing are subsets of signal processing. It has three major subfields: audio signal processing, digital image processing and speech processing. In DSP, engineers most commonly study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. They choose the domain in which to process a signal by making an educated guess (or trying out different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. The autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space.
Since the point of DSP is usually to measure or filter continuous real world analog signals, an analog to digital conversion performed by an analog to digital converter is usually the first step. The target of the signal processing is often another analog output signal which requires a digital to analog converterIn electronics, a digital to analog converter (abbreviated to DAC or D-to-A is a device for converting a digital (usually binary) code to an analogue signal (usually a current (electricity) or voltage). This is done with switches or a network of resistors for translation.
The mathematical calculations and algorithmFlowcharts were often used to represent algorithms. An algorithm is a finite set of well-defined instructions for accomplishing some task which, given an initial state, will result in a corresponding recognisable end-state (contrast with heuristic). Algors required for DSP are sometimes executed in hardware digital signal processorA digital signal processor (DSP is a specialized microprocessor designed specifically for digital signal processing, generally in real-time. DSPs can also be used to perform general-purpose computation, but they are not optimised for this function. Rathers, also abbreviated DSP. Digital signal processors have heavily parallel architectures optimized for DSP computations and are designed to operate in real-time.
1 Signal sampling
A digital signal is often a numerical representation of a continuous analog signal (eg. a real world signal). This discrete representation of a continuous signal will generally introduce some error in to the data. The accuracy of the representation is mostly dependent on two things; sampling frequencySignal Processing and Control Theory In digital signal processing and in control theory, sampling frequency is the rate at which a continuous-time ( analog) signal is sampled into a discrete-time ( digital) signal consisting of digital samples. Sampling f and the number of bits used for the representation. The continuous signal is usually sampled at regular intervals by an Analog to digital converter and the value of the continuous signal in that interval is represented by a discrete value. The sampling frequency or sampling rate is then the rate at which new samples are taken from the continuous signal. The number of bits used for one value of the discrete signal tells us how accurately the signal magnitude is represented. Similarly, the sampling frequency controls the temporal or spatial accuracy of the discrete signal.
The Nyquist-Shannon sampling theoremThe Nyquist-Shannon sampling theorem is the fundamental theorem in the field of information theory, in particular telecommunications. It is also known as Whittaker-Nyquist-Kotelnikov-Shannon sampling theorem. The theorem states that, when converting from, a fundamental theorem of signal processing, states that a sampled signal cannot unambiguously represent signal components with frequencies above half the sampling frequency. This frequency (half the sampling frequency) is called the Nyquist frequencyThe Nyquist rate named after the Nyquist-Shannon sampling theorem, is immediately below the minimum theoretical sampling rate that will fully describe a given band-limited signal, enabling its faithful reconstruction from the samples. If the signal's larg. Frequencies above the Nyquist frequency N can be observed in the digital signal, but their frequency is ambiguous. That is, a frequency component with frequency f cannot be distinguished from another component with frequency 2N-f, 2N+f, 4N-f, etc. This is called aliasingThis article refers to aliasing as it applies to signal processing, including computer graphics. For uses in computer programming, please refer to aliasing (computing In signal processing and related disciplines, aliasing is an effect that causes differen. To handle this problem as gracefully as possible, most analog signals are filtered with an anti-aliasinga) (b) (c) Figure 1 Anti-aliasing in digital signal processing is the technique of minimizing aliasing when representing a high-resolution signal at a lower resolution. In most cases, anti-aliasing means removing data at too high a frequency to represent. filter (usually a low-pass filter) at the Nyquist frequency before conversion to the digital representation.
