Digital signal processing
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Digital signal processing (DSP) is the mathematical manipulation of an information signal to modify or improve it in some way. It is characterized by the reprentation of discrete time, discrete frequency, or
other discrete domain signals by a quence of numbers or symbols and the processing of the signals. Digital signal processing and analog signal processing are subfields of signal processing. DSP includes subfields like: audio and speech signal processing, sonar and radar signal processing, nsor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, control of systems, biomedical signal processing, ismic data processing, etc.
The goal of DSP is usually to measure, filter and/or compress continuous real-world analog signals. The first step is usually to convert the signal from an analog to a digital form, by sampling and then digitizing it using an analog-to-digital converter(ADC), which turns the analog signal into a stream of numbers. However, often, the required output signal is another analog output signal, which requires a digital-to-analog converter(DAC). Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital 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.[1]
DSP algorithms have long been run on standard computers, on specialized processors called digital signal processor on purpo-built hardware such as application-specific integrated circuit (ASICs). T
oday there are additional technologies ud for digital signal processing including more powerful general purpo microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial apps such as motor control), and stream processors, among others.[2]
[edit] Signal sampling
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Main article: Sampling (signal processing)
With the increasing u of computers the usage of and need for digital signal processing has incread. To u an analog signal on a computer, it must be digitized with an analog-to-digital converter. Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence class and quantization is carried out by replacing the signal with reprentative signal of the corresponding equivalence class. In the quantization stage the reprentative signal values are approximated by values from a finite t.
The Nyquist–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 of the signal; but requires an infinite number of samples. In practice, the sampling frequency is often significantly more
than twice that required by the signal's limited bandwidth.
[edit] DSP domains
In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and wavelet domains. They choo the domain to process a signal in by making an informed guess (or by trying different possibilities) as to which domain best reprents the esntial characteristics of the signal. A quence of samples from a measuring device produces a time or spatial domain reprentation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. Autocorrelation is defined as the cross-correlation of the signal with itlf over varying intervals of time or space.
[edit] Time and space domains
Main article: Time domain
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. There are various ways to characterize filters; for example:
∙ A "linear" filter is a linear transformation of input samples; other filters are "non-linear". Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of
different signals, the output is an equally weighted linear
combination of the corresponding output signals.
∙ A "causal" filter us only previous samples of the input or output signals; while a "non-causal" filter us future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.
∙ A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.
∙ 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.
∙ A "finite impul respon" (FIR) filter us only the input signals, while an "infinite impul respon" filter (IIR) us both the
干豆皮怎么做好吃input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.
Filters can be reprented by block diagrams, which can then be ud 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 impul respon or step respon.
The output of a linear digital filter to any given input may be calculated by convolving the input signal with the impul respon.
[edit] Frequency domain就业推荐表自我评价
Main article: Frequency domain
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 pha c
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omponent 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 purpo for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are prent in the input signal and which are missing.
In addition to frequency information, pha information is often needed. This can be obtained from the Fourier transform. With some applications, how the pha varies with frequency can be a significant consideration.
Filtering, particularly in non-realtime work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain. This is a fast, O(n log n) operation, and can give esntially any filter shape including excellent approximations to brickwall filters.
There are some commonly ud frequency domain transformations. For example, the cepstrum con
verts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the frequency components with smaller magnitude while retaining the order of magnitudes of frequency components.
Frequency domain analysis is also called spectrum-or spectral analysis. [edit] Z-plane analysis
Main article: Z-transform
Whereas analog filters are usually analyd in terms of transfer functions in the s plane using Laplace transforms, digital filters are analyd in the z plane in terms of Z-transforms. A digital filter may be described in the z plane by its characteristic collection of zeroes and poles. The z plane provides a means for mapping digital frequency (samples/cond)
向着朝阳to real and imaginary z components, where for continuous periodic
signals and ( is the digital frequency). This is uful for providing a visualization of the frequency respon of a digital system or signal.
[edit] Wavelet
Main article: Discrete wavelet transform
An example of the 2D discrete wavelet transform that is ud in JPEG2000. The original image is high-pass filtered, yielding the three large images, each describing local changes in brightness (details) in the original image. It is then low-pass filtered and downscaled, yielding an approximation image; this image is high-pass filtered to produce the three smaller detail images, and low-pass filtered to produce the final approximation image in the upper-left.
In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet tra
nsform 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 (location in time).
[edit] Applications
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The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, RADAR, SONAR, ismology 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, ismic data processing, analysis and control of industrial process, medical imaging such as CAT scans and MRI, MP3 compression, computer graphics, image manipulation, hi-fi loudspeaker crossovers and equalization, and audio effects for u with electric guitar amplifiers.
