Thursday 17 November 2016

TYPES OF STRUCTURES AND DIGITAL SIGNAL PROCESSING?

TYPES OF STRUCTURES IN DSP


  1. direct form
  2. cascade form
  3. parallel form
  4. transposed form(remaining coming soon)

CANONICAL STRUCTURE 

A canonical structure that is a special featured structure is defined as a structure in which order of  original transfer function is same as the number  of our block diagram delays or same number of delays in block diagram and order of transfer function. Both direct form one and direct form two structures are examples of canonical structures.
output graph of canonical structure

NON CANONICAL STRUCTURE 

A non canonical structure is defined as the structure  in which number of delays present in block diagram representation are not equal to the order of transfer function.

graph of non canonical structure

DEFINITION OF DIRECT FORM STRUCTURE

A particular sort of structure where the coefficients of multiplier components are almost same as the transfer function coefficients is called direct form structure.

FEATURES OF DSP STRUCTURES 

We know the basic difference between direct form I and II that is in direct form I poles are written first then zeros and in direct II zeros are first and then poles are written.Furthermore,in direct form II memory is reduced means our hardware is reduced that means there is less number of adders and multipliers in direct formII. In FIR filters we have only zeros andd in IIR filters we write both poles and zeros as well.Transposed structure is used in FIR filters for the purpose of tapped delay line achievement.

WHICH STRUCTURE IS MORE ROBUST AND STABLE

All the filters have their own specific speed of computation and stability.But if we observe computation speed and stability perspectives of structures in dsp then we can conclude that among all structure sorts parallel structures are the most speedy with respect to computation and direct form structures are the most stable structures.

CATEGORIES OF FIR AND IIR STRUCTURES


             IIR                                                                                                IIR

  1. direct form I&II                                                                           direct form I&II
  2. cascade form                                                                                cascade form
  3. parallel form                                                                                 frequency sampling

Digital signal processing

Digital signal processing (DSP) is the use of digital processing, such as by computers, to perform a wide variety of signal processing operations. The signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency.

Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech signal processing, sonar, radar and other sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control of systems, biomedical engineering, seismic data processing, among others.

Digital signal processing 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.  DSP is applicable to both streaming data and static (stored) data.

Signal sampling

Main article: Sampling (signal processing)
The increasing use of computers has resulted in the increased use of, and need for, digital signal processing. To digitally analyze and manipulate an analog signal, it must be digitized with an analog-to-digital converter. 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.

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. In practice, the sampling frequency is often significantly higher than twice that required by the signal's limited bandwidth.

Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies (quantization error), "created" by the abstract process of sampling. Numerical methods require a quantized signal, such as those produced by an analog-to-digital converter (ADC). The processed result might be a frequency spectrum or a set of statistics. But often it is another quantized signal that is converted back to analog form by a digital-to-analog converter (DAC).

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 choose the domain in which to process a signal by making an informed assumption (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. 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.

Time and space domains

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 a similarly weighted linear combination of the corresponding output signals.
A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses 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 impulse response" (FIR) filter uses only the input signals, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. 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.

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 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.

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 essentially any filter shape including excellent approximations to brickwall filters.

There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the harmonic structure of the original spectrum.

Frequency domain analysis is also called spectrum- or spectral analysis.

Z-plane analysis

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.

Wavelet

An example of the 2D discrete wavelet transform that is used 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 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.Courtesy of wikipedia....







1 comment:

  1. Thank you for sharing information with us, Digital Signal Processing is used for speech compression for mobile phones, as well as speech transmission for mobile phones.

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