dsp3

Paper3 Abstract Digital Signal Processing

Authors Raghava Joshi Email-id:- [email protected] prathimahesh Phone no: 9885013498 ph no:9985625814.

This paper deals with various types of digital signal processing and their uses. With the advent of digital computers, signal processing had made rapid advances .The phenomenal growth of digital signal processing (DSP) has been attributed to the availability of digital signal processor in late seventies or early eighties. This has opened up possibility of replacing analog filters, correlators , spectrum analyzers by versatile but inexpensive DSP based equipment .The theory of DSP has been a step ahead of hardware developments. We have new signal processing algorithms For example singular value decomposition (SVD) based algorithms waiting for faster but inexpensive digital signal processor for their exploitation . Digital signal processor Technology has finally blossomed .Powerful methods of signal processing are used to detect and analyse signals, make transform of different kinds and observe changes in real time with the help of these DSP device based circuitry. The digital signal processing deals with three main features They are discrete signals and systems, digital filtering , spectrum analysis . Discrete signal and system is about signal analysis and modeling of systems the study of discrete signals and systems is also interest in communication , control system, circuit theory. A discrete signal is often derived by sampling continuous signal and digital signal is derived by quantizing the discrete signal thus sampling rate and quantization step size are of immediate concern The digital filter like analog filter are primarily used to enhance the signal in presence of noise. The digital filters are used for interpolation, extrapolation, equalization detection. Spectrum deals with study of energy/power distribution as a function of frequency (energy for deterministic signal and power for stochastic signal). The spectrum of signal is essential when we are looking for discrete sinusoids in a signal, as in communication , radar and sonar and also in optimum filters.

INTRODUCTION

The development of digital signal processing dates from the 1960's with the use of mainframe digital computers for number-crunching applications such as the Fast Fourier Transform (FFT), which allows the frequency spectrum of a signal to be computed rapidly. These techniques were not widely used at that time, because suitable computing equipment was generally available only in universities and other scientific research institutions. DSP, or Digital Signal Processing, as the term suggests, is the processing of signals by digital means. A signal here means an electrical signal carried by a wire or telephone line, or perhaps by a radio wave. More generally, however, a signal is a stream of information representing anything from stock prices to data from a remotesensing satellite. The term "digital" comes from "digit", meaning a number, so "digital" literally means numerical; the French word for digital is numerique . A digital signal consists of a stream of numbers, usually in binary form. The processing of a digital signal is done by performing numerical calculations. The signal is often strongly affected by "mains pickup" due to electrical interference from the mains supply. Processing the signal using a filter circuit can remove or at least reduce the unwanted part of the signal. The filtering of signals to improve signal quality or to extract important information is done by DSP techniques rather than by analog electronics.

Digital Signal Processor chips - specialized microprocessors with architectures designed specifically for the types of operations required in digital signal processing. DSP chips are capable of carrying out millions of floating point operations per second, and like their better-known general-purpose cousins, faster and more powerful versions are continually being introduced. DSPs can also be embedded within complex "system-on-chip" devices, often containing both analog and digital circuitry. DSP technology is nowadays commonplace in such devices as mobile phones, multimedia computers, video recorders, CD players, hard disc drive controllers and modems, and will soon replace analog circuitry in TV sets and telephones AnJ important application of DSP is in signal compression and decompression. Signal compression is used in digital cellular phones to allow a greater number of calls to be handled simultaneously within each local "cell".

DSP signal compression technology allows people not only to talk to one another but also to see one another on their computer screens, using small video cameras mounted on the computer monitors, with only a conventional telephone line linking them together. In audio C D systems, DSP technology is used to perform complex error detection and correction on the raw data as it is read from the CD. The architecture of a DSP chip is designed to carry out such operations incredibly fast, processing hundreds of millions of samples every second, to provide real-time performance: that is, the ability to process a signal "live" as it is sampled and then output the processed signal, for example to a loudspeaker or video display. All of the practical examples of DSP applications mentioned earlier, such as hard disc drives and mobile phones, demand real-time operation.

Classification of Signals

• C ontinuous and discrete time signals • C ontinuous and discrete amplitude signals • Deterministic and random signals • Digital and analog signals • Multichannel and multidimensional signals

Continuous time signal : This signal can be defined at any time instant .The exponential function and sinusoidal function are the examples of continuous time signals.

Discrete time signal : This signal is defined only at sampling instants. These signals are basically represented as array of sample values

Continuous amplitude signals : The amplitude variation is continuous in such signals .Note that the continuous amplitude signals can be discrete or continuous in time.

Discrete amplitude signals: These signals take only discrete amplitude levels.Here Note that the discrete amplitude signals can be continuous or discrete in time. Digital signals: The signals which are discrete in time as well as amplitude are called digital signals .All the signal representation in computers and digital signal processors use digital signals. The digital signal can be binary (one bit), octal(3 bit) Hex(4bit) ,16 bit ,32 bit or even 64 bit. The complete amplitude range of the analog signal is represented by these bit lengths. If the analog symbol has the amplitude range of 16 volts peak, then each level will be of one volt.

Analog signals : The signals which are continuous in time as well as amplitude are called analog signals. For example , the exponential function and sinusoidal function.

Deterministic signal : A signal which is completely described by the mathematical model is called deterministic signal. The value of the deterministic signal can be evaluated at any time without uncertainty. For example , the sinusoidal signal. x (t) =Acos(wt) Random signal : The signals which cannot be described by the mathematical model are called random signals. For example the noise signal or speech signals are random signals. The random signals can be described with the help of their statistical properties.

Multichannel signals : When different signals are recorded from the same source they are called multichannel signals. For example, EC G signal can be recorded in 3 leads or 12 leads for the same person. This results in 3 channel or 12 channel EC G Signal. The multichannel signals are useful in studying correlation properties of the source.

Multidimensional signal : When the amplitude of the signal depends upon two or more independent variables, it is called multidimensional signal. For example , the intensity or brightness at any point in the picture or image is the function of its x and y position . Hence it becomes two dimensional signal. The intensity of any point on the TV screen is the function of its x and y position as well as time. Hence it becomes three dimensional signal.

Discrete time System Previously we discussed about time discrete signals and their classification . Now we discuss about discrete time systems. The discrete time systems is a device or algorithm that performs some prescribed operation on the discrete time signal. Thus the discrete time system has an input or excitation and the output or response. As shown in figure y(n) is response to the excitation x(n). The input output relation ship For a discrete time system is represented as, y(n)=T [x(n)] or T x(n) y(n)

Discrete time System

Here, T represents transformation operation. This transformation operation depends upon the characteristics of the discrete time system.

DIGITAL FILTERING

In signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.

The following block diagram illustrates the basic idea.

raw (unfiltered) signal -> FILTER -> filtered signal

There are two main kinds of filter, analog and digital

An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and op amps to produce the required filtering effect. These filter circuits are widely used in such applications as noise reduction, video signal enhancement, graphic equalisers in hi-fi systems, and many other areas. At all stages, the signal being filtered is an electrical voltage or current which is the direct analogue of the physical quantity involved. A digital filter uses a digital processor to perform numerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialised DSP (Digital Signal Processor) chip.

The analog input signal must first be sampled and digitised using an ADC (analog to digital converter). The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor, which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. If necessary, the results of these calculations, which now represent sampled values of the filtered signal, are output through a DAC (digital to analog converter) to convert the signal back to analog form.

the signal is represented by a sequence of numbers, rather than a voltage or current.

The following diagram shows the basic setup of such a system.

Digital filters can achieve virtually any filtering effect that can be expressed as a mathematical function or algorithm. Digital filters process digitized or sampled signals. They perform an extended sequence of multiplications and additions carried out at a uniformly spaced sample interval. These signals are passed through structures that shift the clocked data into adders, delay blocks, and multipliers. These structures change the mathematical values in a predetermined way. The resulting data represents the filtered or transformed signal. Distortion and noise can be introduced into digital filters simply by the conversion of analog signals into digital data, the digital filtering process itself, and conversion of processed data back into analog. When fixed-point processing is used, additional noise and distortion may be added during the filtering process because the filter consists of large numbers of multiplications and additions that produce errors, creating truncation noise. Increasing the bit resolution beyond 16 b reduces this filter noise.

Any digital filtering means that accepts as its input a set of one or more digital signals from which it generates as its output a second set of digital signals .While being strictly correct, but it does demonstrate the possible extent of application of digital-filter concepts and terminology. Digital filters can be used in any signal-manipulating application where analog or continuous filters can be used. They can be used in exacting applications where analog filters fail because of time- or other parameter-dependent coefficient drift in continuous systems. Because of the ease and precision of setting the filter coefficients, adaptive and learning digital filters are comparatively simple and particularly effective to implement. As digital technology becomes more ubiquitous, digital filters are increasingly acknowledged as the most versatile and cost-effective solutions to filtering problems.

The number of functions that can be performed by a digital filter far exceeds that which can be performed by an analog, or continuous, filter. By controlling the accuracy of the calculations within the filter (that is, the arithmetic word length), it is possible to produce filters whose performance comes arbitrarily close to the performance expected of the perfect models. For example, theoretical designs that require perfect cancellation can be implemented with great fidelity by digital filters. Filters are signal conditioners. Each functions by accepting an input signal, blocking prespecified frequency components, and passing the original signal minus those components to the output. For example, a typical phone line acts as a filter that limits frequencies to a range considerably smaller than the range of frequencies human beings can hear. If the digital filter under consideration is not a linear, time-invariant filter, the transfer function cannot be used. There are many filter types, but the most common are lowpass, highpass, bandpass, and bandstop. A lowpass filter allows only low frequency signals (below some specified cutoff) through to its output, so it can be used to eliminate high frequencies. A lowpass filter is handy, in that regard, for limiting the uppermost range of frequencies in an audio signal; it's the type of filter that a phone line resembles. A highpass filter does just the opposite, by rejecting only frequency components below some threshold.

Finite Impulse Response (FIR) A finite impulse response (FIR) filter is a filter structure that can be used to implement almost any sort of frequency response digitally. An FIR filter is usually implemented by using a series of delays, multipliers, and adders to create the filter's output. Figure shows the basic block diagram for an FIR filter of length N . The delays result in operating on prior input samples. The h k values are the coefficients used for multiplication, so that the output at time n is the summation of all the delayed samples multiplied by the appropriate coefficients.

The logical structure of an FIR filter Advantages of digital filters Digital filters can easily realize performance characteristics far beyond what are implementable with analog filters. It is not particularly difficult, for example, to create a 1000 Hz low-pass filter which can achieve near-perfect transmission of a 999 Hz input while entirely blocking a 1001 Hz signal. Analog filters cannot discriminate between such closely spaced signals. Also, for complex multi-stage filtering operations, digital filters have the potential to attain much better signal to noise ratio than analog filters. This is because whereas at each intermediate stage the analog filter adds more noise to the signal, the digital filter performs noiseless mathematical operations at each intermediate step in the transform. The primary source of noise in a digital filter is to be found in the initial ADC –analog to digital conversion step, where in addition to any circuit noise introduced, the signal is subject to an unavoidable quantization error which is due to the finite resolution of the digital representation of the signal. Note also that frequency components exceeding half the sampling rate of the filter (Nyquist sampling) will be confounded (or aliased) by the filter. Thus a small anti-aliasing filter is always placed ahead of the analog to digital conversion circuitry to prevent these high-frequency components from aliasing.

Discrete signal or discrete-time signal is a time series, perhaps a signal that has been sampled from a continuous time-signal. Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous-time argument, but is a sequence of quantities; that is, a function over a domain of discrete integers. Each value in the sequence is called a sample. When a discrete-time signal is a sequence corresponding to uniformly spaced times, it has an associated sampling rate; the sampling rate is not apparent in the data sequence, so may be associated as a separate data item.

The discrete time signal are obtained by time sampling of continuous time signals. Hence the discrete time signals are defined only at sampling instants. Let us consider the exponential signal Digital signals A digital signal is discrete-time signal that takes on only a discrete set of values. It typically derives from a discrete signal that has been quantized.. C ommon practical digital signals are represented as 8-bit (256 levels), 16-bit (65,536 levels), 32bit (4.3 billion levels), and so on, though any number of quantization levels is possible, not just powers of two. A continuous signal or a continuous-time signal is a varying quantity (a signal) that is expressed as a function of a real-valued domain, usually time. The function of time need not be continuous. The signal is defined over a domain, which may or may not be finite, and there is a functional mapping from the domain to the value of the signal. The continuity of the time variable, in connection with the law of density of real numbers, means that the signal value can be found at any arbitrary point in time. A typical example of an infinite duration signal is:

A finite duration counterpart of the above signal could be:

and f ( t ) = 0 otherwise.

The value of a finite (or infinite) duration signal may or may not be finite. For example,

and f ( t ) = 0 otherwise,

is a finite duration signal but it takes an infinite value for In many disciplines, the convention is that a continuous signal must always have a finite value, which makes more sense in the case of physical signals. For some purposes, infinite singularities are acceptable as long as the signal is integrable over any finite interval (for example, the t - 1 signal is not integrable, but t - 2 is). Any analogue signal is continuous by nature. Discrete signals, used in digital signal processing, can be obtained by sampling and quantization of continuous signals. Continuous signal may also be defined over an independent variable other than time. Another very common independent variable is space and is particularly useful in image processing, where two space dimensions are used. Spectrum analysis A spectrum analyzer is a device used to examine the spectral composition of some electrical, acoustic, or optical waveform It measures the power spectrum. There are analog and digital spectrum analyzers: • An analog spectrum analyzer uses either a variable band pass filter whose mid-frequency is automatically tuned (shifted, swept) through the range of frequencies of which the spectrum is to be measured or a super-heterodyne receiver where the local oscillator is swept through a range of frequencies. • A digital spectrum analyzer computes the Fast Fourier transform (FFT), a mathematical process that transforms a waveform into the components of its frequency spectrum. Spectrum Analyzers require high dynamic range in order to capture bandwidths over wide input frequency ranges. High-speed and high performance ADCs offer the speed and signal-to-noise required for accurate measurement of signals and distortion. Highly accurate clock and DDS products provide sampling clocks and sweep tuning of the Spectrum Analyzer, and amplifiers help to drive the ADCs and increase signal levels in the down-conversion chains. Analog Devices has all the key components for your next generation design.

The spectrum analyzer shows baseband spectra of analog waveforms . The baseband analyzer is integrated with the instruments it serves, so there are no additional settings to adjust. Conclusion Digital signal processing applications are so diverse that they make it necessary to have a number of implementation alternatives. These are summarized in table 1. Clearly, no one solution is best in all cases. The challenge for the system implementers is to choose With the increasing use of computers the usage and need of digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog to digital converter (ADC). Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence classes and discretization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In the quantization stage the representative signal values are approximated by values from a finite set. the solution that best meets their system and market requirements. Real time signal processing is taking the digital revolution to the next step, making equipment that is more personal, more powerful, and more interconnected than most people ever imagined possible. Over the years, different technologies have powered the most innovative creations from the mainframe and minicomputer eras to the PC and today's Internet era. Consumers are driving real time functionality, demanding equipment that is extremely fast, portable, and flexible. To meet those needs, designers are facing more pressures than ever, but they also have more options than ever to address them. areful evaluation of each option clearly shows several viable alternatives for embedded applications. For implementing today's real time signal processing applications, however, DSP is very often the best choice. No digital technology has more strengths than DSP nor better meets the stringent criteria of today's developer.

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