Digital Signal Processing :

Digital Signal Processing is the process of analyzing and modifying to optimize or improve its efficiency on performance.It involves applying various mathematical and computational algorithms to analog and digiatal signal to produce a signal of higher quality than the original signal.

Digital Signal Processing application/Uses :

1.Image Processing :

Pattern recognition

Robotic Vision

Image enhancement

satellite weather map

animation

2.Instrumentation/Control : Spectrum analysis Position and rate control data compression

3. Spech/Audio :

Spech recognition

Spech synthesis

Digital audio

4.Military :

radar processing

sonar processing

missile guidance

5. Telecommunication :

Echo cancellation

data communication

ADPCM transcoders

video conferencing

6. Biomedical :

x-ray storage

ECg analysis

x-ray storage

scanners

ECG brain mappers

Discrete time signal:

discrete time signal is defined only at discrete instants of time.The independent variable has discrete values only, which are uniformly spaced.

Continuous time signal :

Continuous time signal defined for a continuous of values of the independent variable.In the case of continuous time signals the independent variable is continuous.

Example :

i.A speech signal as afunction of time

ii.Atmosphere pressure as a function of attitude.

Sampling

Sampling is a process of converting continuous time signal into discrete time signal.

Convert an analog to digital signal :

1. The signal is first sampled, converting the analog signal into a discrete time continuous amplitude signal.

2. The amplitude of each signal sample is quantized into one of 2^{B}levels, where B is the number of bits used to represent a sample in the ADC.

3. The discrete amplitude lvels are represent on encoded into distinct binary words each of length B bits.The process is depicted in fig(1 .Three distinct types of signals can be identified in the fig:-

4.The analog input signal.The's signal is continuous in both time and amplitude.

5.The sampled signal.The's signal is continuous in amplitude but defined only at discrete points in time.Thus the signal is zero except at time E = nT(The sampling instant).

6.The digital signal, X(n)(n=0,1,2......).This signal exists only at discrete points in time and at each time point can only have one of 2^{B}values (discrete time discrete value signal).

Note the discrete time(That is sampled) signal and digital signal can each be represented as a sequence of numbers X(nT), or simply X(n) (n=0,1,2).

The FIR filter(Finite Impulse Procedure) design procedure :

1. Filter Specification : This may include starting the type of filter, for example the low pass filter, the desired amplitude and/or phase response and the total we are prepared accept, the sampling frequency and the wardlength f the input data.

2.Coefficient calculation : At these stae we determine the coefficients of a transformation.H(z), which will satisfy the specification given in (i).

user choice of coefficient calculation method will be influenced by several factors, the most important of which are the critical requirements in step (i).

3.Realization : This involves the transfer function obtained in (ii) into a suitable filter network or structure.

4.Analysis of finite wordlength effects : The effects of quantizing the filter coefficient of carrying out the filtering operation using fixed wordlength on the filter performance.

5. Implementation : This involves producing the software code and hardware and performing the actual filtering.The five interrelated are summerized in fig(1).

Signal:

A signal is defined as any physical quantity that various with time, space or any other independent variable or variables.

Mathematically, we describe a signal as a function of one or more independent variables.

Ex : x(t) = 10t

x(t) = 5x^{2}+20xy+30y

The Classification of signal :

1. Single channel and multiple channel signals

2. Single dimensional and multiple dimensional signals

3.Continuous time and discrete time signals

4.Continuous valued and discrete valued signals

5.Analog and digital signals

6.Deterministic and random signals

7.Periodic signal and non-periodic signal.

8.Symmetrical(even) and anti symmetrical(odd) signal

9.Energy and power signal.

Digital Signal Processing :

Digital signal processing is concerned with the digital representation of signals and the use of digital processor to analyze, modify or extract information from signals.

The Classification of Digital Signal Processing :

Has two types :

1. Analog signal processing(ASP)

2. Digital signal processing(ASP)

(1) ASP : If the input signal give to the system is analog then system does analog signal processing.

Ex : Resistor, capacitor or indicator, op-AMP etc

Describe the Digital Signal Processing :

If the input signal given to the system is digit then systems does digital signal procesing.

Ex : Digital computer, digital logic circuit etc.

** Most of the signals generated are analog in nature.Hence these signals are converted to digital form by the analog to digital convertor.Thus AD converter generates an array of signals and gives it to digital signal processor.This array of samples or sequences of samples is the digital equivalent of input.THe DSP perform signal processing operators like filtering, multiplication, transformation or amplitication etc operation over this digital signals.The digital output signal from the DSP is given to the DAC.

The Advantages and Disadvantages of DSP over a analog signal processing(ASP) :

1. Physical size of analog systems are quite large while dgital processors are more compact and light in weight.

2. Analog systems are less accurate because of component tolerate ex, R, L, C and active component.Digital components are less sensitive to the environmental changes, noise and disturbances.

3. Digital system are most flexible as software programs and control programs can be easily modified.

4. Digital signal can be stores on digital hard disk, floppy disk or magnetic tapes.Hence becomes transportable.thus easy and lasting storage capacity.

5.Digital processing can be done offline.

6.Mathematical signal processing algorithm can be routing implemented on digital signal processing systems.Digital controllers are capable of performaing complex computation with constant accuracy at high speed.

7.Digital signal processing systems are upgradeale since that are softaware controller.

8. Possibility of sharing DSP processor between several tasks.

9.The cost of microprocessor, controllers and DSP processors are continuously.For some compex control function, it is not practically feasible to construct analog controllers.

10.Signal chip microprocessor, controllers and DSP processors are more versible and powerful.

Disadvantages of DSP over ASP :

1. Additional complex (A/D & D/A converters).

2.Limit in frequency.High speed AD converters are different to achieve in practice.In high frequency applications DSP are not preferred.

Difference between static and dynamic :

static dynamic 1.Static systems are these systems whose output at any instance of time depends at most on input sample at same time. 1.Dynamic systems output depends sample of input 2.It is less memory. 2.More memory system. 3.Ex.y(n)=ax(n). 3.Ex.y(n)=x(n)+3x(n-1)

Difference between Time invariant(TIV)/Shift invariant and Time variant(TV)/Shift variant :

Time invariant(TIV)/Shift invariant Time variant(TV)/Shift variant 1.A system is time invariant if its input output characteristics do not change with time.y(n)=T[x(n)] 1.A system is time variant if its input output characteristics changes with time.y(n)!=T[x(x)] 2.Linear TIV systems can be uniquely characterized by impulse response frequency response or transfer function. 2.No mathematical analysis can be performed. 3.Ex.(a) Thermal noise in electronic components. (b)Printing documents by a printer 3.Ex.(a) Rainfall per month. (b). Noise effect

Difference between Causal System and Non-causal System :

Causal System Non-causal System 1.A system is causal if output of system at any time depends only past and present inputs 1.A system is non causal if output of system at any time depends on future inputs. 2.The causal system, the output is the function of x(n),x(n-1),x(n-2)....and so on 2.In this systems, the input is the function of future inputs also.x(n+1), x(n+2).......and so on. 3.Real time DSP systems 3.Offline systems

Difference between Fourier Series and Fourier Transform :

1.Fourier Series is an expansion of period signal as a Linear combination of sine Q cosine terms while fourier transform is the process of function used to convert signals from time domain into frequency domain.

2.Fourier series is defined for periodic signal and the fourier transform can be applied to a non periodic signal.

IFFT :

1.Inverse fast fourier transform(IFFT) :

2. IFFT is radily obtainable from the FFT algorithm.

3. Its use files in transforming spectra into their corresponding waveform and in checking that the FFT has been correctly computed numbers of multiplication and additions required does not always result in a proportional increase in speed of computation.

4.Decreasing the multiplication may result in more programs code and more additions.

5.If hardware signal processing chips are to be used these will impulse their own limitations which may negate the improvement in the algorithm.

DFT :

The direct calculation of DFT is computationally intense, and consequently slow, malang it unrealistic for real time digital signal processing.This limitation removed by the FFT algorithm. The FFT is simply an efficient method for computing the DFT.It is not only efficient but it also reduces round off errors by a factor of log N/N where N is the number of data samples. If we have N = 2^{n}samples, then only Nlog_{2}N arithmatic operations are required to compute the N-point DFT as compared to the N^{2}EFT operations used by direct computation of the DFT.

Compare betwen DIT and DIF algorithm of FFT :

For the DIF algorithm the order of the input data is unaltered but the output FFT sequence is bit reversed.

Both the DIF and DIT algorithms are in-place algorithm.By re-drawing them it is possible to maintain the order of both the inputs and the outputs, but the resulting algorithms are no longer in place algorithms and extra storage space is required.

The number of complex multiplication required for both algorithms is the same.Overall, there is little to choose between the two.