Operations in DSP

DSP Operation

The basic DSP Operations are :-

1. Convolution.
2. Correlation.
3. Filtering.
4. Transformation.
5. Modulatiom.

                     All the basic DSP operations requires only simple arithmetic operations of multiply, add or substract and shifting.

1. Convolution:-
        
                        It is one of the frequently used operation in DSP espwcially im digital filtering.
 Consider 2 finate and causal sequences x(n) & h(n) of length L and M respectively.


Their linear convolution is defined as,

y(n) = h(n) * x(n)
also y(n) = x(n) * h(n)

Let N = L+(M-1).

2. Correlation:-
                   
                      The correlation is the measure of similarity between 2 signals. There e=are two forms of correlations.

 a. Cross Correlation Function (CCF) and
 b. Auto Correlation Function (ACF)

 a. Cross Correlation Function (CCF):-
       
          Cross Correlation Function is the measure of similarity between two different signals.

Applications of CCf are.

 1. Cross spread analysis.
 2. Detection or recovery of signals from noice.
     eg. Detection of RADAR noice
 3. Pattern matching.


b. Auto Correlation Function (AUF):-
       
                ACF involves only one signal and provides information about the structure of the signal or its behavior in the time domine. It is a special form of CCF and it is used in similar applications.

3. Digital Filtering:-
     
                   It is one of the most importent operation in PSD.
For an importent class of filters digital filtering operations can be defined as

          Y(n) = Summation( k=0 - N-1) [ h(k).x(n-k)].
                 

                     where h(k) [ k=0,1,2,...........N-1] are the filter cofficients and x(n) & y(n) are representing the input and output of the filter. For a given filter the cofficient value are unique and that determine the filter cheracteristic. The common filtering object is to remove or reduce noice from a wanted signal.

4. Discrete Transformations:-

                         Discrete transformation allow representation of discrete time signals in the frequency domain or conversion between time & frequency domain reprecentation. Spectrum of a signal is obtained decomposing it into its frequency components using discrete transformation. Knowledge of the spectrum is necessary in determing Band Width required to transmit a signal. In many DSP applications conversion between time and frequency domain is necessary. It allows for a more efficient implementation of DSP algorithms susch as those for digital filtering, convolution & correlation. DSP  is a most widely used discrete transformation.

5. Modulation:-

Digital signals are transmitted over long distences after modulation.

* To match their frequency cheracteristics to those of the transmission or store media.
* To minimise the signal distortion.
* To utilize the available Band Width efficiency etc ...,

   Two application areas where modulation is extensively employed are telecommunications & digital audio engineerin.
The process of modulation involves varying the property of high frequency signal known as carrier in accordance with modulating signal.

The 3 most commonly used digital modulation techniques over a bandpass channel are....

                      a. Amplitude Shift Keying(ASK).
                      b. Phase Shift Keying(PSK).
                      c. Frequency Shift Keying(FSK).

Posted in Digital Signal Processing