Overlap Add and Overlap Save method

Overlap Add Method(OAM) & Overlap Save Method(OSM)

           When the input sequence is too large, the Convolution of the entire signal at a time is time consuming and tedious. So we break the input sequence.It is an efficient way to evaluate the discrete convolution of a very long signal x [ n ].

           When an input signal x[n] is given to a Digital FIR filter the methods used to get the output sequence are-OAM and OSM.

           The practical implementation of these methods in done in the Lab session. OAM method involves decomposing the input signal and performing linear convolution on each of them individually. The decomposed outputs are then combined together.Similarly OSM method involves decomposing of input.But this method deals with adding some previous values to each decomposed input and then performing circular convolution.

            The decomposed outputs are then combined by removing the first few values from each of them to get the result. This procedure is designed into a code and executed to get the output sequence on the computer when user defined input sequence is typed in Lab session.

Fast Fourier Transform

Fast Fourier Transform(FFT)

         Discrete Fourier Transform is considered as a computationally slow method. So, the best way to reduce addition and multiplication is using Fast Fourier Transform. Speed matters when implementation of this method comes into picture.

         This session involves taking two cases- 4 point input and 8 point input.In both these cases we execute the code for FFT and study its implementation. This execution enable us to prove its computational advantage.

Discrete Fourier Transform

Discrete Fourier Transform(DFT)

        Discrete Fourier Transform is the frequency sampled version of Discrete Time Fourier Transform. Thus, it involves finding the finite set of values .It gives periodic results. This theory is implemented in our practical session.

         Here, we first take a 4 point input x(n) and find its DFT. Finally, we plot its magnitude spectrum by approximation. This process is followed for 8 point sequence- by appending zeros at the end or by placing them at alternate positions in the sequence.This is done by generating a code in C language and displaying the executed result on the Terminal. After execution and value verification of all 3 cases we study the magnitude spectrum pattern. Thus, we infer that as the length of the signal increases the frequency spacing and error decreases.Then we move to the analysis of this method by considering all computations(addition and multiplications) involved and prove that it is slow method.

         

Convolution and Correlation

Convolution and Correlation

          Convolution involves finding relation between input and output of a Linear Time Invariant system.Corrlations provides degree of similarity between  two signals. These operations have to be implemented. This is what we learn in the Digital Signal Processing Practicals.

        Here, the user entered values x(n) are taken as the input along with impulse response h(n). The output we get is y(n) is displayed on the terminal which can be verified. The session involves studying the codes for these operations,compiling and executing them.All types of Convolutions and Correlations are solved using same procedure.

       Thus all the concepts and problems solved manually are verified by the execution. We also thus get a revision of coding involved in problem execution.