EXP 4: Overlap Add and Overlap Save Methods

                 When the input signal is too large , it is helpful to break it into number of  signals of same length. In Digital FIR Filter , OAM and OSM methods are used to get output sequence.
                 In Overlap Add method (OAM),input sequence was decomposed and then linear convolution was performed on each decomposed sequence.The corresponding outputs were combined together for final result. While in Overlap Save method (OSM) ,circular convolution was performed on each decomposed sequence. 

EXP 3: Fast Fourier Transform

         As DFT method is computationally slow ,we use Fast Fourier Transform (FFT). Due to less number of additions and multiplications required in FFT ,its implementation is fast. In this experiment , we studied FFT for 4 point  and 8 point input signals. We used Radix-2 algorithm to perform this experiment.

EXP 2: Discrete Fourier Transform ( DFT)

                  The  Discrete Fourier Transform (DFT) converts a finite sequence of equally-spaced samples of a function into a finite periodic signal . In this experiment,we observed DFT results for 4 point signal, zero padded 8 point signal and expanded signal. We also plotted magnitude spectrum.
               We observed that DFT  gives N coefficient values in frequency domain, it gives approximated spectrum. DFT spectrum is defined in the range [0,2π]. We concluded that as length of signal increases the frequency spacing and error decreases on the other hand resolution of spectrum increases. Expansion of signal in time domain gives compress spectrum in frequency domain. Also due to all computations (addition and multiplication)involved ,DFT is computationally slow.

EXP 1. Discrete Convolution and Correlation.

           The aim of this experiment was to study mathematical operations. In the first part of this experiment,we studied discrete convolution .Under  this part we studied methods like linear convolution,circular convolution and linear convolution using circular.We used C language for coding.We observed outputs for different inputs to the system for result analysis.
            The length of linear convolution output signal was one less than addition of two input signal. Also,if both input signals are causal then output resultant signal was also causal. In circular convolution,the length of input signals should be maximum of two input signals.Circular convolution gives aliased output.
               Discrete correlation was second part of this experiment ,under which we studied auto-correlation,cross-correlation for input signals and delayed input signals.We observed that auto-correlated signal is even signal and auto-correlation of delayed signal is same as original signal. Also cross-correlated signal of input signal and delayed input signal is auto-correlated input signal.