OAM and OSM

           OAM (Overlap Add method) and OSM (Overlap Save Method) were the two methods (implemented in C) that we used to find the output of FIR filter.

           

           The value of N we selected was 8 and L was 5. Hence in OAM, the 13-pt sequence that we entered got decomposed into 3 parts and convolution of each part was calculated using FFT algorithm.

           Similarly, in OSM too the sequence was decomposed into 3 parts and circular convolution is found after which the overlapped part is neglected and the rest becomes the output.

FFT

DSPP Practicals

         FFT (Fast Fourier Transform) has less no. of computations (real and complex addition and multiplication) than DFT, hence it was implemented. 

         There are two types of FFT viz. DIT-FFT (Decimation In Time FFT) and DIF-FFT (Decimation In Frequency FFT) out of which we implemented DIT-FFT using C.

The input signal we used for computing FFT was the same as that used in DFT. It was seen that the output in both the cases was same which proves that DFT and FFT produce same results. 

DFT

DSPP Practicals

         DFT (Discrete Fourier Transform) is basically the sampled version of DTFT (Discrete Time Fourier Transform) signal.

         Depending upon the maximum length of input signal mentioned in the code, an input sequence of length=4 was entered. However if 8-point sequence was entered with the last four values as zero, then the resolution and accuracy increases i.e. between every 2 values of 4-pt DFT output, a new value got added.

         It was seen from the code that DFT requires a number of real and complex additions and multiplications. Hence processing of a signal using DFT takes longer time.

Convolution and Correlation

DSPP Practicals

           Convolution is used to find the output of a given discrete time signal.

           In linear convolution, if the length of input signal is L and  that of impulse reponse is M then length of output signal should be equal to L+M-1. In our code, if the length was exceeding the length given by the above formula, then the last extra values were getting added to the first corresponding values and this is termed as aliasing.

           In circular convolution the length of the output signal is taken as the maximum of the length of the two input signals. This type of convolution hence uses the method of zero padding.

           Correlation is used to find the degree of similarity between the two input signals.

           Auto-correlation is correlation of two same signals. Hence it is seen that the auto-correalation output is an even signal. Cross-correlation of the input signal and its delayed signal gives a shifted/delayed output signal.