OSM & OAM

OSM & OAM methods are efficient ways to evaluate discrete convolution of a very long signal & a finite impulse response of a digital filter. In OAM, Linear convolution of individual L point sequences is calculated whereas in OSM, Circular Convolution is calculated to obtain the output.In OSM, output is directly obtained by discarding few coefficients from individual stages rather than adding coefficients from OAM method.

FFT (Fast Fourier Transform)

FFT is similar to the DFT Algorithm since it is also the frequency domain representation of a signal but FFT is a fast algorithm and hence produces fast results. Cooley-Tukey Algorithm for FFT breaks a DFT signal into many similar DFTs .This reduces the computations that is why it is a fast algorithm.
The simple computations like trivial operations like multiplication by 1 are avoided producing fast results.

DFT (Discrete Fourier Transform)

DFT is basically a frequency sampling of Discrete Time Fourier Transform that produces periodic results. This is because a finite sequence of equally spaced samples of a function can be converted into equivalent length sequences of equally spaced samples. An approximate frequency spectrum of a signal can be obtained using DFT Algorithm.If the length of signal is increased then its DFT produces more compressed frequency spectrum. So we use zero padding to reduce the frequency spacing in the output spectrum. This reduces the approximation error.

Discrete Convolution and Correlation

In this experiment , Convolution and Correlation algorithms were emulated on the DSP Processor TMS320F28335.

For a Linear Time Invariant system,Convolution is basically smearing the input signal with another signal to get the output. Convolution algorithms are used in image processing for smoothing of an image. Correlation is used to measure the extent of similarity between  two signals. The value of correlation coefficient indicates the degree of similarity.